Nelson Maths (Books 1–7) provides creative, stimulating and open-ended tasks allowing children to work at a learning level appropriate to their needs. This series supports the whole class — small group — whole class teaching approach.
Teacher’s Resource
Nelson
Maths
Each Teacher’s Resource Book contains:
Nelson
more than 520 activities over 40 weekly units of work ‘Plain Speak’ Statements (teaching focus), Resources and Maths Talk 81 unit and resource blackline masters 11 assessment and planning blackline masters ideas for setting up an effective mathematics classroom, parent participation, five-minute maths activities, and assessment and monitoring.
Maths T ONY D OYLE
Planning Assessme and nt Tool + TRB
© Nelson Austr alia Pty Ltd, 2004. Jay Dale and Jenny Feely Minimum syst em requirem ents Microsof t® Windows ® 98 or later; MacOS 8.5–9.2. and OSX Adobe® Acro bat® Reader (supplied on CD-ROM) is required to view documents.
N
son Mel aths
Installation instructions PC: Insert CDROM into CD drive for auto matic play, or navigate to CD-ROM with Windows® Explorer and double-click on Title. Mac: Insert CD-ROM into CD drive. Doub le-click on the Title icon, then double-click on Title.
If you experienc e difficultie s using this email Nelson product, Thomson Lear ning Australi helpdesk@th a on omsonlearnin g.com.au
Book
M RO ins
Book
e id
CD -
The complete Teacher’s Resource Book is on CD-ROM and features time-saving and easy-to-use interactive planning and assessment software. The CD-ROM also features an Enabler function which allows teachers to plan across grade levels, and a Correlation Chart linking units in Nelson Maths to individual Education Department syllabuses.
T ONY D OYLE has taught in a number of schools over the past 20 years. He is the author of various maths texts and teacher’s guides. Tony has a passion for integrating learning technologies into the curriculum and has always had a keen interest in the ways in which children learn mathematics. Tony is currently Deputy Head
F ifth
of Sc Ye ho ar ol
and ICT Coordinator for an independent school.
Thomson Learning AUSTRALIA 102 Dodds Street Southbank 3006 Victoria Email
[email protected] Website http://www.thomsonlearning.com.au First published in 2004 10 9 8 7 6 5 4 3 2 1 08 07 06 05 04 Text copyright © 2004 Nelson Australia Pty Ltd Illustrations copyright © 2004 Nelson Australia Pty Ltd Thomson Learning is a trademark used herein under license. Nelson Maths Teacher’s Resource — Book 5 ISBN 0 17012 232 8 The overall structure for Nelson Maths (Books 1–7) was designed and written by: Jay Dale, Anne Giulieri and Lynn Davie Project management by Upload Publishing Services (Jay Dale) Edited by Philip Bryan Cover and text design by Christine Deering Cover and title page adapted by Goanna Graphics (Vic) Pty Ltd Paged by Christine Deering and Alena Jencik (Grand Graphix Pty Ltd) Illustrated by Pat Reynolds Photography by Lindsay Edwards CD-ROM programmed by James Ward Typeset in Grotesque and Plantin Printed in Australia by Ligare Pty Ltd This title is published under the imprint of Thomson Nelson. Nelson Australia Pty Ltd ACN 058 280 149 (incorporated in Victoria) trading as Thomson Learning Australia. Acknowledgements The publishers would like to thank the teachers and students at Broadmeadows Primary School for their willing participation in the photographs on and throughout this book. ‘Zone of proximal development’ diagram on p. 4 is adapted from a diagram by Peter Hill and Carmel Crevola.
Teacher’s Resource
Nelson
Maths T ONY D OYLE
Book
Contents Introduction
4
How Nelson Maths Is Organised
5
Teacher’s Resource Book
6
Student Book
7
What We Know About Learning
8
The Classroom Environment
9
Setting Up Your Maths Classroom
9
Assessment and Monitoring
12
Why Assess? What to Assess? When to Assess? How to Assess? Planning
12
Parent Participation
13
Family Maths (BLMs and game boards)
15
Five-minute Maths
16
An Additional Resource
18
Nelson Maths Teacher’s Resource Book on CD-ROM
12 12 12 13
18
Forty Units of Work Number and patterns
Unit 1
Investigating Place Value
24
Unit 2
Numbers That Count
27
Unit 3
What’s in a Number?
30
Chance and data
Unit 4
Data Collection
33
Number and patterns
Unit 5
Patterns and Relationships
36
Lines in Our World
39
Space
Unit 6
Number and patterns
Measurement
Unit 7
Addition and Subtraction
42
Unit 28 Capacity
Unit 8
Multiplication and Division
45
Number and patterns
Unit 29 Fractions as Operators
Measurement
Unit 9
Measuring and Estimating Angles
48
Unit 10 Analogue and Digital Times
51
Unit 11 Timetables and Schedules
54
Number and patterns 57
Unit 13 Decimals
60
Measurement
Unit 14 Length
63
Number and patterns
Unit 30 Location
66
Unit 16 Numbers in Golf
69
Space
111
Measurement 114
Number and patterns
Unit 32 Multiplication and Decimals
117
Unit 33 More About Decimals
120
Space
Unit 34 3D Objects
Unit 15 Travelling with Numbers
108
Space
Unit 31 Mass
Unit 12 Fractions
105
123
Revision
Unit 35 Revision
126
Number and patterns
Unit 17 2D Shapes
72
Unit 36 Solving Problems
129
Unit 18 Flip, Slide and Turn
75
Unit 37 Four Operations
132
Number and patterns
Space
Unit 19 Value for Money
78
Unit 20 Words and Numbers
81
Measurement
Unit 21 Area
84
Number and patterns
Unit 22 More Multiplication and Division
87
Unit 23 Everyday Numbers
90
93
Chance and data
Unit 25 Chance
135
Number and patterns
Unit 39 Working with Numbers
138
Unit 40 Balance the Numbers
141
Unit and Resource Blackline Masters
144
Assessment and Planning
Measurement
Unit 24 Volume
Unit 38 Make These Shapes
96
Number and patterns
Unit 26 Numbers Close Up
99
Unit 27 Numbers Beware!
102
Blackline Masters
225
Answers to Student Book Pages
236
Introduction Nelson Maths aims to: • implement focused teaching • maintain ongoing assessment • assist students by scaffolding their learning • improve students’ mathematical understandings • develop students’ mental computation skills. Nelson Maths provides a daily mathematical framework, i.e. whole class – small group – whole class. By providing creative, stimulating and openended tasks students will be able to work at a learning level appropriate to their mathematical needs. Teachers of mathematics are committed to interacting with their students to find out the skills they have, and then planning accordingly to build upon those skills.The foundation of mathematics learning and teaching is where students make connections between prior knowledge and new experiences to develop more complex understandings.
children’s own skills and understandings
+
targeted learning experiences planned as part of a rich mathematics program
+
children’s formation of generalisations
=
a transfer of knowledge to develop more complex understandings
Zone of proximal development Focused teaching
Anxiety
What the learner will be able to achieve independently
Z o n e
o f
Level of challenge
Scaffolding occurs through the support of the ‘more knowing other’
p ro x im a ld e ve lo p m e n t
Targeted teaching needs to occur so students are working within their zone of proximal development.
What the learner can currently achieve independently
Boredom What the learner can achieve with assistance
Level of competence
4
Nelson Maths Teacher’s Resource — Book 5
The activities in Nelson Maths: • provide teachers with choices so they are able to meet the needs of individual students and/or groups of students • are open-ended and stimulating, allowing students to work at their appropriate developmental level • encourage students to develop mental computation skills • provide ongoing monitoring and assessment • allow for effective grouping of students.
How Nelson Maths Is Organised There is one Teacher’s Resource Book and one Student Book for each year level.
The program is based on 40 units of work for each year level. Each unit of work provides material for one teaching week. The 40 units can be taught sequentially, or teachers may choose a unit of work on a weekly basis according to the needs of their class and their individual programs. It should be noted that each unit of work provides more activities than could be taught in one teaching week. In other words, Nelson Maths offers teachers choices and teachers should choose only those activities that suit the needs of their class. The four strands of the mathematics curriculum have been covered in each year level. The ratio is approximately Numbers and patterns, 50 per cent; Measurement, 20 per cent; Chance and data, 10 per cent; and Space, 20 per cent.
How Nelson Maths Is Organised
5
Teacher’s Resource Book Each weekly unit is divided into three main sections that relate to the daily mathematics hour. • Whole Class Focus — Introducing the Concept • Small Group Focus — Applying the Concept • Whole Class Share Time. Each unit in the Teacher’s Resource Book provides:
Whole Class Focus
• ‘plain speak’ statements for teachers to refer to when monitoring and assessing students (see ‘During this week look for students who can:’ in each unit).
Independent Maths
• text in a grey panel highlighting the fact that teachers can choose activities for the week’s work that best suit the needs of their class and their mathematics program. It also explains that each common symbol used (e.g. the ‘sun’) in ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ links related activities. For example, if the teacher chooses an activity with the sun symbol in ‘Whole Class Focus’ then the linking activity they should choose in the ‘Independent Maths’ section will also have the sun symbol. This same symbol will carry through to ‘Whole Class Share Time’.
Whole Class Share Time
• Resources — materials needed to implement the unit. • Maths Talk — the vocabulary that the teacher may need to model and use in their teaching, and the language the students should be encouraged to use when discussing mathematical concepts. • Whole Class Focus — Introducing the Concept (10 to 15 minutes).This is time when the whole class joins together to focus on the concept being taught in the unit. Teachers can choose from any of the five to six activities, and program them into their weekly timetable (see BLMs 82–85). During this session, the teacher sets the scene and motivates the students.There is interaction between the teacher and the whole class as they share their skills and understandings, and develop their understandings further. During this session the teacher uses a ‘shared’ teaching approach (see p. 7 for a definition). • Small Group Focus — Applying the Concept (30 to 35 minutes). In this session, the Focus Teaching Group and the Independent Maths (individual, pair, small group) occur at the same time. Focus Teaching Group During this session, the teacher works with a small number of ‘likeneeds’ students to teach level-appropriate concepts. The teacher chooses a modelled, shared or guided teaching approach depending on the level of support the students need (see p. 7 for a definition).The aim of this session is for the teacher to assist students at their point of need and then move them on. This is also an appropriate time to take anecdotal records on individual students. The session usually runs for 10 to 20 minutes. After this time, the students work on related independent tasks, while the teacher ‘roves’ among the class. During this ‘roving’ time, the teacher monitors and assesses students, and notes those individuals to be included in future Focus Teaching Groups. There are three suggested Focus Teaching Group activities provided in each unit.
6
Nelson Maths Teacher’s Resource — Book 5
Independent Maths (individual, pair, small group) During the independent maths activities, students work in small groups, with a partner or individually on more open-ended tasks specifically designed so students can work at their individual level of understanding. The concepts in these activities are linked to the activities introduced in ‘Whole Class Focus’. The majority of Student Book pages have been incorporated into this section. In Independent Maths, most units feature at least one activity that integrates the use of technology, i.e. computers and/or calculators. • Whole Class Share Time (10 to 15 minutes).This is a time for the class to regroup, reflect upon and celebrate their learning. This session also promotes the students’ use of mathematical language, and enables the teacher to gain valuable insights into the students’ mathematical thinking and the strategies they are using.
Student Book The Student Book promotes stimulating and open-ended activities where students can investigate tasks at their own level of understanding. The Student Book includes: • two to three Student Book pages corresponding to each unit in the Teacher’s Resource Book. These pages have been integrated into the ‘Small Group Focus’ section of the Teacher’s Resource Book. • between 25 and 30 ‘Check and Self-assessment’ pages, each page occurring after a one- to three-week block of units/work. These pages enable both the student and the teacher to monitor and assess the student’s mathematical understandings throughout the units of work. The students can complete the page independently or with the teacher. These pages promote a student–teacher partnership in the learning process. They allow students to self-assess and therefore have individual input into their mathematics.The resulting data will assist teachers with future planning and can be used as part of the student’s portfolio (for teacher–parent interviews).
One Bag! Four Counters,
ata Chanc e and d
_________ Date: ______
a cloth bag 1 red counter, 3 blue counters, You will need :
Draw one out, ers in the bag. 1 • Put the count without looking. of your draw. • Record the result bag. er back in the • Put the count steps 40 times! Result • Repeat these Draw Result Draw t Resul Draw 31 Result Draw 21 11 32 1 22 12 33 2 23 13 34 3 24 14 35 4 25 15 36 5 26 16 37 6 27 17 38 7 28 18 39 8 29 19 40 9 30 20 10 _______________ _____ __________ _______________ you? tell s __________ result __________________ 2 What do your __________________ ____ __________________ __________________ __________________ ______ ______ ______ __________________ ______ ______ ____________ are your chances g draw 41. What _ makin ______ are ______ you ______ 3 a Imagine counters? ______ __________ one of the 3 blue __________________ of drawing out __________________ _________ answer. ____________ __________________ b Explain your __________________ _________________ _______________ ______ _________________ ______ ____________ _________________ _____ ______ ____________ of paper. s on another piece 4 Graph your result e pp. 96–98.) (See Teacher ’s Resourc terms of chance. Unit 25 Chance outcomes with defined and apply possible
70
Chance and data
• Identify and order
• a list of the appropriate ‘plain speak’ statements and cross-references to the Teacher’s Resource Book. • a ‘Maths Talk’ section (glossary of maths terms) at the back of the book for students to refer to. Teaching Approaches Modelled — This approach is used with small groups. The teacher provides a strong level of support by modelling the learning experience, presenting effective strategies and illustrating how connections are made. The teacher also models the use of materials and how to record the mathematics involved. Students talk about the presentation and model what they experience. This is an approach where the teacher predominantly models the mathematical concepts. Shared — This approach is used with small groups and as part of a whole class focus. The teacher and the students work together to explore mathematical concepts and to make generalisations. Both the teacher and students use materials and record the mathematics to demonstrate their understandings. This is an approach where the teacher and the students work along side each other to make connections and form generalisations. Guided — This approach is used with small groups. The teacher removes himself or herself slightly from the group, while still gently ‘guiding’ the students and addressing issues as they arise. This is an approach where the teacher provides support while allowing students to make their own generalisations and connections.
How Nelson Maths Is Organised
7
What We Know About Learning • Children learn in different ways. • Children learn from and with others. • Children learn by teaching others.
• Children should have the opportunity to record in different ways. • Children can follow different pathways to reach the same learning milestones. • Children need to be encouraged to take risks in their learning.
• Children learn by being actively involved. • Children need time to grasp the concepts introduced, i.e. time for thinking, reflecting, reacting and sharing the processes and answers in mathematics. • Children learn when they feel good about themselves — self-esteem is critical.
8
The Classroom Environment It is important that the classroom environment: • is stimulating and engaging and immerses students in a mathematical context • incorporates a variety of rich resources that engage students in making mathematical connections • is rich in the language of mathematics • has access to calculators • has access to information technology, which is an integral component of our world; this should be reflected in our mathematical classroom environment • has rich displays where students can make metacognitive links to their mathematics learning • is positive and encouraging, and allows students to take risks in their learning.
Setting Up Your Maths Classroom Here are some ideas on how you can set up your classroom.
Provide step-by-step charts so students can work independently to resolve problems.
Displaying students’ work is important. Allow time to talk about and view maths tasks.
Taskboards are an excellent way to let students know what is expected of them.
The Classroom Environment
9
Ensure students know what maths materials are available. These should be easily accessible.
Value students’ achievements by creating up-to-date displays in the classroom. Display individual student’s expertise so others can learn from them.
Encourage students to work cooperatively in small groups.
10
Nelson Maths Teacher’s Resource — Book 5
Maths can be integrated into other subject areas.
Use charts to display helpful information and promote mathematical language.
Conversion
Chart
Time Facts
Measurement Facts 60 seconds = 1 minu te 10 millimetres = 1 centimetre 60 minutes = 1 hour 100 centimetres = 1 metre 24 hours = 1 day 1000 metres = 1 kilo metre 7 days = 1 week 2 weeks = 1 fortni ght 12 months = 1 year 365 days = 1 year 366 days
= 1 leap year
Include students in upcoming mathematical learning.
Ensure technology is part of the everyday learning environment.
Encourage peer tutoring.
The Classroom Environment
11
Assessment and Monitoring Assessment and monitoring is an ongoing process. It allows teachers to gain a clear picture of students’ understandings. This can then be used to influence planning, as well as to assist the teacher to group students for effective focus teaching. Teachers need to model mathematical language constantly. They need time to talk to and question students, and must allow time for students to respond. Teachers will thereby gain useful insights into how each student is learning and what thinking processes they are using. This information is invaluable for future planning.
Why Assess? To collect data on individual students so their needs can be met and targeted when planning future learning experiences. Teachers use a range of strategies (see ‘How to Assess?’ below) to collect data for their ongoing planning.
What to Assess? The student’s: • attitudes • mathematical understandings (verbal and recorded) • problem-solving abilities • confidence • ability to work with others.
When to Assess? • at the beginning of the school year • at the end of a unit (or block of units) • at the beginning of a unit • on an ongoing basis — during your daily maths sessions • as part of the ‘Whole Class Focus’, ‘Focus Teaching Group’, ‘Independent Maths’, while roving, and during ‘Whole Class Share Time’.
How to Assess? • teacher observations, e.g. anecdotal comments on post-it notes on an A3 list of names • student self-assessment (learning journals, smiley chart, etc.) • peer assessment • file cards, kept for each student • Nelson Numeracy Assessment Kit
12
Nelson Maths Teacher’s Resource — Book 5
p attern s Numb er and
_______________
• portfolio assessment
t NA not apparen B beginning
E
Week
consolidating established
Investigating Place Value
2 Numbers That Count
3 What’s in a Number?
4 Data Collection
5 Patterns and Relationships
6 Lines in Our World
7 Addition and Subtraction
8 Multiplication and Division
9 Measuring and Estimating Angles
10 Analogue and Digital Times
© Thomson Learning,
=
16 – 6
=
5 x
22 + 9 d
15 +
=
x
x
=
60 +
continuing about finding and you find difficult ____________________ 5 a What do __________________ __ __________________ __________________ number patterns? __________________ __________________ concern? __________________ that caused you unit er Numb ________ ng else in this __________________ b Was there anythi ______ ______ __ __________________ __________________ ______ __________________ ______ ______ __________________ __________________
(Date)
1
40 – c
ents ‘Plain Speak’ Statem
Unit
balance the scales. on each pan to 4 Write numbers b a
-ass essm ent Che ck and Self
___________ ________________________ ________________________ Name: ________ Year: __________ Term: __________ __ Year Level: ________
Code:
Unit 5
e Student Profil
BLM 82 C
• ‘Check and Self-assessment’ pages in the Student Book
Date: ns in work out the patter 1 How do you _____ __________________ number sequences? __________________ __________________ _________________ __________________ __________________ ______ ______ ____________ __________________ sequences? _ patterns in these __________________ 2 What are the __________________ 27, 32: _____________ _____ a 13, 18, 20, 25, __________________ __________________ 82: _____________ ___________ b 88, 84, 85, 81, __________________ ______ ______ 24: _____________ c 10, 12, 15, 19, next 7 numbers: patterns for the _____, _____, _____ 3 Continue these _____, _____, _____, 16, 13, 18, _____, _____, _____, _____ a 12, 9, 14, 11, _____, _____, _____, 40, _____, _____, _____, _____, _____ b 10, 20, 25, 35, _____, _____, _____, 36, _____, _____, c 23, 26, 29, 33,
up to 5 digits place in order numbers Read, say, write and the same number t different forms of Recognise and represen digits numbers up to 5 place in order whole Read, say, write and to 5 digits up value in whole numbers Understand place 100 4, 5 and 6 beyond number Skip count by 2, 3, starting at any given and 100s to 1000, Skip count by 10s s collection fractional parts of Find and compare situations decimals in real-life Use, order and compare
sequence. Resource pp. 36–38.) continue a given number n to describe and Unit 5 (See Teacher’s and multiplication. subtraction and multiplicatio
to 5 digits order numbers up 1000 Create, identify and 4, 5, 6, 10, 100 and numbers by 2, 3, Skip count from set
17
addition, subtraction involving addition, • Use rules involving Number and patterns • Complete simple statements of equality
ion to collect informat Conduct surveys to show data ion collected Use Venn diagrams line] to show informat , picture graph and Use graphs [bar (column) displayed ion collected and Interpret informat a to describe and continue on and multiplication addition, subtracti Use rules involving ation subtraction and multiplic given number sequence involving addition, statements of equality Complete simple ent of lines in the environm the characteristics horizontal, vertical, Recognise and describe curved, diagonal, tations of lines (straight, Create pictorial represen cular) parallel, perpendi straight angles acute (sharp) and Describe right, obtuse, of place value, nding understa their te materials to assist Explore and manipula of calculation subtraction and addition s with different methods 4-digit numbers subtraction equation examples of 3- and Solve addition and s using everyday subtraction problem Solve addition and whole numbers are s and equations where problem word multiplication Solve and record or multiples of ten and a single numbers numbers single 3-digit multiplied by and equations using division word problems Solve and record divisor (blunt), create angles [obtuse Identify, name and smallest to largest Order angles from
acute (sharp), right
and straight]
and minutes digital time in hours Read and record 5-minute intervals analogue time to Read and record
225 2004. This page from
Nelson Maths Teacher's
Resource — Book 5
may be photocopied
for educational use
within the purchasing
institution.
• ‘During this week look for students who can:’ (see the first page of each unit in the Teacher’s Resource Book) is a list of ‘plain speak’ statements for teachers to refer to when observing students (these are also listed in checklist form on BLMs 82–85) • Student Profiles (see also BLMs 82–85).
Planning Mathematics planning is ongoing and depends on the needs of the class and individual students. Information obtained from monitoring and assessing students can be used for future planning. Nelson Maths Teacher’s Resource Book provides the following weekly, term and yearly planners to choose from: • four weekly planners (BLMs 86–89) • one term planner (BLM 90) • two yearly planners (BLMs 91 and 92). Please note: The Teacher’s Resource Book is also available on CD-ROM, which enables teachers to plan directly on screen. Student Profiles (BLMs 82–85) can be recorded and filed on screen. Also available on the CD-ROM is the Enabler function which allows teachers to plan across two or more grade levels; and a ‘Correlation Chart’ linking the units in Nelson Maths to individual state and the New Zealand syllabuses.
Parent Participation Research shows that strengthening the partnership between school and home increases students’ chances of success in their education. Therefore, as teachers, we need to encourage parents to be active participants in their children’s learning and, in turn, we need to keep parents informed of the type of learning that is happening in our classroom. In summary, we need to highlight the connections between maths experiences at home and maths experiences at school. Schools need to understand their community, and provide a supportive environment where parents’ attitudes and goals for their children are respected. Teachers need to encourage parents to be partners in their children’s numeracy education. Parent Participation
13
Parents need to have a true picture of how maths is taught today, how current teaching practices are different from their own maths education, and why things have changed. Teachers need to communicate to parents the content of their mathematics program, and the teaching strategies and resources used. Teachers and parents need to work together to provide their children with additional assistance. Through the assessment and reporting program, parents can be informed of their child’s mathematical progress, and goals can be set to extend the child’s development. Teachers can provide parents with hints and a range of enjoyable, hands-on activities to do at home that will support children’s mathematical development (see ‘Family Maths’ BLMs). There are many strategies to keep parents informed and involved such as: • holding sessions to outline the current mathematics program, i.e. individual classroom teachers providing parents with information about the class mathematics program and/or school-based information nights where all teachers, staff and/or guest speakers are involved in the presentation • conducting sessions at which parents can discuss their child’s progress and the type of mathematics they are involved in — the Nelson Maths Student Book provides samples of the student’s work (see also ‘Check and Self-assessment’ pages in the Student Book) • giving parents the opportunity to complete some of the activities students are involved in, i.e. ask parents into the classroom to actively participate in the mathematics program • distributing newsletters to inform parents of the current mathematics program and/or providing open-ended tasks for parents to do with their children (see ‘Family Maths’ BLMs) • erecting display boards outside the classroom with family maths problems to solve (see ‘Family Maths’ BLMs), and/or maths tasks to be done at home or at school for the week • having open maths times during the week/term/year to which parents are invited to interact with and/or observe the class in action • making digital photo montages of maths activities to display outside the classroom • posting video footage of the class maths program on the school intranet or burning a CD for parents to view. It is very important to make parents aware that many of their day-to-day activities with their children involve mathematics, e.g. cooking, going shopping, carpeting or tiling floor spaces, building, collecting and sorting objects, etc. It is also very important that the lines of communication are open between home and school, and that parents are informed of the type of mathematics program their children are involved in. It is crucial that parents feel welcome to participate in the program in any way acceptable to them, e.g. working with a group of students; preparing, sorting and/or organising resources. Parents and teachers need to work as partners to enhance the education of their children.
14
Nelson Maths Teacher’s Resource — Book 5
• You can help your children at home by involving them in mathematical activities and talking to them about mathematics and its everyday uses. Be positive! Praise your child's success. Encourage your child to have a go at measuring, calculating, counting, estimating and solving problems. Invite children to investigate and make discoveries for themselves. Encourage them to find their own answers. Don't be too quick to tell them the answers. • Show children how you use maths in your everyday activities, e.g. measuring ingredients, estimating costs, calculating change, timing how long things take to cook, preparing shopping lists, using calibrated containers, using kitchen scales, tendering money, playing card and board games, telling the time, looking for patterns in the environment, reading road signs, reading number plates. Materials to have on hand: dice; dominoes; number cards 0–9; 100 chart; games such as UNO and Snakes and Ladders. • Cooking at Home Children can help you prepare shopping lists, work out the quantities of ingredients needed, weigh the ingredients and check on the cooking time. Involve children in selecting new recipes. • Keep the Calendar Up–to–date Mark any special events on the calendar, e.g. family and friends’ birthdays, outings, holidays, etc. Look for patterns in the number squares. Encourage children to make their own calendars or to keep a diary. • Mass and Height Keep a record of your child's mass and height. See how much they have grown each year. Do this for everyone in the family. Graph the results using various types of graphs.
Family Maths Blackline Master 1
Cut out the snippets (suitable for the middle school) below and reproduce them in the school’s weekly newsletter.
• Mapping When travelling, provide children with a street directory or map and discuss directions. Point out speed limits, distances to towns, populations in towns, etc. When you are driving along in the car, ask children to guess how far it is to the next light post, the next town, etc. Calculate the distance travelled or the distance yet to travel. Involve the whole family. Measure the distances with your speedometer. • Make My Target Number? Play with a partner or a small group. Write down the numbers 1 to 9. In turn, select a target number, e.g. 65.The object of the game is to be the first person to use three of the numbers written down to make the target number using addition or multiplication or both. A number can only be used once. Each person must record their equation, e.g. 7 x 8 + 9 = 65.The first person to write down a correct equation wins that round. • Take One or Take Two Put out 11 blocks in a row between two players. In turn, remove one or two blocks at a time. The object of the game is to make your partner pick up the last block. • Tossing a Coin Ask, ‘How many times do you think a coin will land on heads if you toss it 30 times?’ Write down your guess.Test your guess and record how the coin lands. Compare results. • Weather Chart Keep a weather chart. Older children can record weather conditions and daily temperatures from the newspaper and graph the results over a month. • Dice Games Throw two dice and have children multiply them together to reinforce times tables. Throw two dice and have children add the numbers and multiply the total by 1 to 12 to reinforce times tables. Throw three or four dice and have children record the largest and smallest numbers they can. After a number of throws, have children order all the numbers from smallest to largest. © Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 5 may be photocopied for educational use within the purchasing institution. Family Maths Blackline Master 1
15
Family Maths Blackline Master 2
Cut out the snippets (suitable for the middle school) below and reproduce them in the school’s weekly newsletter. There are three take-home game boards (pp. 17–19) provided. All use simple equipment. Copy onto card and send home. • Bounce into Maths Many children love to play ball games. Help your child to learn their tables by playing a ball game with them. First, ask a tables question, e.g. 7 x 9. If your child answers correctly then they can have a shot at the basket or a kick for goal, etc. Ensure you score so effort is rewarded, e.g. a goal = two points; if the ball hits the ring without going inside, then score one point. Your child then asks you a tables question. You can also play in teams. • The Clock is Ticking You need a ball and a timer (the timer on the stove will do) for this game. Set the timer for five minutes, ask a tables question that your child should know and then throw the ball to them. After your child answers correctly, they ask you (or another player) a new question as they throw the ball to them. Questions and answers continue in this way until the timer rings. The person holding the ball at this time is out. • Number-plate Knockout When travelling by car you can play games that help children to understand numbers. In Number-plate Knockout, take turns to decide on a number range, e.g. a number between 200 and 270. The first player to spot a number plate within that range, e.g. BTM 239, wins one point and selects the next number range. The player with the most points after a certain time wins. • Money, Money, Money When doing the supermarket shopping, ask your child to work out the coins and notes that will be handed over to the shop assistant. Ask them to check for the correct change. Talk about rounding up or down when buying single items. • The Big Half Ask you child to help when things need to be shared amongst the family, e.g. children could count out strawberries or pour drinks so that everyone has an equal share. Talk about ways of doing this, e.g. measuring cups next to each other, counting, cutting food in half and then in half again. It is often helpful to follow the rule that one child shares, while the other chooses which share they will take! • Fitness Fans Children can be encouraged to set and reach fitness goals when they see a tangible record of their progress. Help them to draw up charts showing, for example, how far they have run, how many goals they have shot, the number of minutes spent dancing, etc. These records could be simple bar (column) graphs or why not mark the distance run each day on a map, e.g. running to Sydney. • Playing Around Many childhood games involve lots of maths. Games with dice and cards often involve adding or subtracting. When playing such games talk about the maths being used. Encourage your children to check each other’s working out. Take turns to keep score. • Seeing Daylight Encourage your child to notice the changes that happen in the sky, e.g. What time is sunrise and sunset each day? When does the moon rise each day? What shape is the moon each night? If living near the sea, what happens to the tides? • My Time Have your child use a clock to keep track of how they spend their time after school. Have them record, for example, how much TV they watched. How much time they spent playing/ doing their homework/playing on the computer. Talk about whether this is the way they want to spend their time.
© Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource—Book 5 may be photocopied for educational use within the purchasing institution.
16
Nelson Maths Teacher’s Resource — Book 5
Family Maths Blackline Master 2
Ups and Downs You will need : a dice, a different-coloured counter per player (different coloured beans could be used) (For 2 to 4 players) How to play: • Each player starts with 50 points and puts their counter on a circle of their choice. • In turn, throw the dice. Move that many places in either direction. Each player must then follow the instructions on the circle they land on, e.g. + 12. • The first player to reach 100 points wins. To vary the game change the starting and winning points, e.g. start with 850 and try to get to 925.
+6
–4
+2
+11
+3
–13 +12
+8 –10
–7 +6
–12
–1
–2
+3 +5 –4 –8
+8
–8
+5
+10 +5
–7
+11 –3 +6 +9 –2 –0
+2 –9
© Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 5 may be photocopied for educational use within the purchasing institution. Game board 1
17
Table Star You will need : 2 dice and some counters (For 2 players) How to play: • Chose the game you are playing. • In turn, throw both dice. Work out table and you throw 5 and 3; your 3 are added to make the 8. Cover • The first player with three numbers
your score, e.g. when playing the 4 times score will be 32 because (4 x 8 = 32); 5 and that number (32) on the playing board. covered in their row wins.
Game 1 (2 times table) Player 1 2 4 6 Player 2 2 4 6
8 8
10 10
12 12
14 14
16 16
18 18
20 20
22 22
24 24
Game 2 (3 times table) Player 1 3 6 9 Player 2 3 6 9
12 12
15 15
18 18
21 21
24 24
27 27
30 30
33 33
36 36
Game 3 (4 times table) Player 1 4 8 12 Player 2 4 8 12
16 16
20 20
24 24
28 28
32 32
36 36
40 40
44 44
48 48
Game 4 (5 times table) Player 1 5 10 15 Player 2 5 10 15
20 20
25 25
30 30
35 35
40 40
45 45
50 50
55 55
60 60
Game 5 (6 times table) Player 1 6 12 18 Player 2 6 12 18
24 24
30 30
36 36
42 42
48 48
54 54
60 60
66 66
72 72
Game 6 (7 times table) Player 1 7 14 21 Player 2 7 14 21
28 28
35 35
42 42
49 49
56 56
63 63
70 70
77 77
84 84
Game 7 (8 times table) Player 1 8 16 24 Player 2 8 16 24
32 32
40 40
48 48
56 56
64 64
72 72
80 80
88 88
96 96
Game 8 (9 times table) Player 1 9 18 27 Player 2 9 18 27
36 36
45 45
54 54
63 63
72 72
81 81
90 90
99 99
108 108
Game 9 (10 times table) Player 1 10 20 30 Player 2 10 20 30
40 40
50 50
60 60
70 70
80 80
90 90
100 110 120 100 110 120
© Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 5 may be photocopied for educational use within the purchasing institution.
18
Nelson Maths Teacher’s Resource — Book 5
Game board 2
Difference Dilemmas You will need : 2 buttons (or counters) per player (For 2 to 4 players) How to play: • For every round, each player flips two buttons (one at a time) onto the game board. • The player then works out the difference between the two numbers, e.g. the difference between 45 and 72 is 27 (72 – 45 = 27). • The player whose answer is closest to zero wins a point. • The player with the most points at the end of the game wins. You can vary the game by adding the numbers rather than subtracting them or by changing the numbers on the board.
97
20
14
35
88
18
31
67
27
8
45
59
11
49
50
62
72
90
81
78
© Thomson Learning, 2004. This page from Nelson Maths Teacher’s Resource — Book 5 may be photocopied for educational use within the purchasing institution. Game board 3
19
Five-minute Maths At the beginning of each maths session, or when time allows throughout the day, spend five minutes doing some quick and enjoyable maths activities to reinforce and revise concepts previously taught, and/or revise number facts, counting sequences, shapes, etc.Traditionally, Number has been the focus of the five-minute maths session. However, featured below is a range of activities across all maths strands to provide a broader classroom focus.
Number • Have students write the ordinal number for their birthday on a card. Time the class as they order themselves, without speaking, from highest to lowest number . • Start at any number between 1 and 10, and skip count by 5s.Tap a ruler on the desk to complete the counting. Students calculate the next number after the tapping stops. • Have students take turns to create ‘Who am I?’ numbers, e.g. ‘I am larger than 20, smaller than 40 but not divisible by 5.Who am I?’ • Give each student a card showing the ordinal number for their birthday. Have students walk around the room displaying their number, then ‘cluster’ together to make a target number, e.g. 40. • Pose problems for students to solve, e.g. ‘Find the number halfway between 18 and 108. Find the number halfway between 26 and 260.’ Ask students to share the strategies they used to solve these problems. • Give students a time allocation to create addition problems. Have them use the following digits and signs to create problems where the answer is more than 50, but less than 80: 1 2 3 4 5 6 7 8 9 + =. • Have a student select a ‘secret decimal’ between 0.01 and 0.99. Ask the class to estimate how many turns it will take them to guess the ‘secret decimal’, then find out. The selected student can only respond to the guesses with ‘higher’ or ‘lower’. • Play the game ‘How Much is My Name Worth?’ e.g. A = $1 and Z = $26. Have students mentally calculate how much their first and last names are worth. Repeat, using the names of Australian cities, or vary the amount allocated to each letter, e.g. $2, $4. • Have students start with an imaginary $100. Provide junk mail catalogues and calculators. Ask students to subtract the cost of various products until they reach zero dollars. Allow only three minutes. Shorten the time available as students become more proficient. • Ask students to calculate how many days have already gone this year and how many still to go. Repeat, asking students to work out how many days since their last birthday, and how many days until their next birthday. • Gather assorted phone numbers and have students add up each phone number mentally, e.g. 9968 3185 = 49. Use calculators to check the answers. • Make an A3 copy of a newspaper page that has a mix of advertisements, photos and text. Ask students to estimate what fraction of the paper consists of advertisements, photos, text, blank space.
20
Nelson Maths Teacher’s Resource — Book 5
Measurement • Cut up three coloured strips of paper: one 30 centimetres long, one slightly longer and one slightly shorter. Have students predict which strip is exactly 30 centimetres. Once the 30 centimetre strip has been determined, have students predict the real measurements of the other two lengths. • Give each student a 50 centimetre length of string; ask them to arrange it so it appears as ‘short’ as possible. Review how to make a long line look short. • Fill four milk cartons with a different mass of sand and ask students to order them from lightest to heaviest. Allow each student only twenty seconds to heft all four and make their decision. • Have students work in pairs to record how many sit-ups they can do in one minute. Repeat the task for five days in a row, then have each student graph their results. • Ask each student to predict how many times they can write their first name in 60 seconds.Test predictions. Repeat with a 30 second time limit.
Space • Place the names of three quadrilaterals on cards above the heads of three students. Have each of the three students ask questions about the identity of their shape.The class can only respond with ‘yes’ or ‘no’. • Have students follow instructions, e.g. ‘Draw a triangle inside a circle, inside a square, inside a pentagon.’ Students can then make up their own instructions for a friend to follow. • Secretly select a shape. Describe the shape and ask students to draw it from the description you give. • Provide magnetic 2D shapes. Allow students 30 seconds to make a recognisable picture that uses all the shapes. • Provide several ‘pairs’ of boxes, e.g. two identical cornflakes boxes, two Weetbix boxes, etc. Open out one of each box and display the nets. Hide the labelling and ask students to match each net to its box. • Provide a bag of balloons that are the same size and shape. Have students work in pairs of attempt to blow up balloons that are congruent with each other. Have pairs review each others’ attempts at congruency.
Chance and data • Using a coin, have each student attempt to toss three heads in a row. Ask them to record how many throws it took. Repeat, asking students to throw the pattern: head, tail, head, tail. • Have each student record an event in their life where they could honestly record the probability statement ‘not a chance’. Have them review their statement and record the probability of it happening in the future. • Have students record the total number of pages in the phonebook. Ask one student to open the book at exactly half way. Record the number of turns it took to reach half way. Have another student repeat the task. Predict how many turns it will take a third student to open the book at the half-way mark. • Ask, ‘What is your favourite colour?’ Provide students with four or five options and ask them to create a ‘human graph’. Ask another question, e.g. ‘What is your favourite food?’ and again create a ‘human graph’.
Five-minute Maths
21
• Provide a shuffled deck of playing cards. Ask students to predict how long it will take before a picture card appears as each card is turned over. Test students’ predictions. Repeat, using an odd number, a number above 5, etc. • Record the favourite songs of the class. Rank them in order to make a class ‘Top Ten’. • Collect graphs and tables from the newspaper. Over time, make a class display of the different types of graphs. Discuss the differences.
An Additional Resource Nelson Maths Teacher’s Resource Book on CD-ROM A planning and assessment CD-ROM accompanies everyTeacher’s Resource Book in the Nelson Maths series.Teachers will find that: • all 240 pages of the Teacher’s Resource Book can be viewed on screen • all blackline masters can be printed from the CD-ROM • a ‘Correlation Chart’ is available linking the units in Nelson Maths to individual state and the New Zealand syllabuses • the CD-ROM is interactive, allowing teachers to keep assessment records of individual students and plan their weekly, term and yearly maths program on screen.
Assessment Using the CD-ROM The ‘plain speak’ statements (included in each unit) are featured in the assessment section of the CD-ROM. Teachers select the ‘Student Administration’ button, and follow the options available. A Student Profile for each class member can then be developed by entering the student’s name, the unit being studied and selecting from NA (not apparent), B (beginning), C (consolidating) and E (established) for each ‘plain speak’ statement featured. Graphing facilities provide a summary of each student’s achievements.
Weekly, Term and Yearly Planning on CD-ROM By following the ‘Planning’ menus teachers are able to plan their weekly, term and yearly maths program for one grade or multiple grades on CDROM. To plan their weekly program, the teacher selects the week, the term, the date, the unit to be explored, the teaching focus for the week and their choice of activities from Whole Class Focus, Independent Maths, Whole Class Share Time and the Focus Teaching Group section. All activities selected can then be edited and teachers may choose to key in favourite tasks and activities of their own. Term and yearly planners function in a similar way to the weekly planner; however, they feature only the units to be covered and their corresponding teaching focus. All three planners can be viewed on screen and/or printed out. The CD-ROM’s planning and assessment functions are very simple to use and will save teachers valuable time.
22
Nelson Maths Teacher’s Resource — Book 5
Nelson
Maths U NITS 1– 40
unit
Investigating Place Value
1 Number and patterns
Student Book pp. 5–6
BLMs 1, 2 & 3
During this week look for students who can: • read, say, write and place in order numbers up to 5 digits • recognise and represent different forms of the same number. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources 10-sided dice, white flash cards, large sheets of butchers’ paper, BLM 1 ‘Rounding Off ’, BLM 2 ‘Place Value Dice Roll’, BLM 3 ‘A–Z Number Plates’ Maths Talk Model the following vocabulary in discussion throughout the week: place value, ones, tens, hundreds, thousands, tens of thousands, estimating, rounding up/down, extended notation, equivalence
Whole Class Focus — Introducing the Concept Place-value Knowledge Organise the class into small groups. Ask, ‘What do you know about 4-digit numbers?’ Have students brainstorm what they know, recording on a large piece of paper. Guide students by using prompts, e.g. the number of digits, the value and range of digits, etc. At the completion of each group’s discussion and recording, come together as a whole class. Compile responses onto one large sheet to provide a record of pre-existing knowledge; students can add to the page as the unit develops. What’s in a Digit? Record on the whiteboard four 4-digit numbers where eight occupies a different place value, e.g. 8 467, 9 823, 2 081, 3 398. Ask, ‘What is common about each of these numbers?’ Share responses. Prompt by asking, ‘What do you notice about the position (or value) of the 8 in each number?’ Record ways of writing the value of the 8, e.g. 80, 8 tens; 8 000, 8 thousands, 80 hundreds, 800 tens. Ask students to produce their own 4-digit examples. Rounding Numbers Off Ask, ‘Where do we find rounding off in our world today?’ Seek a variety of responses and record them on the whiteboard, then ask, ‘Why do shopkeepers round off numerals?’ Ask students for several 4digit numbers, then ask individuals to identify which digits are tens, hundreds, etc. Seek informal ‘formulas’ for rounding off ones, tens and hundreds, e.g. numbers below 499 round down; 500 and above round up, etc. Stretch a Number Write on the whiteboard ‘extended notation’; discuss the phrase to check if students are familiar with the concept. Write on the
24
Nelson Maths Teacher’s Resource — Book 5
whiteboard: 2 906. Ask, ‘How do you show this as extended notation?’ Record students’ responses. Point out that 2 906 can also be recorded as 29 hundreds and 6 ones. Experiment with other ways of recording ‘traditional’ forms of extended notation. Who Am I? 1–9 999 Write a 4-digit number on a card and tally how many attempts it takes students to guess the number. You may only answer, ‘Higher’ or ‘Lower’ to their guesses. Repeat, with students supplying the number. Ask, ‘What is a good strategic number to start with?’ (e.g. 5 000.) Record students’ responses.
Small Group Focus — Applying the Concept Focus Teaching Group • Rounding Off! Give each student a copy of BLM 1 ‘Rounding Off ’ and ask them to note something about the numbers on the page, e.g. all numbers have 4 digits; all numbers are under 10 000; etc. Ask, ‘How do you round off a digit such as 5?’ Demonstrate how to round ‘up’ and ‘down’. Discuss how rounding off alters the appearance — and sometimes the value — of a number.Work together to complete the listed examples, then supply students with individual numbers to complete independently. Alternatively, students could write five 4-digit numbers of their own, then swap with a partner and round off each other’s numbers. • Extended Notation Write 7 415 on a flash card. Ask, ‘What is the value of the 7?’ Record different ways of representing 7 000. Apply the same strategy to each digit in turn. Use tape or string to extend the original flash card so that it contains four more cards, now showing 7 415, 7 000, 400, 10, 5.
On the back of each card, write the number values as words. Distribute 5 blank cards to each student and have them model the task with their own 4-digit number. • The Value of 8 Record on the whiteboard four 4-digit numbers, each showing 8 in a different value position, e.g. 3 778, 8 372, 7 385, 9 811. Ask, ‘What is the value of the 8 in each number?’ Record students’ answers; emphasise that a digit such as 8 can have several different values. Introduce ‘Wipe Out’ to the whole group. ‘Wipe Out’ is where a designated digit and its value is subtracted from a number, e.g. ‘9 834: wipe out 8’ is 9 034 not 934. Provide a variety of Wipe Out numbers for students to work on independently, e.g. ‘5 894: wipe out 9’, ‘8 430: wipe out 3’.
Independent Maths Individual, pair, small group
Dice Roll Game Have students work in pairs. Give each pair a copy of BLM 2 ‘Place Value Dice Roll’ and four 10-sided dice. Students take turns to roll the dice, then create and record the largest and smallest numbers possible from the rolled digits. When they have finished, have students record any number patterns or interesting facts they observed. A-Z of Number Plates Have students work in small groups. Give each group a customised copy of BLM 3 ‘A–Z Number Plates’. Before copying the BLM, select four different digits for each group, and a direction of ranking (highest to lowest, or lowest to highest). Unit 1 Investigating Place Value
25
Rounding Off School Number Plates Have students work in small groups. Ask them to record the digits on the number plates of all the cars in the staff car park; when they return, have them round each number to the nearest ten and hundred. Fast finishers can then rank the cars in order, from lowest to highest number. Also Known As (Student Book p. 5) Discuss the ways a number can be differently represented. Model a number. e.g. 180: 180 ones, 18 tens, one hundred and eighty. Discuss numbers with thousands, e.g. 1 280: 1 280 ones, 128 tens, one thousand two hundred and eight. Ask students about the spelling of hundreds and thousands. In pairs or small groups, have students complete Student Book p. 5. Numbers for Cash (Student Book p. 6) Have students order the 4-digit telephone numbers, then apply place value to the number ‘7’ to find out how many days bill-free each ‘lucky 7’ family won.
Whole Class Share Time Ask the dice rollers to explain the strategies they used to create a large number and a small number from the same digits.
Today I learnt …
There is a pattern to identify when creating 4-digit number plates. Ask two groups to explain the strategies they used to make all 24 plates. (Start with one digit in the thousands place, then try all other numbers in the hundreds, tens and ones.Then put the next highest or lowest number in the thousands place and repeat the process.) Select five students to each provide a number plate number and then round it off to the nearest ten and hundred. Ask, ‘What rules did you follow when rounding your number up/down?’ Choose a pair or small group to provide four alternative ways of presenting a number, e.g. 1 400. Select students to share their numbers from Student Book p. 5. Ask students to share what they did in the ‘Numbers for Cash’ activity. Ask, ‘What was a good number to have?’
26
Nelson Maths Teacher’s Resource — Book 5
unit
2
Numbers That Count Student Book pp. 7–8
Number and patterns
BLMs 4 & 5
During this week look for students who can: • • • • • •
read, say, write and place in order whole numbers up to 5 digits understand place value in whole numbers up to 5 digits skip count by 2, 3, 4, 5 and 6 beyond 100 skip count by 10s and 100s to 1 000, starting at any given number find and compare fractional parts of collections use, order and compare decimals in real-life situations.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources dice, calculators, counters, Unifix, flash cards, pre-cut cardboard circles, fruit, a block of chocolate, stopwatch, BLM 4 ‘Skip-counting Challenge’, BLM 5 ‘Skip-counting Grids’ Maths Talk Model the following vocabulary in discussion throughout the week: digit, ones, tens, hundreds, thousands, pattern, rank, order, largest, smallest, predict, before, next, after, more, less
Whole Class Focus — Introducing the Concept Buzz by 5 Have students sit in a circle to play ‘Buzz’. Each student says the next consecutive number, except for multiples of 5, which are replaced with the word ‘Buzz’. Extend the parameters of the game by starting a second round with a number such as 22 or 34 (making 27 or 39 the next ‘buzz’ number, as they are 5 numbers on from the starting number). How Fast Can You Say the Alphabet? Ask three students to say the alphabet as quickly as they can. Time each student with a stopwatch and place their times on the whiteboard. Ask the class, ‘How can we order these attempts from fastest to slowest?’ Select one time and write it on the whiteboard.Write a comparison time next to it, e.g 12.10 sec, 12.15 sec. Ask ‘How do we order the times when they have the same number in the tenths place?’ 1
What Does 2 Look Like? You will need a pear, an orange and a block of chocolate for this activity. Cut the pear in half longways and quarter the orange. Ask a selected student to show what half of each piece of fruit looks 1 1 like: 2 the pear is one piece, but 2 the orange is two pieces. Ask, ‘Is there 1 more than one way to show 2 ?’ Halve an eight-piece slab of chocolate and 1 show 2 (four pieces). Unit 2 Numbers That Count
27
The Silent Count On In a quiet environment, start a number pattern at 9 and count by threes, tapping the desk with a ruler as you count. Encourage the students to count silently by themselves; after tapping five, six or seven times, ask, ‘What number comes next?’ This will involve students in continuing the pattern and reacting quickly to predict the next number in the sequence. Order and Counting Write the even numbers from 80–104 on white flashcard offcuts, then jumble them up in a pile on the floor. Ask, ‘Can you identify the number pattern?’; then, when the pattern has been identified, ‘Can you spot the starting number?’ Ask selected students to order the numbers from lowest to highest. Shuffle the cards again and have students order them from highest to lowest.
Small Group Focus — Applying the Concept Focus Teaching Group • Can You Follow the Rule? Present this counting pattern: 1, 6, 9, 14, 17. Give the group time to identify the skip-counting pattern (+5, +3). When students identify the pattern, ask, ‘What was the easiest part of the pattern to work out?’ Provide paper. Ask the group to start with 5, then add 6 and take away 3; they should then continue the pattern for the next 8 numbers. If time permits, students could create their own 2-step counting patterns for the rest of the group to identify. • Ordering Fractions Provide a large container of Unifix (or counters). 1 Present this task: ‘Show me 3 of 24 blocks.’ View each student’s 1 representation, then record the answer: 3 of 24 is 8 blocks. Still with the 1 same 24 blocks, ask, ‘What is 4 of 24?’ After viewing their 6 blocks, make 1 1 links between the two answers by asking, ‘Is 3 larger or smaller than 4 ?’ Repeat the task using 12, 30 or 36 counters to show the comparison between different fractions. Students can work on this task independently if their level of understanding is solid. • 100 Metre Sprint Times Write these running times on cards: 12.0, 12.10, 12.1, 12.2, 12.21, 12.22. Shuffle the cards, then give six students one timecard each and have them stand in a line. Ask, ‘If these were the times of a 100 metre race, what would the order be?’Take suggestions from the group as to the order. Pose the questions, ‘What do you notice about 12.1 and 12.10?’ (They’re the same time.) ‘What do you notice about the direction of times when you look at the placings in a race?’ ‘With 12.2 and 12.21, how do we work out who is fastest when one has one decimal and the other has two?’ Provide another set of cards with different times and have students order them independently.
Independent Maths Individual, pair, small group
The numbers you write will depend on the ability level of the student or group.
28
Skip-counting Dice Challenge Have students work in threes. Give each group a copy of BLM 4 ‘Skip-counting Challenge’ and four dice. Two students play the game, each with 2 dice. The first dice rolled gives the starting number; the second dice gives the number they will skip count by. When both players have their starting points and skip numbers, start the game. The first player to correctly skip count seven times wins the round. The third student is the ‘judge’; they take on the winner in Round 2. Skip-counting Grid Give each student a copy of BLM 5 ‘Skip-counting Grid’. Write four ‘count by’ numbers for students, then have them write down their skip-counting patterns.
Nelson Maths Teacher’s Resource — Book 5
The Great Shoelace Tie-up Have students work in small groups. Give each group a stopwatch and ask them to time how long it takes each person to tie up both of their shoes. They should record each time to two decimal places, then rank their results in order from fastest to slowest. If time allows, students can repeat the activity several times, then use a calculator to find the difference between their best times. The Fraction Pizza Divide Have students work in small groups. Give each group five pre-cut circular pieces of cardboard which are to become paper pizzas. Ask students to rule and divide each paper pizza into a different number of pieces: 4, 6, 8, 10 and 12 pieces. When they have done that, ask each group to shade in the parts that are represented by half of the pizza. Have the group mount the pizzas on coloured card and complete 1 a statement for each pizza, e.g. ‘When a pizza is cut into 12 pieces, 2 is 6 represented by 6 pieces: 12 ’. Count On! (Student Book p. 7) Have students complete each skipcounting pattern using the number shown in the left-hand column.They can then make up a pattern of their own. Counting by 5 (Student Book p. 8) Before starting, ask if anyone can spot how all the numbers on the page are connected. (They are all multiples of 5.) Make sure that students understand the order in which the numbers are to be recorded (lowest to highest), and that after ordering they are to first add 5 to each number, then subtract 5.
Whole Class Share Time Ask the group to share their results. Ask, ‘Which were the easiest numbers to skip by?’ and ‘Which number was the most difficult starting point regardless of the skip required?’
Today I had problems with …
Have the group report on the times they took to tie up their shoelaces. Check on who was the fastest. If students had sufficient time, see who improved their time when the experiment was repeated a second and third time. Ask, ‘What was the time difference between the fastest and slowest times?’ Have the group read out the ‘half ’ statements from their pizza fractions, then ask, ‘What have you learnt from this activity?’ Ask the group, ‘Were there any obvious patterns showing when you completed the task?’ Ask one student to list all the numbers in order, from lowest to highest. Make sure that the answers are correct. Ask the group, ‘What strategy did you use to get the numbers in order?’ Have the group share their responses.
Unit 2 Numbers That Count
29
unit
What’s in a Number?
3 Number and patterns
Student Book pp. 9–10
BLMs 6 & 64
During this week look for students who can: • create, identify and order numbers up to 5 digits • skip count from set numbers by 2, 3, 4, 5, 6, 10, 100 and 1000. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources calculators, white flash cards, large dice, MAB blocks, BLM 6 ‘Rolling 5-digit Numbers’, BLM 64 ‘5-digit Place-value Chart’ Maths Talk Model the following vocabulary in discussion throughout the week: ones, tens, hundreds, thousands, skip count, extended notation, patterns
Whole Class Focus — Introducing the Concept Hand Out the Digits Write each digit from 0–9 on a flash card. Give the cards out to ten students and ask them to walk around in a confined circle, keeping their digit card hidden. Call out a group size, e.g. ‘Form groups of three!’ Students group in threes and have to make the largest (or smallest) number they can with their collective digits. Repeat, calling for groups of 4 and 5; later, extend the activity by providing two ‘0’ flash cards. Call Me Another Name Write on the whiteboard: 26, 170, 2 400. Ask students to read the numbers aloud, then write the words below the digits. Revisit extended notation and record 26 = 2 tens + 6 ones, etc. Pose the question for 170: ‘Is there another way of recording 170 apart from 1 hundred + 7 tens?’ For 2 400, ask, ‘How could you record this so it is different from 2 thousands + 4 hundreds?’ Up by 100, Up by 1 000 Ask students to pick a number between 1 and 100. Record three responses on the whiteboard. Ask, ‘What is 100 more on each of those numbers?’ Write the number, then ask, ‘And 100 more?’ Record 10 more responses for each number. Repeat the steps, this time asking for 1 000 more for each number. Ask, ‘What patterns do you see from both of these counting tasks?’ ‘Make Me’ Place-value Chart Write on the whiteboard: H, T, O. Ask, ‘What do you think of when you see those three letters?’ Take answers from students, and ask them to provide examples of numbers that have H, T, O. When using the term place value, ask, ‘What comes next after hundreds?’ ‘What comes after thousands?’ Create a chart on the whiteboard that reads
30
Nelson Maths Teacher’s Resource — Book 5
Tth,Th, H,T, O. Give students a copy of BLM 64 ‘5-digit Place-value Chart’. Ask, ‘What is different between tens of thousands and thousands?’ Give examples of both, then create a number using the extended chart. Suitable starting numbers are 17 528, 25 197. Give Me Ten Select a student to throw two large dice, e.g. 6 and 2. Ask the student to decide which number will be in the tens column and which will be in the ones. Record the number on the whiteboard, e.g. 26 (this is the starting number). Select another student to throw one dice.This is the skipcounting number, e.g. 5. On the whiteboard, record the next ten numbers in the sequence, e.g. 26, 31, 36, etc. Repeat a number of times with students suggesting the numbers in the skip-counting patterns.
Small Group Focus — Applying the Concept Focus Teaching Group • Stop Right There Each student will need a calculator and a piece of paper. Ask students to enter 51 on their calculator, then press + 4 =. The calculator screen should show: 55. If they press the = key again, the calculator will continue to count by 4. Ask students to record the next ten numbers from 51 counting by 4s, as they press the = key on their calculators. Repeat, counting from 62 by 3, and from 39 by 5. Ask, ‘What does the calculator do to continue the counting pattern?’ As an independent activity, have students use the calculator to create their own counting patterns.They can record these as they work. • Wipe Out Have students show 21 469 on their calculator screens.Then ask them to ‘wipe out’ a specific digit and record what is left, e.g. ‘21 469: wipe out the 4’. Place value understanding is important when playing ‘Wipe Out’: students need to ask themselves what the 4 is really worth (400): 21 469 – 400 = 21 069.Try examples where a digit is removed or wiped out from all placevalue positions. Students can continue playing ‘Wipe Out’ in pairs, using 19 873, 28 371, 11 272, 10 893. • Lucky Seven Write on the whiteboard: 7 777. Ask students to say the number. Then, using a different colour each time, write the number in different ways: 7 thousand, 7 hundred, 7 tens and 7 ones; seven thousand, seven hundred and seventy-seven; 77 hundreds + 77 ones. Ask, ‘Which way of showing 7 777 is the most different? Why?’ Discuss responses, then ask, ‘Why don’t we say 77 hundreds or 77 ones?’ Discuss why it is possible to represent numbers in different forms. Write on the whiteboard: 1 717, and have students record four different ways of showing it. Support the students as they work.
Independent Maths Individual, pair, small group
Rolling 5-digit Numbers Give each pair of students a dice and BLM 6 ‘Rolling 5-digit Numbers’. The aim is to make the largest number possible from the digits obtained by rolling a dice 5 times. For each dice roll, students must decide which column to record the digit in, aiming to create the biggest number possible.The winner is the student who wins the most rounds. Any Other Names? Have students work in small groups; give each group 4 dice. The dice are dropped at once and each student is required to write down any 4-digit number they can create with those digits. They write the number in extended notation, then write the number in words, then write the number in another form: Unit 3 What’s in a Number?
31
2 thousands, 6 hundreds, 1 ten, 2 ones two thousand, six hundred and twelve 26 tens and 12 ones
Players check each other’s answers, then the dice are rolled again. 100, 1 000 More Have students work in small groups with MAB blocks. One student creates a 3-digit number with MAB blocks; the others in the group close their eyes. Then they open their eyes and write the next five numbers when 100 is added each time.They repeat these steps, adding 1 000 each time. Secret Orders (Student Book p. 9) Provide copies of BLM 64 ‘5-digit Place-value Chart’; have students use the charts to find and colour the specified places in each number on the Student Book page. 10 in a Row! (Student Book p. 10) The large number at the start of each box is the starting number. Have students continue each pattern 10 times, counting by the number at the beginning of each row. Then have students write their own sequences to share. Units 1–3 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 11).
Whole Class Share Time Have students explain to the class the rules of the game and the strategies they used. Ask, ‘Where did you place a 6 when you rolled it first?’ and, ‘What did you do when the 5th number was a low digit?’
Today I found out …
Have students in the group explain the rules of the game they were playing. Ask, ‘Were there any numbers that you had trouble writing in another form?’ Record examples of ‘problem’ numbers on the whiteboard and invite solutions from the class. Ask, ‘What did you find hardest to count by: 100 or 1 000?’ Ask students for their preference; have them explain the reason for their choice. Ask, ‘What did you learn about place value from this task?’ ‘Who was the mystery person who could help you?’ (007) Ask students to show their work; ask, ‘Did you find any patterns or short cuts as you completed the page?’ Have several students share the sequences they created for the class to solve.
32
Nelson Maths Teacher’s Resource — Book 5
unit
4 Chance and data
Data Collection Student Book pp. 12–13
BLMs 7, 65 & 66
During this week look for students who can: • conduct surveys to collect information • use Venn diagrams to show data • use graphs [bar (column), picture graph and line] to show information collected • interpret information collected and displayed. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources large sheets of white paper, a list of the students’ first names, Excel, Kid Pix Studio Deluxe, Inspiration 6, BLM 7 ‘Blank Survey Form’, BLM 65 ‘My Graph’, BLM 66 ‘Venn Diagrams’ Maths Talk Model the following vocabulary in discussion throughout the week: tally, tallying, tally marks, collecting sorting, information, Venn diagram, questionnaire, selection, data, decide, least popular, most popular, predict, prediction, summarise, survey
Whole Class Focus — Introducing the Concept What is Your Favourite Colour? This task introduces the process of tallying. Ask the class, ‘What is your favourite colour?’ Record colour names horizontally on the whiteboard. Ask, ‘How can we tally your responses?’ Have students offer suggestions, then introduce the term ‘tally marks’ and explain how they work (4 vertical marks, with the 5th running diagonally). Complete the survey by having students vote for each colour and recording the votes with tally marks under the name of each colour. Revisit different types of graphs [bar (column), picture graph, line] and discuss which graph would be best to display the information. Vegemite or Not Vegemite? Ask, ‘Do you like Vegemite: Yes or No?’ Survey the class on the question.Tally responses, then discuss the outcome. Propose making a survey on favourite breakfast spreads. Ask, ‘Does the Vegemite result help you in finding out favourite spreads?’ Discuss responses, then ask, ‘What is the purpose of a survey that only wants a yes/no response?’ Record the weaknesses and strengths of such a survey. Internet or Computer Games Ask a question that will obtain an either/ neither/both response, e.g. ‘Which do you prefer: surfing the Internet or playing computer games?’ Record the votes using tally marks. Draw a Venn Unit 4 Data Collection
33
diagram (with two intersecting circles) on a large piece of paper, and transfer the votes for Internet, Computer games, Both and Neither onto it. (‘Neither’ votes are placed outside the diagram.) Put a ✗ for each vote. Ask, ‘What information can you find out from this Venn diagram?’ Soft Drink Survey Ask, ‘Do you like soft drinks?’ Survey the class and place the data under two headings: ‘Students who like soft drink’; ‘Students who don’t like soft drink’. Ask students to interpret the data. Ask, ‘What does this data show?’ More importantly, ask, ‘What doesn’t this survey show?’ (It doesn’t show what the people who don’t like soft drink actually like to drink.) Heads or Tails Take two 20c pieces. Say, ‘If I toss both coins at the same time, what combinations might I get?’ Discuss responses, and write the combinations on the whiteboard: HH; HT;TT. Ask, ‘What do you predict the results will be, if I toss the coins 30 times?’ Discuss predictions, then toss the coins 30 times, recording each result. Compare predictions with the results.
Small Group Focus — Applying the Concept Focus Teaching Group • Toss Your Own Coin Ask, ‘If you were to toss a coin, what chance do you have of it being a head?’ List students’ responses, e.g. 1-in-2, 50-50. Say, ‘What result would you expect if you tossed a coin 30 times?’ Ask each student to toss a 20c coin thirty times and record the results. Once they have finished, combine the results and discuss any trends or major differences. • How Many Letters in Your Name? Ask, ‘If we asked every student in the class, “How many letters in your first name?”, what do you think the most common response would be?’ Record each student’s response. Give the group a list of students’ first names and ask them to use tally marks to find the result. When they have finished, ask, ‘Which number of letters has the highest tally? What was the second most common number of letters?’ • Large Amounts of Data Present this data: ‘The colour of cars driving past the school were recorded for 30 minutes. The results were: White cars: 90; Red cars: 28; Blue cars: 45; Green cars: 15; Silver cars: 22. ‘Say, ‘Imagine you want to show this data on a picture graph, but you don’t have room to show 90 cars. What could you do?’ Discuss responses. Lead discussion towards the idea of having one picture represent several cars. Have the group decide on the key, e.g. one picture equals 10 cars. Say, ‘That is easy for showing the white cars, because they are multiples of 10, but how will you show the other cars?’ Record suggestions, e.g. using half a picture to represent 5 cars, then have students record their graph on chart paper.
Independent Maths Individual, pair, small group
Happy Birthday Have groups survey the class with the question, ‘When is your birthday?’ Have them record the results with tally marks. Each group will then need to decide which type of graph they will use to display the information, then construct it. Bar (column) graphs can be constructed using BLM 65 ‘My Graph’. Some students may like to graph their results using graphing software, Kid Pix Studio Deluxe or Excel. Make Your Own Ask students to plan and construct a simple class survey using BLM 7 ‘Blank Survey Form’. The survey question must have more than a ‘yes/no’ response. After completing the survey, students tally the results and make statements that show their understanding and interpretation of the collected data.
34
Nelson Maths Teacher’s Resource — Book 5
Your Own Venn Diagram Give each group an A3 copy of BLM 66 ‘Venn Diagrams’ and ask them to construct a question that will give the class five options for answering: (a), (b), (c), (a & b) or (b & c), e.g. ‘Who likes plain milk? (a) Who likes chocolate milk? (b) Who likes strawberry milk?’ (c) Two Venn diagrams are provided on BLM 66; select the Check each group’s question to make sure it contains the full range of diagram that suits the group’s responses, then have students indicate responses by marking an ✗ in ability level. the appropriate area of the Venn diagram. Tennis Anyone? (Student Book p. 12) Make sure students understand how a three-option Venn diagram operates, then have them complete the questions. Students then create a Venn diagram about a sport of their choice. This could be completed on the computer using Word, Kid Pix Studio Deluxe or Inspiration 6. Favourite Flavours (Student Book p. 13) Students read and interpret the data on the graph, then complete the questions. Coin Toss Give each pair of students two 20c coins and the two-circle Venn diagram from BLM 66. Have them label the Venn diagram to show the three possible outcomes: HH, HT,TT. Students then toss the coins 20 times and record the results with an ✗ in the appropriate section of the diagram, using the same colour pen each time. Then have them repeat the activity, marking the results with a different colour pen and creating a key to distinguish between first and second attempts. Unit 4 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 14).
Whole Class Share Time Have students present their graphs. Compare how different students showed the same information Today I created …
Ask, ‘What was the hardest part about constructing your own survey question?’ Ask several groups to share their thoughts on this question, then have them share the information they gained from their surveys. Have members of the group show their Venn diagrams. Ask, ‘Were you able to show all the responses on the Venn diagram?’ Discuss the strong and weak aspects of recording data on a Venn diagram. Ask, ‘What are the negative aspects of surveys that have only a set number of responses? Was the graph easy to interpret?’ Select a pair of students to demonstrate the activity. Ask, ‘Did you get the same results each time? Why do you think they varied?’
Unit 4 Data Collection
35
unit
Patterns and Relationships
5 Number and patterns
Student Book pp. 15–16
During this week look for students who can: • use rules involving addition, subtraction and multiplication to describe and continue a given number sequence • complete simple statements of equality involving addition, subtraction and multiplication.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources stopwatches, calculators, dice, Word Maths Talk Model the following vocabulary in discussion throughout the week: gap, patterns, sequence, bridge, code, balance, count on, test, predict
Whole Class Focus — Introducing the Concept Count That Pattern Write this number pattern on the whiteboard: 1, 4, 7, 10. Ask, ‘What is the gap (or bridge) in this skip-counting pattern?’ Point out the gap of three between each number, then ask, ‘What are the next three numbers in this pattern?’ Have a volunteer write on the whiteboard the next three numbers in the sequence. Pose the question, ‘What is the 20th number in this pattern?’ Discuss strategies for answering this question, e.g. some students may suggest using the 3 × table, i.e. 1× 3 = 3 + 1 (4), 2 × 3 = 6 + 1 (7), 3 × 3 = 9 + 1 (10). Secret Codes in Numbers Write these numbers on the whiteboard: 1, 3, 8, 10, 15. Ask, ‘Can you see the pattern in this number sequence?’ Take suggestions from the class; revise the method of creating a gap (or bridge) between each number to identify the pattern. After uncovering the code (+ 2, + 5), create a code that uses subtraction and addition e.g. + 5, – 1, which starts the sequence 1, 6, 5, 10, 9. Big Dice Roll Select a student to roll a large dice. Record the number rolled, e.g. 5. Ask five students to record an equation each where 5 is the total.Tell students there is a rule, however; if an odd number is rolled, they must record subtraction equations and if an even number is rolled they must record addition and/or multiplication equations. Repeat a number of times.
36
Nelson Maths Teacher’s Resource — Book 5
How Far Ahead? Record the first 15 numbers when counting by 2s, then counting by 3s. Work with each pair to record the gap between the highest number reached by each sequence (30, 45). Then repeat the task, counting by 5s. Again, note the gap that occurs between highest numbers (30, 45, 75) and ask students to identify any patterns they see occurring, e.g. ‘The further the pattern, the bigger the gap.’ Unlucky For Some Write the number 13 on the whiteboard. Draw thirteen large clouds around it. Ask, ‘What addition equations can you think of that equal 13?’ Write students’ suggestions in the clouds in blue, then ask for thirteen subtraction equations and record them in the clouds in red. If time allows, explore multiplication and division for 20 in the same way, using 6 clouds.
Small Group Focus — Applying the Concept Focus Teaching Group • A Calculator Can Tell You! Calculators are great counting-sequence extenders. Have each student enter into their calculator: 1 + 3 =. Ask, ‘What answer is on your screen?’ Then, without clearing the screen, have students press = = = =. Ask, ‘What happened on the display screen? What is the calculator doing?’ Invite students to explain what the calculator is doing. Repeat, using a more traditional pattern, e.g. 5 + 5 = = = =. Have students work independently to answer questions such as, ‘What is the 20th number in the pattern that begins: 3 + 5 = ? What is the 25th number in the pattern 2 + 4 = ?’
16
16
• 4 × ❐ is 16 Draw a pan balance on the whiteboard.Write 16 in the left pan; draw these signs in the right pan: +, –, ×. Ask students for addition equations +–× that equal 16, e.g 11 + 5. Select one addition equation and write it on the right pan. Repeat these steps for subtraction and multiplication equations (to obtain responses such as 20 – 4, 4 × 4). Encourage suggestions, then take 11+5 a multiplication equation and replace the number 16 with it.This will result in something like 4 × 4 = 11 + 5. Emphasise the importance of both pans balancing for the pan balance to work. Cross out 11 + 5 and write 20 – 4. 4×4 11+5 Cross out the 4 × 4 and write 16 above it. Do the same with 20 – 4; now 16 = 16. Repeat, using 24 or 30. • Processes in the Right Order Note: Only introduce this activity if students show a readiness to learn the order of operations. Write these equations on the whiteboard: 6 + 4 × 5 and (6 + 4) × 5. Ask, ‘How are these equations different?’ Introduce BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction). Discuss the first equation: multiplication must be completed before addition. In the second equation, the brackets come before any addition or multiplication task. Point out that although both equations have the same numbers and signs, they each have different answers: 26 and 50, respectively. Have students work independently in pairs to select three other numbers and see if they can obtain different answers through the use of brackets or the placement of + or × signs.
Independent Maths Individual, pair, small group
Patterns Using Dice In pairs, have students throw two dice. The first dice is the starting number, e.g. 4 and the second dice is the skip-counting number, e.g. 5. Have pairs record ten numbers in the counting sequence, Unit 5 Patterns and Relationships
37
e.g. 4, 9, 14, 19, etc. Ask students to use any known strategies to guess the twentieth number in the sequence, then continue the next ten numbers to check their guess. Students can repeat the activity a number of times. Secret Agents Ready Have students work in small groups to prepare a two-step number sequence (e.g. + 6, –3), then declare the first five numbers in that pattern. All members of the group must check the pattern to make sure it is correct.Then groups swap their sequences and one group times the other with a stopwatch to find how long it takes their ‘opposing agents’ to break the code and provide the next five numbers in the sequence ‘in order to save the world’. Groups then swap roles. See how many patterns each team can solve in two minutes. Give Me Six Have students work in pairs with a dice and a piece of paper. Students take turns to roll the dice, then both players create the matching number of equations, e.g. if you roll 6, you have to create six equations where the answer is 6. If an odd number is rolled, they must be subtraction equations; if an even number is rolled, addition and/or multiplication equations. Point out that combinations such as 4 + 2 = 6 and 2 + 4 = 6 both count, as the order the numbers are added in doesn’t change the answer. The first player to complete the task wins the round. Number Patterns (Student Book p. 15) Before commencing the activity, make sure students understand what a two-step number pattern involves, e.g. + 5, – 1: the number increases by 5, then decreases by 1. Balance the Scales (Student Book p. 16) Have students complete the balance scale activities. Make sure they see the importance of the equations balancing.They can make up more balancing equations for friends to solve. These could be done on the computer in Word in this simple format: 14 + 7 = 3 × ___; 4 + 6 = ___ × ___ ; 5 + ____ = ___ - ___. Unit 5 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 17).
Whole Class Share Time Select pairs to share their findings. Ask, ‘What strategies did you use to find the twentieth number?’ Some patterns will be easier to identify than others. Ask each group, ‘What was the easiest pattern you were given? Why was it easy?’ Repeat the question, seeking the hardest pattern they had to crack. Today I discovered …
Ask one pair to demonstrate how the game operates. Ask all players, ‘What strategies come into your mind when the number is rolled? Which equations were easiest to record?’ Ask, ‘Were some patterns easier to complete than others?’ Take suggestions from the group, then pose this question: ‘If someone was going to make an error completing this page, where would it occur and why?’ Ask, ‘What strategies did you use when you tackled these balancing pan equations?’ Select responses, then have students share their results for the last two problems.
38
Nelson Maths Teacher’s Resource — Book 5
unit
6 Space
Lines in Our World Student Book pp. 18–19
BLMs 8 & 9
During this week look for students who can: • recognise and describe the characteristics of lines in the environment • create pictorial representations of lines (straight, curved, diagonal, horizontal, vertical, parallel, perpendicular) • describe right, obtuse (blunt), acute (sharp) and straight angles When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources newspapers, magazines, street directories, kinder scissors, digital camera, maths dictionaries, 2 cm ‘slices’ of coloured cover paper, rulers, paste, plain cover paper, games of Checkers, BLM 8 ‘Letters of the Alphabet’, PowerPoint, Word, BLM 9 ‘Line Descriptors’ Maths Talk Model the following vocabulary in discussion throughout the week: geometric, straight, vertical, horizontal, curved, parallel, diagonal, lines, angles, perpendicular, environment, shapes
Whole Class Focus — Introducing the Concept Vertical, Horizontal, Diagonal Establish the class’s existing knowledge on vertical, horizontal and diagonal lines. Record accurate and meaningful definitions. Have students check the definitions of these terms in maths dictionaries. Ask, ‘Where in our environment would we find examples of these lines?’ Record examples, then ask each student to tag two vertical, two horizontal and two diagonal items in the classroom, using post-it notes labelled ‘V’, ‘H’ and ‘D’. Perpendicular: Where Are You? Draw on the whiteboard a flagpole on level ground and a large capital T. Ask, ‘What do these items have in common?’ Record responses next to each object. Introduce the term ‘perpendicular’ and ask for a definition from a maths dictionary. Emphasise the relationship of perpendicular lines to both horizontal and vertical lines, and how they are always right angles. Brainstorm examples of perpendicular lines. Diagonal Lines Ask students to name examples of diagonal lines in the school environment. Have students trace their scissors onto a sheet of paper. Scissors are a great example of diagonal lines that intersect. Emphasise that when diagonal lines meet a vertical or a horizontal line, they make an angle other than a right angle. Have students open their Unit 6 Lines in Our World
39
Use kinder scissors for safety reasons.
scissors to less than a right angle, and trace and label this angle. Repeat, having students open their scissors wider than a right angle, then tracing and labelling it. Keep this introduction to acute (sharp) and obtuse (blunt) angles informal. Now All the Lines Use coloured paper strips to create a code for each type of line, e.g. red = horizontal, green = vertical, etc; include curved, parallel, perpendicular and curved lines as well. Distribute the strips and have students draw everyday examples of that specific line.The strips could be pasted onto card or paper. Extra elements, such as horizontal greenery in trees, can be added with pencils or textas. What Are Right Angles? Revise the concept of right angles; make reference to the meeting of a vertical and horizontal line to create a right angle. Provide post-it notes and have students identify and label classroom features that have right angles. Ask, ‘Can you have parallel lines that are at right angles to each other? Why not?’
Small Group Focus — Applying the Concept Focus Teaching Group • Draw with These Lines! (Student Book p. 18) Revise all the lines covered in this unit: vertical, horizontal, curved, parallel, diagonal and perpendicular lines. Preview Student Book p. 18, and place examples of the required lines, in no particular order, on the whiteboard.This will provide a ready line reference for students.
Right angles
• The Alphabet Give each student a copy of BLM 8 ‘Letters of the Alphabet’. Write ‘vertical’ and ‘horizontal’ on the whiteboard. Ask, ‘Which letters of the alphabet are vertical lines, horizontal lines, or a combination of both?’ Identify the six letters and highlight them on the BLM: E, F, H, I, L, T. Point out the letter ‘T’. Ask, ‘What other way could we describe T?’ Discuss responses, then draw out that ‘T’ has two right angles. Examine the right angles on E, F, H and L. As an independent activity, have students draw a picture using only horizontal and vertical lines. This could be done on the computer using Word and the Draw function. • Lines Make Angles Establish that the group has an understanding of right angles and that right angles can be found where horizontal and vertical lines meet. Ask, ‘Do all lines meet at a right angle?’ Brainstorm answers where lines don’t make right angles. Discuss the concept of angles being just rotations of lines. Draw up a chart with three columns; label the columns Less than right angles; Right angles; and Greater than right angles. Include a diagram of each angle. Have students draw these angles on the computer in Word in the Draw function, adding relevant labels.
Independent Maths Individual, pair, small group
Three-letter Words Have students work in small groups with BLM 8 ‘Letters of the Alphabet’. Students cut out the letters and take turns to create a threeletter word.They then give ‘line’ clues to the group, so that they can pick the right letter and guess the word, e.g. for the word FIT: ‘The first letter has one vertical line and two horizontal lines; the second letter has 1 vertical line; the third letter has a horizontal and vertical line.’ Magazine Search Have students work in pairs. Provide partners with BLM 9 ‘Line Descriptors’ and a selection of magazines. Ask pairs to find examples of pictures that feature vertical, horizontal, diagonal, parallel,
40
Nelson Maths Teacher’s Resource — Book 5
curved and perpendicular lines.They should use the line descriptors to label the pictures and present their work as a collage. Checkers Have students work in pairs to play ‘Checkers’, a game where all movements are in diagonal lines. The checkerboard could also be investigated as a source of vertical, horizontal and parallel lines. Playground Digital Photos Have students work in small groups to take photos of vertical, horizontal, curved and diagonal lines that exist in a playground. Upon their return, have the group prepare a PowerPoint presentation with the digital photos. Name the production, ‘Lines in our Playground’. This activity can also be undertaken with students drawing and labelling lines from the playground and presenting their work on a poster. A House of Lines (Student Book p. 19) Provide coloured pencils, erasers and rulers and ask students to create a house and yard by combining vertical, horizontal, perpendicular, curved and diagonal lines. Suggest that they complete the drawing in lead pencil before adding colour. Unit 6 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 20).
Whole Class Share Time Discuss some of the words the group created and the clues they gave. Ask, ‘Which letters of the alphabet were the hardest to find clues for?’
Today I investigated …
Have the groups present their line collages to the class. Discuss how the groups planned their collages. Ask, ‘Which lines were the easiest to find in magazines? Why do you think that is?’ Choose one group to explain the rules of ‘Checkers’ and how they connect with this topic. Pose the question, ‘How would this game work if you were allowed to move horizontally or vertically?’ Set aside time for the PowerPoint presentations of lines in the playground. Ask, ‘What were the easiest lines to identify and photograph?’ Have other members of the group suggest where the lines were found. Have groups display their ‘house’. Ask individual group members, ‘What have you learnt from this activity?’
Unit 6 Lines in Our World
41
unit
Addition and Subtraction
7
Student Book pp. 21–22
Number and patterns
During this week look for students who can: • explore and manipulate materials to assist an understanding of place value, subtraction and addition • solve addition and subtraction equations with different methods of calculation • solve addition and subtraction problems using everyday examples of 3- and 4-digit numbers. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources dice, flash cards, Australia Post postcode book, Yellow Pages A–K phonebook, list of students’ heights, cassette recorder, scrap paper, http://www.prongo.com/math/addition.html, stopwatch, http://www.auspost.com.au/postcodes/ Maths Talk Model the following vocabulary in discussion throughout the week: thousands, hundreds, tens, ones, renaming, trading, carrying, regrouping, digits, postcodes
Whole Class Focus — Introducing the Concept Pick a Number Give pairs of students three white flash cards each. Have them write their name on one side of a card and a number between 100–999 on the other side. Have them then total their two numbers together and write it on the third card. Students can then make subtraction and addition equations using their three cards and +, – and = cards, e.g. ‘400 + Harry = 786; 786 – Mira = 386’. Pairs team up with another pair and attempt to solve each other’s equations. How High Are We? Before the activity, measure students’ heights in centimetres and record them on a whole class sheet. Provide each student with a copy. Have students work in pairs to combine their heights to make a ‘double student’, e.g. Liam + Sian = 198 cm. Pairs should then find other pairs that equal (or are close to) their combined height. At a later stage, this total length could be drawn on the school oval with a trundle wheel.
42
Make Your Heights Provide groups of five with MAB blocks and the class list of students’ heights. Have the students add their five heights together. Provide masking tape and have each group mark a line on the floor, showing their combined heights in centimetres. Compare the lines. Together, add each group’s combined height to find the height of the combined class.
Nelson Maths Teacher’s Resource — Book 5
Two Numbers, Three Dice Model rolling three dice and recording the largest and smallest numbers that can be made from those digits. Use the digits to create two equations: ‘largest number – smallest number’ and ‘smallest number + largest number’. Invite students to suggest totals; they can check these with calculators. Students can then do the same activity in pairs or small groups.
3872 3872 + 4350 = 8222 4350 4350 – 3872 = 478
Home and Away Have a postcode book or website available. Ask students to record their home postcode on a card, then compare numbers with other members of the class. Have them look up the postcode of a place they have visited or had a holiday at, and record that number on the other side of the card. Students then use the two postcodes to create a subtraction and an addition equation. They can swap cards and check each other’s equations using a calculator.
Small Group Focus — Applying the Concept Focus Teaching Group • Addition with Double Carrying Write these two equations on the whiteboard:134 + 149, 189 + 237. Ask two students how they would solve each equation. Ask the group, ‘Apart from the digits, what is different about these two equations?’ Discuss the concept of ‘double carrying’; explain how the complexity of a simple addition equation changes when two columns (tens, hundreds) change as a result of carrying or renaming numbers. Have students suggest other similar equations where single and double carrying occurs. Have students complete similar problems, with MAB blocks as support if needed. • Addition with Missing Numbers Write on the whiteboard: 135 + ___ = 500. Ask, ‘How do we find out what the missing number is?’ Have students explain their methods, then highlight counting on and subtraction and reversing. Counting on involves counting on from 135 to reach 500. Subtraction and reversing turns an addition equation into a subtraction equation: 500 – 135 = 365. Ask, ‘Which method do you prefer? Which method do you use to work out equations?’ Place two more equations on the whiteboard: 350 + ___ = 600; 219 + ___ = 340. Again, ask students how they would approach and solve these equations. Have students write five 3-digit equations (e.g. 225 + ___ = 580) and then swap with a partner and solve each other’s work. • Subtraction with Zeroes Subtracting with zeroes is a difficult concept for many students.Write on the whiteboard: 600 – 281. Ask several students to explain how they would solve the equation. As they do this, tape their explanations without offering any assistance; play the explanations back on completion to identify the steps taken. Using renaming (or trading) the 600 actually becomes 500 + 90 + 10. Have a student use MAB blocks to show different ways the 600 could be renamed. Create other equations that use 400, 900 and 700 to show renaming of hundreds. Have students solve subtraction equations that include zeros. Encourage them to model their equations with MAB blocks.
Independent Maths Individual, pair, small group
Car Park Number Plates Have students work in small groups to record the number plate numbers of each car in the school car park. On returning to the classroom, have students pair up and make subtraction and addition equations with two or more of their numbers.
Unit 7 Addition and Subtraction
43
Phone Book Flick Have students work in small groups. Provide the A-K section of the Yellow Pages. Ask students to look up 10 occupations, then use the occupations and page numbers to create subtraction and addition equations, e.g. dressmakers (p. 921), bricklayers (p. 381), furriers (p. 1302): furriers – dressmakers = bricklayers. Batter Up Baseball Have students work in small groups to access the prongo website (see ‘Resources’) and locate ‘Batter Up Baseball’. By selecting ‘addition activities’ and ‘doubles’, the groups are to play the game by completing 2- and 3-digit equations. Teams take turns in working and selecting answers. Provide scrap paper and pencils for each group. Pitching Equations Students not working on the computer can work in threes. Provide 2- and 3-digit addition equations, a baseball diamond drawn on a large sheet of paper and a stopwatch. One player ‘pitches’ the equation, one ‘bats’ the answer, and the third times with a stopwatch. The ‘batter’ advances one base for each correct answer, attempting to reach the homebase in 20 seconds. Players then swap roles. Snake Subtraction and Adders! (Student Book p. 21) complete the addition and subtraction equations.
Have students
Postcode Equations (Student Book p. 22) Have students use the postcodes for common Australian place names to complete and create number equations.
Whole Class Share Time Have students share their findings. Ask, ‘Did you find anything unusual about the number plates you recorded?’ Today I did not understand …
Have several students read their word problems to the class, and have another explain the equations. Ask members of the group, ‘How could you play this activity where you offer multiple options for an answer?’ Ask players in each team, ‘What was interesting about the numbers offered as the solutions to each task?’ (They all look like the answer, or are very close.) Select a player from one team to explain the rules. Ask, ‘Which equations did you prefer to solve: addition or subtraction?’Tally the votes; ask several students to justify their answers. Select students to explain their approach to solving the postcode activities. Ask, ‘What did you notice about different states’ postcodes?’
44
Nelson Maths Teacher’s Resource — Book 5
unit
8 Number and patterns
Multiplication and Division Student Book pp. 23–24
BLM 10
During this week look for students who can: • solve and record multiplication word problems and equations where whole numbers are multiplied by single numbers or multiples of ten • solve and record division word problems and equations using 3-digit numbers and a single divisor. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources white flash cards; Yellow Pages phonebooks; Blu-tack blindfold; Unifix; cards labelled ‘quotient’, ‘divisor’ and ‘dividend’; BLM 10 ‘Multiplication and Division Roll’ Maths Talk Model the following vocabulary in discussion throughout the week: division, dividend, divisor, quotient, share, multiply, how many, word problems, evenly
Whole Class Focus — Introducing the Concept The Great Easter Egg Division Present this problem: ‘Imagine you have to share 27 Easter eggs among 5 children. How would you do it?’ Discuss responses, then substitute Unifix for eggs and have several students act out the dividing. Highlight students’ methods without applying any formal names. There will be two eggs ‘left over’; ask, ‘When we do this activity as an equation on the whiteboard, how do we acknowledge the two eggs left over?’ (They remain as whole eggs left over, and are not divided up.) Back and Forward Write on the whiteboard: 32 ÷ 4. Discuss the written and mental computation strategies needed to solve the division. Ask, ‘How could you use multiplication to solve this division equation?’ (8 × 4 = 32.) Emphasise the relationship between the two equations, then ask, ‘How do we solve 320 ÷ 4 = _____?’ Make the connection between 32 and 320, and point out how the zero does not change the approach to the task. Multiplication Sentences Review the phrasing used in multiplication sentences. Ask, ‘What are some words you always find in multiplication sentences?’ Record suggestions, e.g. how many, altogether, each. Write on the whiteboard: 5, 48. Ask students to make up a multiplication word problem using these numbers, e.g. ‘There are 5 paddocks. There are 48 Unit 8 Multiplication and Division
45
sheep in each paddock. How many sheep altogether?’ Have students write another word problem about 5 and 48, this time with a birthday party theme. Ask students to read out their problems. Blindfold Grab Provide a blindfold and a tub of Unifix. Blindfold a student and ask them to gather as many Unifix as they can in one grab, using both hands.They then remove the blindfold and record the total. Say, ‘How could we show that grab as an equation?’ Discuss suggestions, then record: 12 blocks × 1 grab = 12 blocks. Ask, ‘If we were to grab the same number each time, what would be the equation for 3, 5 and 10 grabs?’ Repeat, with different students wearing the blindfold. Act it Out Ask 10 students to walk around in a circle, without stopping or looking at the other students. Then say, ‘Make groups of five!’ See how quickly they can do it; ask the seated students, ‘What equation was created?’ Record the equation on the whiteboard. Have the students circle again, say, ‘Make groups of two!’ Record the equation and answer. Repeat, saying, ‘Make groups of three!’ Note the groups formed; ask, ‘How are we going to write the equation with one left over?’ (10 ÷ 3 = 3 with 1 remainder.)
Small Group Focus — Applying the Concept Focus Teaching Group • Multiplication and Division Facts Ask students to volunteer five division or multiplication equations they know the answers for. Record them on the whiteboard, using different colours for division and multiplication equations. Check that the answers are correct, then select a division equation and ask, ‘What multiplication equation is directly related to (for example) 27 ÷ 3 = 9?’ Pick out a division equation and repeat the process. Provide five division and five multiplication equations and answers; ask students to supply the corresponding multiplication or division equation. • Divide by Definition Have ready cards labelled ‘quotient’, ‘divisor’ and ‘dividend’ written on them. Have students check a dictionary to find definitions for each word. Discuss the definitions and record them on the whiteboard. Write on the whiteboard: 20 ÷ 5 = 4. Have students Blu-tack the appropriate word card next to each part of the equation. Repeat, using other equations. Have students write the definitions in their maths dictionaries. Students can then work independently to write five division word problems using the language of division. • Let’s Multiply and Divide Present the group with two equations: 11 × 5 and 55 ÷ 5. Before any calculations take place, ask, ‘Which equation will have the largest number? Why?’ Discuss responses, then have students solve the problems. Discuss the strategies used. Ask, ‘Which equations do you prefer solving?’ Discuss the relationship between the two equations. Ask students to suggest other equations where three numbers are closely linked, e.g. 40, 5, 8; 36, 9, 4. Ask students to find five other sets of three numbers that work for multiplication and division.
Independent Maths Individual, pair, small group
46
Yellow Pages Division Task Have students work in small groups using the Yellow Pages. Students flick back from p. 1 000, stop at random and see if they can evenly divide the number stopped at by the number of students in their group, e.g. 734 ÷ 3. Have each group record ten equations; they can then swap and check each other’s equations.
Nelson Maths Teacher’s Resource — Book 5
Multiplication and Division Roll Give each pair of students three dice and a copy of BLM 10 ‘Multiplication and Division Roll’. Students roll the three dice, one at a time.The first two dice give the number to be multiplied; the third dice gives the multiplicand (see example in margin). Students then write the multiplication equation, and use the same numbers in the same order to make a division equation: 26 ÷ 5. Some dice combinations will give remainders; refer to these as numbers ‘left over’. Airport Word Problems Have students work in small teams to create three division and three multiplication equations on an airport theme, e.g. ‘48 passengers queued in 4 lines; how many in each line?’ Students can swap their equations with another team; teams can check each other’s answers. Divide and Conquer (Student Book p. 23) Ask students to solve the division equations, which are presented in two formats. They can then write three equations of their own for a friend to solve. Multiplication Mystery (Student Book p. 24) Students should work out the multiplication equations, then solve the puzzle. They can then create their own multiplication mystery. Dice Roll Have students work in pairs to roll four dice.They take turns to use three of the rolled digits to make the smallest number possible, keeping the fourth number as the divisor. The player records and solves the equation. Their partner checks their answer with a calculator; they then swap roles. Units 7–8 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 25).
Whole Class Share Time Have students explain what they had to do with the Yellow Pages. Ask, ‘What did you learn from this activity?’ Ask students to share their equations they created. Ask, ‘How does knowing the answer to a multiplication equation help you with a division equation with the same numbers?’ Today I worked out …
Ask students to read examples of the word problems they created. Ask each group to select another group’s word problem that they found challenging and interesting. Discuss the two ways of writing a division equation. Ask, ‘Which setting out do you prefer when dealing with division equations?’ Have students share some of the equations they created. Have students explain the task. Ask, ‘How does knowing your tables help you with this task?’ Invite students to share the mysteries they created. Have students share their equations and describe how they recorded them.
Unit 8 Multiplication and Division
47
unit
9 Measurement
Measuring and Estimating Angles Student Book pp. 26–27
BLM 67
During this week look for students who can: • identify, name and create angles [obtuse (blunt), acute (sharp), right and straight] • order angles from smallest to largest. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources compasses, craft sticks, white flash cards, glue, magazines, junk mail, clock with moveable hands, flash cards showing 15 angles that are less than 90°, chalk, Word, BLM 67 ‘Centimetre Grid’ Maths Talk Model the following vocabulary in discussion throughout the week: compass rose, cardinal points (north, south, east, west), right, left, forward, straight, acute (sharp), obtuse (blunt), degree, right angle, corner, square, full turn, half turn, quarter turn, three-quarter turn
Whole Class Focus — Introducing the Concept North, South, East and West Create a compass rose on the whiteboard and label the cardinal points. If you have a set of class compasses, pass them around. Have the class find north and turn to face that direction. Review the directions of west and east when facing north. Say, ‘Now turn to face east.’ 1 When completed, explain to the class that they have made a 4 turn: a ‘right 1 angle’. Ask, ‘If turning east from north is a 4 turn, what sort of turn is turning south from north?’ Have students make the turn, then discuss the 1 term ‘ 2 turn’. Repeat, having students turn right, from facing east to facing 3 north; discuss what has happened, emphasising ‘ 4 turn’. What is Right About This Angle? Revisit quarter and half turns. Emphasise that a quarter turn is also called a ‘right angle’. Have each student in the class fold a flash card in half and, after checking their angles, have them find a part of the room where their right-angle fits. Craft Stick Angles Provide craft sticks. Model a right angle, an obtuse (blunt) angle and an acute (sharp) angle. Give each student six sticks and ask them to make the three angles by gluing the ends of two sticks together; on completion, ask students to order their angles from smallest to largest angle. Have students form small groups to compare their angles, then repeat the ordering task.
48
Nelson Maths Teacher’s Resource — Book 5
Angles in the Real World Provide magazines and junk mail. Ask students to find and cut out pictures or advertisements that feature right, obtuse (blunt), acute (sharp) and straight angles. Label four charts: Right angles, Acute angles (or Sharp angles), Obtuse angles (or Blunt angles), Straight angles. Have several students check that the angle pictures are being glued on the correct chart. Display the completed charts; encourage students to add to them during the unit. Alternatively, you could use a large clock with moveable hands to revisit the angles. Angles in the Sun On a sunny day, take students outside to a hard surface. Have them use their arms to create straight, right, obtuse and acute (sharp) angles. They can then work with a partner, using chalk to trace and label the angles they have created.
Small Group Focus — Applying the Concept Focus Teaching Group • Place These in Order Prior to the session, prepare flash cards showing 15 angles that are less than 90°. Distribute four angle cards; ask the students with the cards to order themselves from largest to smallest angles. Repeat, using different cards. Increase the number of cards as students become more confident with comparing and ordering. Students can then draw their own set of angle cards, include angles less than 90°, and swap with a partner; have students order each other’s cards from smallest to largest angle. • Ordering Angles Provide craft sticks and ask students to create an acute (or sharp) angle. Some angles will be very different and some will be the same. Ask, ‘How can we tell which sticks have the largest (or smallest) angle?’ Discuss suggestions, then have students measure and compare angle sizes through direct comparison, and by tracing the angles onto paper. Have students continue to make acute (sharp) angles independently. • Angles: It’s All in the Name Write on the whiteboard: right angle, acute (or sharp) angle, obtuse (or blunt) angle and straight angle. Use maths dictionaries and students’ experiences to write a definition of each angle. Check students’ understanding of each angle, then allocate an angle to each student and ask them to draw ‘their’ angle. After every student has completed the four angles, ask, ‘What have you discovered about angles?’
Independent Maths Individual, pair, small group
Angles on a Compass Give students copies of BLM 67 ‘Centimetre Grid’; ask them to draw a simple path on the grid, then write six instructions so that other students can recreate their path, e.g. ‘Start at the 1 bottom of the page.Travel north for nine squares. Make a 4 turn to the right. 3 Go forward six squares. Now make a 4 turn to the left.’ Have partners sit back to back with another copy of BLM 67 each, and ask them to read their instructions for their partner to follow, marking the path with a pencil. Students can then name the angles in their paths. Computer Angle Trek The activity above can also be done on the computer. Have two students sit side by side and make a 10 × 10 or 20 × 20 grid in Word. One student gives instructions, as the pair mark their way across their individual grids using the line function in Autoshapes. Have student list the angles created. Angles by Rotations Have students work in pair with a compass. Ask them to find as many obtuse (blunt), straight and right angles as they can by Unit 9 Measuring and Estimating Angles
49
moving from one compass point to another, e.g. ‘West to East is a straight angle.’ Students could use BLM 67 ‘Centimetre Grid’ to plot the angles and help visualise the cardinal points, by adding North, South, East and West and a central point to the grid. Digital Angles Have students work in small groups, taking digital photographs of angles around the school. Buildings, play equipment and landscaping provide a vast source of angles. Have each student take two photographs. Picture Angles On chart paper (or BLM 67), have pairs of students create a design that contains at least one of each of these angles: right, straight, acute (sharp) and obtuse (blunt). Have students label each angle used. Geometric blocks could be used for students to trace over or copy when making their designs. Timely Angles (Student Book p. 26) Revise straight, right, obtuse (blunt) and acute (sharp) angles, then have students complete the activities. Clock Angles (Student Book p. 27) Have students complete the task, drawing hands on each clock and recording the angle created. Unit 9 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 28).
Whole Class Share Time Select two students to demonstrate giving instructions and drawing a path. Have the class compare the path with the original.
Today I learnt …
Select groups to demonstrate a collection of the angles they created with compass points. Ask, ‘Why can’t we show an acute (sharp) angle with cardinal compass points?’ Have students display their photographs on a computer. Have them quiz the class, pointing to a specific angle in a photo and asking, ‘What kind of angle is this?’ Display the students’ photographs, with labels. Ask students to reclassify the times as angles; have them compare their responses with a partner. Ask, ‘Which times caused the most confusion?’ Have students share the angles they drew. Have students show examples of each of the four angles by showing times to the class. Ask, ‘What angle is created when the clock shows home time?’
50
Nelson Maths Teacher’s Resource — Book 5
unit
Analogue and Digital Times
10
Student Book pp. 29–30
Measurement
BLMs 11, 12 & 13
During this week look for students who can: • read and record digital time in hours and minutes • read and record analogue time to 5-minute intervals. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources stopwatches, split pins, sheets of butchers’ paper, large analogue clock, classroom analogue clock with moveable hands, lamination sheets, digital clock, BLM 11 ‘Analogue Clock’, BLM 12 ‘Clocks’, BLM 13 ‘Digital Clocks’ Maths Talk Model the following vocabulary in discussion throughout the week: analogue, digital, clock face, hands, positions, hours, minutes, to, after, half past, quarter past, quarter to, time, timetable, electronic, super eight numbers
Whole Class Focus — Introducing the Concept
analogue
digital
Venn Diagram Draw a two-circle Venn diagram on a large sheet of paper. Make sure the overlap is large. Label the circles ‘analogue’ and ‘digital’. Start with analogue time. Ask, ‘What do you know about analogue time?’ Record responses in the circle. Repeat for digital time, using a different coloured pen. Record elements common to both in the overlap area. Display the chart, and have students add to it as the unit progresses. Clock Face Recall Draw a circle on the whiteboard. Say, ‘Imagine this is a clock face. What is missing?’ Add students’ suggestions, e.g. numbers, hands. Highlight the single minute indicators that occur between each fiveminute interval. Ask, ‘What is the connection between five and twelve?’ (5 × 12 = 60; 12 five-minute intervals = 60 minutes.) 60 seconds and 60 minutes Review the basic elements of time: 60 seconds in a minute; 60 minutes in an hour. Refresh students’ understanding of intervals, such as a second, 10 seconds and one minute. Start a stopwatch and ask students to put their hand up when they think 10 seconds has passed. Repeat, using intervals such as one minute, 20 seconds, one second, 30 seconds. Compare times on an analogue clock and a digital clock. Take particular note of the ‘super 8’ structure on a digital clock and what lines are highlighted at certain times. Quarter to and Quarter Past Display a large analogue clock. Ask, ‘Which numbers on an analogue clock help you to read ‘quarter past’ and ‘quarter to’?’ Highlight those numbers. Ask, ‘Will 3 and 9 help you find quarter to and Unit 10 Analogue and Digital Times
51
quarter past on a digital clock?’ Discuss the difference. Ask, ‘What numbers do we need to look for on a digital clock if we want to refer to quarter to and quarter past?’ Discuss responses, and record any links between digital and analogue times, e.g. 15 on a digital clock and quarter past on analogue; 30 and half-past; 45 and quarter to.
5:15
Give Me Five Minutes Use an analogue clock with moveable hands as a prompt. Show a series of times using five-minute intervals, and ask students to record them as digital times. Begin with 1:15, 1:45 and 1:30, then use the 5-minute intervals in between.
Small Group Focus — Applying the Concept Focus Teaching Group • Where Are the Hands? Give each student BLM 11 ‘Analogue Clock’ and a split pin, and have them construct their own analogue clock. Revise the hand position for on-the-hour times. Say, ‘Show me where the hand is when it shows half the hour.’ Ask students to justify where they have placed the hour hand. Repeat, focusing on quarter past and quarter to. Ask, ‘How can you tell the minutes past if you can only see the hour hand?’ • Past and To Discuss how we use past and to when describing analogue time, e.g. five past four is also 55 minutes to five, but we don’t use that way of recording. Ask, ‘When do we use the term ‘to the hour’, and when do we use ‘past the hour’?’ Also discuss how digital clocks have changed the way we refer to time, e.g. 8:40 used to be known as ‘twenty to nine’. Give students copies of BLM 12 ‘Clocks’, and have them work independently to write matching analogue and digital times. Write eight times, using 5-minute intervals, on the whiteboard, e.g 20 past 9, 25 minutes to 7, 5 minutes past 1, 10 to 8. Have students show these times on both clocks. • Super 8: Digital Time Prepare an A3 copy of BLM 13 ‘Digital Clocks’ and have it laminated. Provide a working digital clock. Discuss how the makers of digital clocks use a combination of strokes to make ‘Super 8’ digital Provide a working numbers. Select a number between 1–12, e.g. 9; ask, ‘Which strokes are digital clock for students to refer “blacked out” to make a nine?’ Repeat for 0, 2, 5, 4. Select a student to to as they work independently. The demonstrate the creation of each digit, using a non-permanent texta. students could be writing the times as they appear on the Discuss how the numerals change to show a new hour, e.g. from 9:55 to digital clock. 10:00, highlighting all the numerals used in each minute from 9:55 to 10:00. Provide each pair with a laminated copy of BLM 13 and a texta. Have them colour the ‘Super 8’ strokes to make six times that are one minute apart: 10:55, 10:56, 10:57, 10:58, 10:59, 11:00.
Independent Maths Individual, pair, small group
Clock Dominoes Give three copies of BLM 12 ‘Clocks’ to each group. Ask the group to determine 20 times, using 5-minute intervals, e.g. 9:25, 8:10, 6:45, 1:10, 10:40, etc. Students decide within the group who is writing which time, then they cut out the cards and write a different analogue and digital time on each card. Once completed, they should shuffle the cards, share them out and use them to play dominoes. One Hand Right; One Hand Wrong Have students work in small groups, each with a clock made from BLM 11 ‘Analogue Clock’. Set each group the challenge of placing one clock hand in the correct position and one in an incorrect position. Ask, ‘If the hour hand is right on 10, why can’t the minute
52
Nelson Maths Teacher’s Resource — Book 5
be on six?’ Have each group prepare 15 times for the other group, where one hand is in the wrong position. The groups then take turns to say what is wrong with each time and put it right. Make This Digital Time Give each student a laminated copy of BLM 13 ‘Digital Clocks’, black textas and a cleaning cloth. One member of the group shows an analogue time, using the clock made from BLM 11; the other members of the group show the digital version of that time by blacking out the letters on the ‘super 8’ structures. Each member of the group has a turn at being leader. Three-way Time (Student Book p. 29) Read through the instructions together; emphasise that o’clock or half-past times cannot be used as the set time. A Day in the Life of … (Student Book p. 30) Discuss what this task requires; encourage students to use pencil and an eraser, as they will probably need to alter part of their sequence. Unit 10 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 31).
Whole Class Share Time Today I discovered …
Have three students explain the basis of ‘Clock Dominoes’. Ask, ‘Were there any times that were easier to match than others? Why?’ Ask the group, ‘When a clock reads 20 past 3, what is a common mistake people often make with the minute hand?’ Ask each member of the group, ‘What is the hardest (easiest) number to create on a digital clock?’ Ask, ‘What did you learn from playing this three-way time game?’ Select one of the group to read out the order of the daily events and the correct times. Ask, ‘Is your timetable similar to this one in any way?’
Unit 10 Analogue and Digital Times
53
unit
Timetables and Schedules
11 Measurement
Student Book pp. 32–33
BLMs 14, 15 & 16
During this week look for students who can: • explore periods of time and elapsed time • explore and use everyday calendars and schedules to plan events. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources old and current calendars, fridge calendars, train timetables, weekly television programs, stopwatches, Excel, Publisher, digital camera, digital photographs, white flash cards, Kid Pix Studio Deluxe, BLM 14 ‘Blank Month’, BLM 15 ‘Time Cards’, BLM 16 ‘Blank Calendar’, http://www.vline.vic.gov.au/timetables/southwest/vline_glng.htm Maths Talk Model the following vocabulary in discussion throughout the week: estimate, guess, actual time, elapsed time, calendars, clocks, stopwatches schedule, timetable, events, ordinal numbers, centuries, decades, years, leap years, months, weeks, days, hours, minutes, seconds, measured, units
Whole Class Focus — Introducing the Concept This Year’s Calendar Using this year’s calendar, mark in important dates, such as Easter, Chinese New Year, Christmas, our seasons, term beginning and endings, public holidays. Ask, ‘If the Melbourne Cup is always on the first Tuesday in November, what date will it be this year?’ Go through the calendar together to find which month has the most Mondays, Tuesdays, etc. Estimating Short Periods of Time Have the class estimate how long 10 seconds is; start a stopwatch and have students put their hands up when they think 10 seconds has passed. Discuss strategies for counting seconds without using a watch, e.g. saying ‘one cat and dog’ or ‘one thousand’ for each second. Ask students to ‘count’ in their heads, and put their hands up when 20 seconds is up. Note down the successful students. Repeat, for 20, 30, 45 and 60 seconds. Discuss working strategies for calculating short periods of time. Symbols for the Seasons Brainstorm words to do with time. Introduce the idea of icons as simple designs to represent seasons, special days, etc; icons don’t use words, but their message is clear. Provide various icons as examples. Say, ‘If we had to create icons for summer, winter, spring and
54
Nelson Maths Teacher’s Resource — Book 5
autumn, which simple designs would we use?’ Do the same for days of the week: schooldays, weekends, school holidays, last day of term or year, Christmas Day, Boxing Day, New Year’s Eve. School Time and Holiday Time Display a calendar that has school and public holidays indicated. Together, calculate the number of days dedicated to school, and to holidays. Ask, ‘How many days are there from the end of Term 1 to the beginning of Term 2?’ Point out the public holidays. Ask, ‘How many public holidays are there, compared to school holidays and schooldays?’ Use Excel to create a pie (sector) graph together, showing the distribution over one year of school, school holidays and public holidays. Television Time Write on flash cards the names and times of popular TV shows. Select programs that have different running times, from five minutes to an hour. Ask students to sequence the cards from least time to most time.Then say, ‘Imagine you had a time limit and could only watch TV for 90 minutes a day.Which of these shows could you watch?’ If time, repeat, using 60- and 30-minute time limits.
Small Group Focus — Applying the Concept Focus Teaching Group • How Long to Do What? Write several time periods on the whiteboard, e.g. 5 seconds, 10 seconds, one minute, one hour. Ask students to identify activities that can be undertaken in that period of time. Suggestions may differ, but compile a list that shows what can be done during each time, and is agreed upon by the group. Ask, ‘How long does it take you to write your name? Does it take a day?’ Discuss responses, then ask, ‘What would be a more realistic time for that activity?’ Write on the whiteboard: 1 second, 1 minute, 1 hour, 1 day. Have students copy the headings and list at least five things that happen (or that they can do) in each time category. • Using a Train Timetable Get a timetable for the Melbourne — Geelong train from your local station, or access this website: http://www.vline.vic. gov.au/timetables/southwest/vline_glng.htm. Provide copies of the timetable for the group. The first train for the day leaves Melbourne at 5:45 am and arrives in Geelong at 6:58 am. Ask, ‘How can you work out how long it takes the train to get from Melbourne to Geelong?’ Discuss methods and strategies for ‘counting on’ to find the elapsed time. Say, ‘The 8:48 am train from Melbourne arrives in Geelong at 9:47 am. Why is that trip so much quicker?’ Discuss the concept of express trains; work out how much quicker the express train is than the regular train. Set tasks for students to complete, based on the timetable, then have them write timetable problems for others to solve. • Your Birthday On a large calendar of the year, mark the birthday of each student in the group. Identify and circle the first birthday of the year; ask, ‘How can we work out how much time there is between the first and second birthdays of the year?’ Discuss the concept of counting on in weeks and months, then calculate the time difference between the birth dates. Have students work independently to calculate the time differences, from birthday to birthday, for the whole class.
Independent Maths Individual, pair, small group
Create Your Own Calendar Have students work in pairs using Publisher or Word to create a calendar for the month of their birthday. They could even scan a photo of themselves and add it to their calendar. Have each Unit 11 Timetables and Schedules
55
student prepare 10 questions they can ask their partner, based around their birth date. Questions should include number (‘How many Thursdays in your birth month?’) and counting on and back (‘What is the date two weeks after your birthday? What is the date one week before your birthday?’). Students without computer access can record the dates of their birthday month on BLM 14 ‘Blank Month’, prior to completing the activity. nds seco Ten nds seco 0 se 30 cond s es inut O m ne m One inute Five m in ut Five minutes
30 minutes
How Long Does It Take? Have students work in small groups to compile a list of five to seven tasks that all students can complete in a short period of time, e.g. ‘How long does it take you to write the alphabet? ... do 10 star jumps? ... tie your laces?’ Have group members estimate the amount of time required for each activity, then undertake the activities using a stopwatch for timing. Icons Provide white flash cards. Ask students to create their own icons for the four seasons, and for three well-known occasions during the year.These icons could be produced on the computer using Kid Pix Studio Deluxe. Five Minutes, an Hour, a Day Have students work in small groups using enlarged copies of BLM 15 ‘Time Cards’. Ask the groups to create a matching card for each time period, using a combination of words and pictures.The completed cards can be used to play ‘Snap’ or ‘Concentration’. Using the Calendar (Student Book p. 32) Have students use BLM 16 ‘Blank Calendar’ to make their own calendar for the year. Make sure students can count on in weeks; revise the idea of ‘special days’. Each student will need their own copy of this year’s calendar to complete the Student Book page. Television Time Detective (Student Book p. 33) Read through the questions together to ensure all students understand how they are to use the TV ‘timetable’. Unit 11 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 34).
Whole Class Share Time Have the group share their calendars. Ask, ‘Is there anything distinct about the month of your birthday?’ e.g. five Mondays. Then, without talking, have them place themselves in the correct order of their birth months and dates. Ask each group, ‘Which task was the easiest to estimate the time for?’ ‘Did any activity take much longer than your estimate?’ ‘Which activity was the easiest (hardest) to complete? Why?’ Today I really liked …
Have students share their icons, and their work from BLM 15. Discuss the icons. Ask, ‘Which icons are the easiest to recognise? How can you tell which time period they represent?’ Ask the class to suggest additional icons for the easily recognised time periods. Ask, ‘What do you notice about the spread of special days over the year?’ Have students share when these days occur. Ask, ‘How do you know how long a show goes for when you read a program guide?’ Discuss how students worked out which child watched the most TV.
56
Nelson Maths Teacher’s Resource — Book 5
unit
Fractions
12 Number and patterns
Student Book pp. 35–36
BLMs 17, 18, 19, 67 & 68
During this week look for students who can: • identify, name and represent fractional parts of models, charts and collections • compare and order simple common fractions • identify unit fractional parts of discrete collections • use fractions as an operator. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources lamination sheets, Scrabble letters, Unifix, white card, coloured paper, paper strips (32 cm × 3 cm), poster paper, coloured paper shapes (circles, squares, triangles and rectangles), Kid Pix Studio Deluxe, Microworlds, BLM 17 ‘Fraction Wall’, BLM 18 ‘Build Your Own Fraction Wall’, BLM 19 ‘Woolloomooloo in Gold’, BLM 67 ‘Centimetre Grid’, BLM 68 ‘Fraction Cards’ Maths Talk Model the following vocabulary in discussion throughout the week: fraction, half, third, quarter, fifth, sixth, seventh, eighth, ninth, tenth (etc), equal, equivalent, same, less than, greater than, larger than, smaller than, whole, part, order, smallest, largest, numerator, denominator
Whole Class Focus — Introducing the Concept Smallest to Largest Provide five students with a fraction card each from 1 1 1 1 1 BLM 68 ‘Fraction Cards’, e.g. 2 , 3 , 5 , 8 , 16 . Give the students 30 seconds to order themselves from smallest to largest, without speaking. Repeat
1 __ 4
Celebrity Fraction Use cards from BLM 68 ‘Fraction Cards’. Select a 1 student to wear a headband featuring a fraction, e.g. 4 ; make sure the student cannot see the number. The student asks questions in order to 1 reduce the range of possibilities and guess the fraction, e.g. ‘Is it less than 2 ?’ 1 1 ‘Is it more than 4 ?’ ‘Is it 3 ?’The questions can only be answered ‘yes’ or ‘no’. Bigger Than Select three students. The first student names a fraction 1 between 0–1, e.g. 6 . The next student must name a fraction that is bigger 1 1 than 6 but still below 1, e.g. 5 . Players continue to take turns until forced out by giving a fraction that is smaller, or being unable to give a fraction below 1. Dominoes Have students fold flashcards in half and draw a line along the fold. Ask them to write a fraction in words on one half, and draw a different Unit 12 Fractions
57
3 4
fraction in signs on the other half. Check that each card features two different fractions, then have students shuffle them and use them to play dominoes.
3 5 1 2 1 3
Top Ten Fractions Create a class ‘Top 10 chart’, similar to a pop music chart. Give each group a collection of suitable fractions from BLM 68 ‘Fraction Cards’ and ask them to place the fractions in the ‘Top 10’, where 7 number 8 is the fraction closest to 1.
Small Group Focus — Applying the Concept Focus Teaching Group • The Value of My Name Have students use textas to write out the letters of their first names. Their name now becomes the whole, and each letter is an equal part of the whole. Have each student select a letter in their name. Ask, ‘What fraction is that letter?’ Provide ‘Scrabble’ letters for students who require hands-on materials. Students could then work independently to write and translate into fractions the names of other members of their family. • Fold and Unfold Provide coloured paper strips 32 cm long and 3 cm wide. Ask students to fold the strip in half. Then have them unfold it and leave one half untouched. Students continue to fold the other section in half, over and over. Have them unfold the strip and work in pairs to name all the fractions they have created. Discuss the equal fractions that can be seen. Ask questions such as, ‘What is the smallest fraction you could fold to? What 1 equivalent fractions did you discover as you were folding? What is 2 equal to?’ As an independent activity, have students colour and label BLM 17 ‘Fraction Wall’.
• Colourful Shapes Provide coloured paper circles, squares, triangles and rectangles. Ask individual students to prepare a selection of fraction demonstrations by folding, cutting and pasting the shapes onto white card. They should label each fraction. Provide more coloured shapes and have students work independently to create their own fraction poster.
Independent Maths Individual, pair, small group
58
Computer Fractions Have students use Kid Pix Studio Deluxe or MicroWorlds to make a sheet showing simple fractions pictorially.They can use different line weights for borders, and flood fill to make them colourful. Fraction Wall Have students work in pairs to colour and label BLM 17 ‘Fraction Wall’, then write 10 fraction statements that can be answered True 1 1 1 2 or False, e.g. ‘ 2 is more than 3 : True or False?’ ‘ 3 is the same as 6 : True or False?’ Students can question each other. Build Your Own Fraction Wall Have students follow the procedure on BLM 18 to make a fraction wall. Have them select different borders, then print out the ‘wall’ and use textas to shade it.
Nelson Maths Teacher’s Resource — Book 5
Chocolate Bar Fractions (Student Book p. 35) This activity involves colouring fractions of chocolate bars and using them to answer questions. Provide Unifix if necessary. Magic Oranges Have students work in pairs to create five ‘magic oranges’ from coloured paper. Each orange is able to produce the following number of orange drinks: 8, 12, 16, 20 and 24. Have them cut each magic orange into quarters, and paste them onto poster paper. Have them label each orange according to the number of drinks it produces: 8, 12, 16, 20, 24. 1 Have them add a statement to each orange, e.g. ‘ 4 of magic orange 8 will 1 provide 2 drinks’, ‘ 4 of magic orange 20 will provide 5 drinks’, etc. Pizza Fractions (Student Book p. 36) pizza fractions.
Have students complete the
Capital City Vowels In pairs, have students write the capital of each Australian state onto square grid paper (BLM 67), using one letter per square. Have them record the total number of vowels in each city as a fraction of the word. Woolloomooloo in Gold Give each child a copy of BLM 19 ‘Woolloomooloo in Gold’ and Scrabble letters. Ask them to find the number of letters in ‘Woolloomooloo’, the number of vowels, the fraction of the total word they represent, etc.
Whole Class Share Time Have students share their experiences of building fraction walls. Ask, ‘Which fractions are easy to make? Why?’ Promote discussion on how the computer can make the wall into accurate fractions. Ask, ‘What fractions don’t have equals or equivalents? Why?’
Today I understood …
Discuss the fractions that occur in common chocolate bars. Cut up a simple bar and discuss each collection as a fraction of the whole bar. Share students’ posters and statements. Ask, ‘What did you discover about each orange and the number of drinks it can produce?’ Have selected students share their thoughts on the size of quarters and sixths when dealing with pizzas. Ask students to share their findings on each capital city. Ask, ‘Which city has the largest fraction of vowels?’ Discuss students’ discoveries of towns with many vowels. Ask, ‘Will more vowels lead to a large increase in the value of the name?’
Unit 12 Fractions
59
unit
Decimals
13
Student Book pp. 37–38
Number and patterns
BLMs 20, 21, 22 & 69
During this week look for students who can: • • • •
read, write, compare and order decimals to two decimal places use decimals to compare familiar objects interpret decimal numbers to the first decimal place recognise that a position of a decimal point affects the size and value of a number.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources calculators, 10-sided dice, stopwatch, Centicubes, post-it notes, decimal flash cards, supermarket dockets, BLM 20 ‘Decimal Points and Numbers’, BLM 21 ‘Decimal Cards’, BLM 22 ‘Cents and Millilitres’, BLM 69 ‘Hundreds,Tens, Ones,Tenths & Hundredths Chart’ Maths Talk Model the following vocabulary in discussion throughout the week: equal, decimals, decimal point, tenths, hundredths, rounding off, rounding up, rounding down, relevant and non-relevant zeros, order, largest, smallest
Whole Class Focus — Introducing the Concept Money as Decimals Have students enter an amount (less than $10) in dollars and cents into their calculators. Record each amount on a chart and compare the decimals. Ask, ‘Which numbers are close to each other? Which numbers are equal?’ 10-sided Dice Roll Select a student to roll a 10-sided dice three times. Record the number as a decimal with two decimal places, e.g. 3.25. Continue the activity, recording the numbers rolled each time. Ask, ‘Which number is larger (smaller)?’ Repeat; this time record the highest or smallest number possible from three rolls. Non-verbal Decimals Provide five students with a decimal card. Each card should feature a different 3- or 4-digit decimal, e.g. 1.25, 2.25, 2.5, 3.75, 13.85. Ask students to order themselves, without talking, from smallest to largest. Use a stopwatch to record the time it takes them to order themselves correctly. Repeat, using different decimal cards and another group. Continue until all students have been involved in the activity. Discuss the order of the cards; have students explain how they worked out which number came first, second, etc.
60
Nelson Maths Teacher’s Resource — Book 5
Decimal Point Magic Use the cards from BLM 20 ‘Decimal Points and Numbers’ to show students how the position of the decimal point can influence the size and value of a number. Take the digits 3, 2 and 1 and a decimal point. Ask, ‘What is the biggest number we can make with these three digits?’ Continue to experiment with the position of the decimal point and record all the decimal numbers you can make. Discuss place value positions from hundreds to hundredths. Ordering Decimal Cards Have individual students order the decimal cards from BLM 21 ‘Decimal Cards’. As a class, discuss the decimals. Ask, ‘Which decimals are equal?’ (1.1 and 1.10; 11.1 and 11.10) Investigate relevant and non-relevant zeroes. Ask, ‘When we have three chocolate bars, why don’t we say we have 3.0 chocolate bars?’ Discuss situations when zeros have to be included and when they can be left out. Discuss the difference between .05 and .50. Ask, ‘What role does zero play in a decimal number?’
Small Group Focus — Applying the Concept Focus Teaching Group • How Do Shops Round Decimals? Discuss techniques for ‘rounding up’ and ‘rounding down’ decimals. Provide students with supermarket dockets. Ask, ‘Why does the supermarket round an amount like $2.32 to $2.30, then refer to it as $2.3?’ Discuss the reasoning behind this practice. Provide students with supermarket or hardware catalogues. Have them cut out amounts and paste them onto paper. Beside each amount, have students rewrite the value ‘rounded up’ or ‘rounded down’, e.g. ‘$2.99 is $3.00 is $3.’ • Remove the Zeros Write these numbers on the whiteboard: 10.25, 9.20, 8.03. 7.20, 15.0, 6.05, 03.24. Ask, ‘Which zeros can be removed without altering the value of the number?’ Discuss the concept of relevant and nonrelevant zeros. As an independent activity, have students record ten numbers, all of which contain zeros and two decimal places. Ask each student to give their set of numbers to a partner. Have the partner cross out the irrelevant zeros and rewrite the numbers in order, from smallest to largest. • Decimals and Familiar Objects Discuss and identify decimals in 1 everyday living, e.g. money, metres, kilograms, etc. Ask, ‘What is 2 of $1?’ Have students suggest other ways of expressing fractions of a dollar. Look at 1 equivalences with decimals. Ask, ‘If 10 of $1.00 is 10c, then what is 0.1 of $1.00?’Together, create a group fraction/decimal equivalence chart. Review the number of millilitres in one litre (1 000), then have students complete BLM 22 ‘Cents and Millilitres’. Ask questions such as, ‘How many millilitres 1 1 in 4 of a litre?’ ‘If I drank 2 a litre of milk, how many millilitres would be left over?’
Independent Maths Individual, pair, small group
Adding and Ordering Have students work in pairs to record four unequal amounts of money which together equal exactly $10. Encourage them to use calculators to work out the amounts; they can then order the amounts from largest to smallest. Repeat, using $20, $50, $100, etc. Detective Doug Decimal (Student Book p. 37) Prepare 26 Centicubes; each Centicube must have an amount from 0.1 to 4.0 on one side, and a letter of the alphabet on the other. (You could use post-it notes.) Hide the Centicubes around the classroom. Have students hunt for the Centicubes and use them to complete Student Book p. 37. Unit 13 Decimals
61
Decimal ‘Who Am I?’ Have students create a ‘Who am I?’ poster for a 4digit decimal (e.g. 12.53) by writing clues about its identity. The clues must not mention any of the four digits, e.g. ‘6 and 6 make my whole number. I have two decimal places. If you add my two decimal places up, you will get 8’, etc. Encourage students to make three or four posters; they swap posters with a partner and work out each other’s decimal numbers. Decimal Point Motion Have students choose four different digits to work with, e.g. 5, 7, 8, 3. Using BLM 69 ‘Hundreds, Tens, Ones, Tenths & Hundredths Chart’, have students create the 24 numbers possible with these digits, keeping two numbers on each side of the decimal point. As an extension, students could then order the numbers from smallest to largest. Create a Price Have students create ‘Petrol Price Signs’ where there is only 0.5c difference between four stations. Long-jump Olympics (Student Book p. 38) Have students complete the activity, which involves ordering and rounding off numbers to one decimal place. Units 12–13 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 39).
Whole Class Share Time Have students share their experiences of ‘building’ $20. Ask, ‘Which decimals were easy to work with? Why?’ Have the group share their experience with Detective Doug Decimal. Ask, ‘Which decimals were easiest to order? Which were not? Why?’ Select students to share their decimal number patterns and the reasoning behind them. Today I did not understand …
Ask selected students to read their clues aloud. Have the class members try to guess the number before all the clues are read. (The partner of each selected student cannot participate!) Ask, ‘What strategies did you use to find all 24 number combinations?’ Discuss strategies, then ask, ‘Which decimals were the closest in value?’ Have a selected group show three of their signs. Ask, ‘Which price is missing from the 0.5c range?’ Discuss how students ordered the place-getters on Student Book p. 38. Have them explain their reasoning. Ask, ‘What is the purpose of rounding off decimals?’
62
Nelson Maths Teacher’s Resource — Book 5
unit
14 Measurement
Length Student Book pp. 40–41
BLM 23
During this week look for students who can: • measure everyday items using formal and informal units • estimate and measure using centimetres and metres. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources butchers’ paper, metre rulers, trundle wheels, tape measures, height chart, magazines, sporting profiles, string, chart paper, coloured stripping, Kid Pix Studio Deluxe, Word, http://www.npl.co.uk/npl/about/history_ length/02.html, BLM 23 ‘Measurement Data Sheet’ Maths Talk Model the following vocabulary in discussion throughout the week: metre, centimetre, ruler, trundle wheel, estimation, estimate, accuracy, actual, cubit, record, informal, formal
Whole Class Focus — Introducing the Concept Centimetres and Metres Informally discuss centimetres and metres, and where they are used. Ask, ‘When do you measure in metres, and when do you measures in centimetres, and when do you measure in both?’ Draw a large two-circle Venn diagram on a sheet of butchers’ paper. Label the circles: Centimetres, Both, Metres. Brainstorm with the group, recording their responses on the diagram. Before Rulers? Provide a collection of rulers, tape measures and trundle wheels. Ask, ‘What do you think people used to measure with before rulers were invented?’ Discuss responses; lead students towards the idea of using body parts such as handspans as informal measuring units. Introduce the ‘cubit’; this was the length of the arm from the tip of the finger to the elbow. Use the tape measure to measure the ‘cubit’ of several members of the class. Contrast their measurements. Ask, ‘Was there a problem using measurements such as cubits?’ Brainstorm other informal units we could use today. Ask, ‘What is a formal unit and what is an informal unit?’ Measuring Our Heights Measure each student’s height; record the measurements in three forms, e.g. 122 centimetres, 1 metre 22 centimetres, 1.22 metres. Have students record their measurements on a card, and write the date on it for later use. Ask, ‘Which of the three ways of recording is used to describe a person’s height?’ Display a sports magazine; point out that Unit 14 Length
63
heights are recorded in centimetres. Ask, ‘Why would this be the way to record heights?’ Brainstorm answers. Have students use the cards to order the top 5 tallest students in the class. How High? Ensure all students’ heights are recorded. Offer the challenge, ‘How high is the door frame?’ Encourage students to make sensible estimates using their own heights as a guide. Record responses, then use a tape measure or metre ruler to accurately measure the height of the frame (in cm). Ask, ‘Whose estimate was within 10 centimetres of the actual measurement?’ Now say, ‘What is the height of your desk?’ Measure the heights and see if students’ estimates were more accurate this time. Measuring Curved Lines Straight lines are easier to estimate than curved lines. Draw a curved line on the whiteboard. Ask, ‘How can we measure a curved line?’ Discuss responses, then demonstrate using a piece of string to measure the line. Provide 30 cm lengths of string; have students see how many ways they can arrange the string so that it appears to be less than 30 centimetres in length.
Small Group Focus — Applying the Concept Focus Teaching Group • Metre or Centimetre It is important students see that each unit of measure has specific applications. Ask, ‘What items would you measure in metres, and what items would you measure in centimetres?’ Brainstorm items and situations where both these units of length are used. Get a large piece of paper and divide it in two. Label one half Centimetres, the other half Metres. Provide magazines and have students cut out pictures and decide which side of the chart to glue them. For each picture, e.g. a truck, ask, ‘Would you measure the length of a truck in metres or centimetres?’ • How Long? Take the group to a basketball court; have students use a metre ruler to compare their armspans. Say, ‘Now use your armspans as a guide to estimate the length of this basketball court in metres.’ When students finish their estimates, use a trundle wheel and a metre ruler to find the length (usually 26 metres). Discuss students’ responses and their estimates. Then have students estimate the width of the court (usually 14 metres) and compare it with the measurement. Students can then work independently to estimate and record other lengths. • Make a Tape Measure Have students use lengths of coloured stripping to create their own 30 centimetre and one-metre measuring strips. They can use their own rulers to construct the 30-centimetre strip, then use the strip and a ruler to make the one metre strip. Have students use their two strips to measure and record objects and spaces in the school playground.
Independent Maths Individual, pair, small group
Estimation and Accuracy Have students work in pairs using BLM 23 ‘Measurement Data Sheet’, selecting items in and around the school to measure. Remind students that they need to make an estimate of each object before measuring its length. How Big is Your Hand? (Student Book p. 40) Have students measure the ten ‘handspans’ on the page, using a 30 cm ruler. They should record each length, then order the handspans from biggest to smallest (1st to 10th).
64
Nelson Maths Teacher’s Resource — Book 5
Students can then measure and compare their own handspans. If time allows, students could measure and compare the height of their hands as well, measuring from wrist to tip of the index finger. World Record Attempt Tell students this amazing true fact: the world long jump record is 8.95 metres, and is held by Mike Powell of the USA. Have each group use a trundle wheel or metre rulers on a grassed surface to mark 8.95 metres. Then have students record how many jumps it takes them, from a standing start with both legs together, to cover 8.95 metres. Draw a TV (Student Book p. 41) Have students design their own television set, following the instructions provided. Make sure they rule all lines, and that all measurements are in whole centimetres. Computer Art Have students draw simple pictures or designs on the computer using Kid Pix Studio Deluxe or Word. Print out the designs and have other students use 30 cm rulers to accurately measure (and mark) the length of each line. Thirty Centimetres? Have students take a good look at their 30 cm ruler, to see if they can memorise how long it is, then put it out of sight. Give each group a large sheet of paper. Say, ‘Can you draw a line 30 cm long without referring to a ruler?’ Have each student make three attempts, then have the others in the group use a ruler to check the lengths. Repeat this activity; this time students draw a curved 30 cm line and measure their estimates with string and a 30 cm ruler. Unit 14 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 42).
Whole Class Share Time Have the group explain what their task was. Ask, ‘Were there any objects that you were very accurate in estimating?’ and ‘Was there any estimate that was way out?’
Today I discovered …
Check the handspan answers. Ask, ‘How did your handspan compare with the handspans in the Student Book? How do your handspans compare with each other? Which is longer: the length of your hand or the width of your handspan?’ Ask several groups how many jumps it took them to reach the world record long jump distance. Ask, ‘What does 8.95 metres really mean in terms of metres and centimetres?’ Have several students model their TV designs. Ask, ‘How did you decide on the width of the screen? Which part of the TV did you draw first?’ Have students explain the task. Ask, ‘Did anybody actually draw a 30 cm line in their three tries?’ Try the task on the whiteboard. Repeat, drawing a curved 30 cm line.
Unit 14 Length
65
unit
Travelling with Numbers
15 Number and patterns
Student Book pp. 43–44
BLMs 24 & 25
During this week look for students who can: • use knowledge of addition, subtraction, division and multiplication to solve problems • use methods of calculation to determine the best way to reach an accurate outcome. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources dice, small chalkboards, chalk, phonebooks, cloth bag, BLM 24 ‘Head, Paper, Calculator’, BLM 25 ‘Travelling Game’ Maths Talk Model the following vocabulary in discussion throughout the week: tenths, hundredths, odd, even, halves, doubles, scale, distance, methods, calculate, process
Whole Class Focus — Introducing the Concept Roll, Add, Double Take three dice and roll them on the floor. Take the numbers rolled, e.g. 2, 6, 3, and add them together (11), then double the total to reach 22. Have students split into teams to play this game, using mental addition only. Teams have to work together, writing their answers on small chalkboards or sheets of paper. If a team yells out the answer, ignore them for that round. After the game, ask, ‘What processes did your mind go through to come up with the answer?’ As a variation, roll and add, then halve. Roll and Move Give each student a dice; tell them they are to apply the scale of 100 km to each number they roll, i.e. 1 = 100 km, 2 = 200 km, etc. They then subtract the distance rolled from 1000 km to find how far there is to go. As a variation, increase the distance and have students record their rolls; other students can check the kilometre countdowns. My Error Write an addition, subtraction, multiplication and division equation on the whiteboard. Include answers. Alter one number in each equation so each one is correct. In pairs have students work out the error. Discuss their strategies when trying to find the error. Roll Three then Halve Demonstrate rolling three dice, adding all three digits rolled, then halving the total, e.g. 2 + 6 + 5 = 13; halved, this becomes 1 6 2 or 6.5. Play the game with the class, using large dice. The first student to call out the correct answer wins the round
66
Nelson Maths Teacher’s Resource — Book 5
Flip and Write Have students sit in a circle, taking turns to shut their eyes and flick the phonebook open to a page at random. They then call out the page number. The other students must double the number called, then halve it. Discuss the strategies students can use when an odd number, such as 121, needs to be halved, e.g. half 100 is 50, half 20 is 10, half 1 is .5; the answer is 60.5 or 60 and a half.
Small Group Focus — Applying the Concept Focus Teaching Group • Out of the Bag Write ten 3-digit numbers between 100–999 on small post-it notes and put them into a cloth bag. Tell students that you are going to take a number out of the bag and subtract it from 1 000. Have students draw three bags in a row. On the first bag they write 1 000; on the second, they write the number taken out of the cloth bag; and on the third, they record the number left, e.g. 1 000 – 333 = 667. Before starting, ask, ‘What mental strategies could you use to solve this equation? Could you use more than one process? How can we check the accuracy of our responses?’ Students can use calculators, if needed. Ensure that students can subtract numbers with zeroes confidently. Have students complete several of these equations independently. • Double it Most return train tickets are almost double the single price. Write these single-ticket amounts on the whiteboard: $1.80, $2.25, $3.50, $4.74, $5.10. Have students record these amounts, then work out the price of a return ticket. Ask them to describe how they obtained their answers, then have them use the calculator to check. On large sheets, record the methods students used: double addition, multiplication by 2, estimation, rounding up or down. Ask, ‘Which method works best for you?’ • Head, Paper, Calculator Write a 3-digit number on the whiteboard, e.g. 375. Ask, ‘Without using paper or a calculator, will this number divide by 2, 3 and 5? If it can be divided, what is the answer?’ Discuss responses and the strategies used in mental computation: odd numbers not divisible by 2; numbers ending in 5 are divisible by 5; if the sum of the digits (e.g. the sum of 375 is 15) in the dividend is divisible by the divisor, the extended number will be too; estimation. Have students check their answers with pencil and paper, then, to confirm the process, with a calculator. Have students give five examples of equations that could be solved by each method, e.g. head 5 × 5; paper 124 × 5; calculator 124 × 68. Give each student a copy of BLM 24 ‘Head, Paper, Calculator’, which involves using head, paper and calculator to find whether numbers can be divided (or multiplied). The 3-digit numbers needed can be rolled by dice, pulled from a hat or written on the whiteboard.
Independent Maths Individual, pair, small group
11 Kilometres to School Give each pair three dice and a copy of BLM 25 ‘Travelling Game’.The aim is to use the three dice to travel 11 kilometres in the lowest number of rounds and dice rolls. The number on each dice represents a decimal fraction, which is then added, e.g. 3, 5, 2 = 0.3 + 0.5 + 0.2 = 1.0 km. Students can keep a running record in the total column, as well as scoring each round. Use the Atlas and Travel Each group will need an atlas, ruler and paper for calculations. The groups are to travel around Australia, visiting each capital city, but making the trip as short as possible. Have students use their Unit 15 Travelling with Numbers
67
rulers to measure the distance in a straight line between cities, e.g Melbourne to Hobart.They record the distance (in cm) and use the scale to work out the distance in kilometres; 1 cm equals 100 kilometres. (Vary the scale depending on the students’ skill levels.) Point out the scale they are using is not accurate. Calculators may be used. Tell the Truth Each student in the pair writes an addition, subtraction, multiplication and division equation for their partner to solve. Before swapping, and after checking their equations with a calculator, they alter one answer to make one incorrect equation. Partners swap and use pen and paper to work out the correct and incorrect equations. Melbourne to Brisbane (Student Book p. 43) Students use a travel line to calculate intermediate distances on a trip from Melbourne to Brisbane. Half-way and Return Trip (Student Book p. 44) Students complete the travel details between capital cities, where the distances are either halved or doubled.
Whole Class Share Time Have pairs explain how the game operates. Ask, ‘How did you keep track of how far you had travelled?’ Investigate who took the fewest rounds and rolls to reach 11 kilometres, and who took the most. Today I understood …
Select one group to read their travel plan; have other groups check and challenge their accuracy. Ask the groups, ‘What strategies did you use when you had half a centimetre?’ Determine which group completed their trip in the fewest kilometres. Have students share their strategies for finding the incorrect equation. Share students’ answers; discuss the methods they used to work out the distance travelled. Ask, ‘Is there a point on the trip to Brisbane that is close to half way?’ Discuss how the return trips were divided into days. Ask, ‘If you divided a trip by 3 days and it didn’t work evenly, what did you do?’
68
Nelson Maths Teacher’s Resource — Book 5
unit
16 Number and patterns
Numbers in Golf Student Book pp. 45–47
BLM 26
During this week look for students who can: • double and halve numbers to work out equations • round off numbers to assist with estimations • select the appropriate operation and computation method to solve problems. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources Microsoft Excel, Word, golf course cards, golf equipment (cards, balls, tees, clubs), cassette recorder, BLM 26 ‘Create a Golf Course’ Maths Talk Model the following vocabulary in discussion throughout the week: rounding up, rounding down, estimate, calculate, exact, estimations, order, hundreds, tens, ones, method, approach
Whole Class Focus — Introducing the Concept Using the Four Signs Roll three dice, e.g. 1, 6, 2. Ask, ‘What is the biggest number you can make with these three digits?’ List responses, then repeat for the smallest number. Have students create addition and subtraction equations using the three digits, e.g. 6 + 1 – 2 = 5. Emphasise that addition tasks must be completed before subtraction. Multiply All the Dice Roll three dice, then multiply the digits rolled, e.g. 2, 6, 3 becomes 2 × 6 × 3 = 36. Ask, ‘If we change the order of the digits, will the answer change?’ Discuss responses, then multiply 6 × 2 × 3 and 2 × 3 x 6. Emphasise that changing the order in a multiplication equation doesn’t alter the answer. Rounding Up and Down Write on the whiteboard: 88, 862, 849. Ask, ‘How do you round off these numbers to the nearest hundred?’ Discuss the rules for rounding: 49 and below, down; 50 and above, up. Ask, ‘Why does 88 round up to 100? What would the answer be if we were rounding to the nearest 10?’ Repeat, using 862 and 849. Ask, ‘If we were rounding off 862 to the nearest 10, would the answer be 860 or 870?’ Produce a set of class rules for rounding off to the nearest ten, hundred and thousand. Add on to Work it Out Write 150 and 900 on the whiteboard; put a brainstorm cloud around them. Ask, ‘How can we work out the difference between these numbers?’ Brainstorm possibilities, e.g. complementary Unit 16 Numbers in Golf
69
addition; counting on; estimation; deleting the last zero to create 15 and Students could also 90. Have students use one of the patterns to find the difference. use calculators and approximation. Have students use computer software Big Numbers Become Small Have students write this (such as Inspiration 6, Kid Pix Studio problem in their books: 16 golf clubs cost a total of $880. Ask, Deluxe or Word), to prepare a presentation on how they worked out the difference ‘How can we work out the unit price for a single golf club? What between 150 and 900. Students without processes will we need?’ Brainstorm responses, e.g. division, need computer access can complete calculator, etc. Pose the question, ‘How can we work this out in only the task on paper using a brainstorm cloud. four steps?’ Model the halving strategy: 16 clubs for $880; 8 for $440;
4 for $220; 2 for $110; 1 for $55. Create another word problem; have students show how halving both the large and the small number helps to solve the problem.
Small Group Focus — Applying the Concept Focus Teaching Group • Add These Up Write on the whiteboard: 26, 19, 77. Ask, ‘How can we work out the total of these three numbers without using a calculator or doing an addition equation?’ Revisit rounding up and down; ask, ‘What does 26 round off to?’ Discuss responses, then round 26 to 30. Do the same for 19 and 77, rounding them to 20 and 80. Say, ‘We now have 30, 20 and 80. But is there an even easier way to calculate the answer — without using a calculator or paper?’ After discussion, record 3 + 2 + 8 = 12; point out that the answer to 26 + 19 + 77 is therefore close to 120. Have students check with paper and a calculator. Provide further sets of three numbers for students to add using mental strategies. • Double Up and Add Golf tees usually come in bags of 15 to 20. Ask, ‘If one tee costs 18 cents, how can we work out how much 16 tees will cost — without using a calculator or doing a written equation?’ Take students’ suggestions; classify them as mental calculations, and tape each suggestion on a cassette recorder to play back at the end of the task. Write on the whiteboard the ‘double approach’: 1 for 18c, 2 for 36c, 4 for 72c, 8 for 144c, 16 for 288c. Ask, ‘If the price is $2.88, what will the golf shop round off the price to?’ Have students work out a similar problem independently, with each golf tee costing 22c. • Count On or Take Away Have students record a 3-digit number between 500 and 999. Then have them select a number between 100 and 499. Ask students what their two numbers are. Put your own example on the whiteboard: 837, 162. Ask, ‘How do I work out the gap between these two numbers?’ Most students will suggest a subtraction equation: 837 – 162. Record this with your example, then model the counting-on method: 162: add 8 for 170; add 30 for 200; add 600 for 800; add 37 to reach 837. Have each student write their own version of counting on. Estimating is a third way of working out the gap: 837, say 850; 162 round back to 150; 850 take away 150 is close to 700. Have students use the estimation method to find the gap between their numbers.
Independent Maths Individual, pair, small group
70
Create a Golf Course Give each group BLM 26 ‘Create a Golf Course’ and three dice. Have the groups roll the dice, one at a time, and record the numbers in the columns. Dice 1 is recorded in the hundreds column; Dice 2 in the tens; Dice 3 in the ones. Students use the numbers to create the distance of each hole on a golf course. Teams create their course, use 1 1 calculators to add up the total distance, then estimate 2 and 4 of the length of each hole in metres.
Nelson Maths Teacher’s Resource — Book 5
Graphs Create Equations Give each group a golf course card; have them use Excel or Word to graph the distances by placing hole 1, hole 2, hole 3, etc, in column A and the distance in column B. (They should not enter m or metres.) They then print the graph and use it to create equations, e.g. hole 4 – hole 18. Students without computer access can complete the task using graph paper and coloured pencils. Cash Registers (Student Book p. 45) Students estimate (by rounding the amounts up or down) how much each cash register has in it, then use a calculator to provide the exact amount. They then calculate the difference between the exact amount and their estimate. Big Dave Off the Tee (Student Book p. 46) Ensure that students understand the concept of driving a golf ball off a tee. Students need to note how far Dave drives the ball, then calculate the distance required (the difference) to complete the hole. Golf Balls by the Box (Student Book p. 47) Have students work out the unit price of a single golf ball, when purchased in bulk. Units 15–16 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 48).
Whole Class Share Time Discuss how the golf game was played. Ask, ‘Which numbers were easiest to halve? What have you learnt from doing this activity?’ Have students show their graphs; they can pose examples of the golf equations to other groups, who then use pen and paper and calculators to work out the answers. Today I worked out …
Pose this question: ‘How did you round up or down to estimate the amounts of money?’ Have students explain their approaches; see whose estimates were closest to the exact amount. Have students display their answers. Ask, ‘What strategy did you use to work out the distance left in the hole?’ Discuss responses, then ask, ‘If Dave can drive 220 metres and more, why did he only drive 101 metres on the fourth hole?’ Have students compare their answers about the prices of the golf balls. Ask, ‘What processes did you use — apart from a calculator — to work out the price of a single golf ball?’
Unit 16 Numbers in Golf
71
unit
17
2D Shapes
Space
Student Book pp. 49–50
BLMs 27, 28, 29 & 70
During this week look for students who can: • • • •
recognise, name, describe and construct simple 2D shapes use rulers and computer software to draw lines, shapes and angles construct recognisable objects using combinations of shapes draw and explain lines of symmetry in regular 2D shapes.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources Kid Pix Studio Deluxe, atlases, flags of the world, magnetic and nonmagnetic 2D shapes, attribute blocks, squares of coloured paper, cartridge paper, www.plcmc.lib.nc.us/kids/mow/, poem ‘Tiger, Tiger’ by William Blake: www.everypoet.com/archive/poetry/william_blake/william_blake_ songs_of_experience_the_tiger.htm, book on tigers, BLM 27 ‘Three Triangles’, BLM 28 ‘Who Am I?’, BLM 29 ‘Tangram’, BLM 70 ‘Square Dot Paper’, BLM 78 ‘Isometric Dot Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: shape, geometric, circle, oval, rhombus, polygon, triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, sides, scalene, righ tangle, equilateral, equal, unequal, lines, vertical, horizontal, parallel, characteristics, identify, differences, similarities, regular, irregular, symmetry, line of symmetry, symmetrical, non-symmetrical
Whole Class Focus — Introducing the Concept About 2D Shapes Write ‘two dimensional’ and ‘2D’ on the whiteboard; ask, ‘What do we mean by these terms? What is a “dimension”?’ Record responses. Brainstorm what students know about 2D shapes, recording on a large sheet of paper. (Use only one colour, so that new facts can be added in another colour later in the unit.) What’s Different Here? Draw a square and a rectangle on the whiteboard; make sure both shapes are accurate. Ask, ‘What are the differences between these shapes?’ Record responses, then ask, ‘How are these shapes the same?’ Discuss responses; introduce the concept that both belong to the family of quadrilaterals. Compare, discuss and revise other known 2D shapes. Symmetry Read the poem ‘Tiger, Tiger’ by William Blake; show a photo of a tiger’s head. Ask, ‘What other creatures are symmetrical? Where else in the natural world can we find symmetry?’ List responses. Discuss the idea of
72
Nelson Maths Teacher’s Resource — Book 5
symmetry, lines of symmetry, and symmetrical and non-symmetrical shapes. Have a ‘nature walk’ in the schoolground; have students note symmetrical objects and shapes. Sides Match the Name All polygons have examples that we can find in the everyday environment. Write the heading ‘Quadrilaterals’ on a large sheet of paper; ask, ‘What are the features of quadrilaterals?’ (They have 4 sides and 4 angles.) ‘What are some shapes that have 4 sides?’ Record the names: square, rectangle, rhombus, trapezium, parallelogram. Brainstorm where each polygon might be seen, e.g. rectangle: window; trapezium: measuring cup, stage; parallelogram: the ‘vertical’ face of a step. Students could draw a picture of each real-world example on the poster. What Can We Make? Using magnetic shapes on a whiteboard, present the challenge of constructing a recognisable picture with 2 circles, 2 triangles, 2 squares, 2 rectangles. Have students volunteer to construct a picture. For variety, increase or decrease the number of magnetic shapes. Ask, ‘Which shapes were easiest to work with? Which shapes were the hardest to work with?’
Small Group Focus — Applying the Concept Focus Teaching Group • Lines of Symmetry Give each student a square of coloured paper and a large sheet of cartridge paper. Have students use their rulers to plan geometrical shapes on coloured paper, making sure the shapes start from the edge. They then cut the shapes out (starting from the edge), put the coloured paper on top of the white paper to show the cut out, then glue the rotated shape on the white sheet to give a ‘mirror image’. More complex shapes can be cut into the rotated shapes to allow an even greater level of complexity and design. • Three Triangles Give each student BLM 27 ‘Three Triangles’. Write on the whiteboard: triangle, equilateral, rightangle, scalene. Ask, ‘What do these three shapes have in common?’ Record responses; emphasise that Students can make the they are all triangles but have different names and features. Define three types of triangles on the ‘equilateral’. Have students guess which triangle is equilateral, then computer using Kid Pix Studio Deluxe or Word. Have them flooduse their rulers to check. Students can then use rulers or right angle fill, add labels and print copies for testers to find the right-angled triangle. Then have them measure the the remainder of the class. sides of the scalene triangle. Ask, ‘How is this triangle different from the equilateral triangle?’ Have students affix the labels. • Polygons Galore Provide copies of BLM 28 ‘Who Am I?’ and a set of 2D shapes. Ask students to match each model with its name. They should then cut out the 2D shapes and matching names and glue them onto paper. Point to the irregular pentagon. Ask, ‘What did you name this shape?’ Discuss responses. Establish that it is a pentagon, because it has 5 sides. Ask, ‘How is it different from a regular pentagon?’ Repeat for the irregular hexagon and heptagon. Emphasise that regular pentagons (hexagons, etc.) have all sides the same length and all angles the same.
Independent Maths Individual, pair, small group
Shape Profiles Have students work in pairs using attribute blocks. Ask each pair to create a written profile of a triangle, a square, a rectangle and a pentagon (select shapes appropriate to students’ understandings); they should cover features such as lines, sides, angles and lines of symmetry. They can trace the blocks onto card and write the profiles underneath. Unit 17 2D Shapes
73
This activity could also be done on the computer using Kid Pix Studio Deluxe or Word.
2D Who Am I? (Student Book p. 49) Have students work in pairs. Each student has their own book, but works with their partner to decipher the clues and find the correct 2D shape names.
Symmetry on Kid Pix Studio Deluxe Have students work in pairs using Kid Pix Studio Deluxe to construct symmetrical shapes and pictures using the paint brush tool on the studio program. Ask them to replicate faces and designs, as well as traditional polygons (which can be made through the symmetry tools). Students not working on the computer can work on BLM 70 ‘Square Dot Paper’ or BLM 78 ‘Isometric Dot Paper’. Have students rule a line of symmetry vertically down the page, then draw one half of a geometric design, using the dots for guidance.They then swap with their partner who completes the other half. Alternatively, students could rule two lines of symmetry and take turns to flip the design into each quarter. Tangrams Provide groups with BLM 29 ‘Tangram’ and large sheets of coloured paper. Have students carefully cut out the eight tangram pieces and use them to create a picture or sign. Students then take turns to hide their tangram and give verbal instructions so that other students can reproduce it. Encourage the use of shape and positional language, e.g. ‘Put the large triangle in the bottom left-hand corner of the paper.’ Flags of the World (Student Book p. 50) Students use reference material, such as websites or atlases, to research, draw and describe the geometric shapes used in six flags of the world.
Whole Class Share Time Ask the students to display their work. Ask, ‘Which shape was the hardest to create a profile for? Why?’ Select a student to read out a clue, to see if the class can guess the shape. Ask, ‘Which shapes were easy to identify from their listed attributes? Which shapes were difficult?’ Today I investigated …
Select pairs of students to show their presentations on Kid Pix Studio Deluxe. Encourage other students to discuss the shapes created. Have the students who created the shapes then explain how they were produced. Have students show their tangrams; ask selected students, ‘Which piece of the tangram was the hardest to place in your design or picture?’ Ask, ‘Why do you think countries use block shapes in their flag designs?’ (They are simple to design and sew.) ‘Which countries have used geometric designs in a more creative and colourful way?’ Ask each student in the group to nominate their favourite flag; note any common choices.
74
Nelson Maths Teacher’s Resource — Book 5
unit
18 Space
Flip, Slide and Turn Student Book pp. 51–52
BLMs 27, 30, 71 & 72
During this week look for students who can: • identify and use the terms slide, turn and flip when manipulating shapes • identify shapes that will and will not tessellate • create a series of tiles that involve sliding, turning and flipping. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources atlases, Word, coloured cover paper, hard cardboard, mirror, attribute blocks, white cardboard squares, textas, BLM 27 ‘Three Triangles’, BLM 30 ‘Flags to Flip’, BLM 71 ‘Triangle Shape Grid’, BLM 72 ‘Tesselating Shapes’ http://www.plcmc.org/forkids/mow/ Maths Talk Model the following vocabulary in discussion throughout the week: translate, rotate, reflect, tessellate, flip, slide, turn
Whole Class Focus — Introducing the Concept This Rectangle Place a rectangle from a set of attribute blocks on a large sheet of white paper on the floor; have a student trace and colour the rectangle. Place a mirror against the drawn image; ask, ‘What can you see?’ Write the word ‘reflection’ on the whiteboard; ask, ‘What do you think a reflection is?’ Discuss responses, then write ‘flip’ next to ‘reflection’. Place the attribute block over the coloured tracing and flip it to show what the reflection looked like. Repeat, using a square, a triangle and a circle. Make Your Own Pattern Take an attribute block and ask students to join shapes to create a giant tile. No gaps must be evident and the giant tile must have equal outer sides. If you have more sets of attribute blocks, repeat this activity, nominating the number of tiles they must contain. Trace and Turn Have students select a polygon from a box of attribute 1 blocks. Revise the term ‘ 4 turn’. Have students trace the polygon onto white 1 card and name it, then rotate it 4 turn right and trace it again. Have them 1 1 repeat these steps, making a series of 4 turns and labelling each one: 4 turn, 1 3 2 turn, 4 turn. Discuss which shapes remain the same after turning, and which shapes have changed. Try Triangles Copy the right-angle triangle from BLM 27 ‘Three Triangles’ onto card and have students use it as a template to cut further triangles out of paper of different colours. Ask them to use the right-angled Unit 18 Flip, Slide and Turn
75
triangles to make a square tile. Once they have done this, have them draw the tile in their books in lead pencil, and label the colours they used. Students then swap books and see if they can duplicate each other’s squares. Make Your Own Shape Give students several minutes to create their own shape from cover paper. Then have them sit in a circle, with their shapes in front of them. Give a series of instructions for students to carry out, e.g. ‘Rotate your shape to the right. Flip your shape. Turn your shape upside-down and slide it along.’ Discuss the different shape movements; ask, ‘Did you notice anything about the appearance of your shape when we did those actions?’ Have students explain the changes they observed.
Small Group Focus — Applying the Concept Focus Teaching Group • White Tile Design Give each student four white cardboard squares to use as ‘tiles’. Have students use textas to make several simple designs — that they can easily repeat — on a tile.Then have them produce four tiles in a row where the pattern is the same. Ask, ‘Where do we find tile patterns used like this? Use the term ‘slide’; discuss how tilers often translate patterns on bathroom walls. As a follow up, ask students to move their tiles to create different patterns. • The Language of Movement Cut out the right-angle triangle from BLM 27 ‘Three Triangles’ and make multiple copies of it on coloured paper. Stick the original to the whiteboard. Ask students to make a pattern any way they can, by sticking three coloured copies next to the original.When the pattern is complete, ask, ‘How has the pattern been continued?’ Emphasise what has happened by writing flip, slide and turn underneath the appropriate parts of the pattern. Provide more coloured right-angle triangles and have each student make their own pattern by flipping, sliding and turning the triangles. Have them glue their pattern onto white paper. • Move These Tiles Provide textas and large cardboard squares for use as ‘tiles’. Have students draw two or three simple — and easy to repeat — designs on each tile.Then have them place two tiles the same in a row. Ask, ‘What do we call a pattern that repeats? (A slide pattern.) Place the original tile down, and have students rotate the copy 90° to the right. Ask, ‘What do we call this movement?’ Use the terms ‘turn’ and ‘rotate’. Finally, have students put down the original and flip the copy. Have students repeat the task but drawing a known object, such as a person, a clock face or a smile.
Independent Maths Individual, pair, small group
Flags to Flip Have students work in pairs. They will need coloured pencils, textas, a ruler and BLM 30 ‘Flags to Flip’. They will also need an atlas or access to the flag website (see ‘Resources’). Students select a continent, then choose five countries from it and draw their flags. They redraw the flag as it is slid, turned and flipped. Create Your Own Tile Have students work in pairs to prepare eleven 10 cm × 10 cm squares: ten on coloured paper; one on hard card. Students take the hard card square and cut an abstract shape from one corner. They take the piece they cut off and tape it onto the corner diagonally opposite. Have them trace this template onto the ten coloured squares, cut them out, then stick them onto white paper to show how they tesselate.
76
Nelson Maths Teacher’s Resource — Book 5
Shapes in Word Have students work in pairs using Word to create shapes that can be rotated and flipped. Have them open a new page and access Autoshapes, where they can create either prepared shapes from Basic Shapes or create their own from lines. Students will need to copy their shape four times before commencing any rotations or flipping. The Draw toolbar allows access to the Rotate (or flip) command. Shapes can be floodfilled with colour; students can use text boxes to label the original and altered shapes, then print their finished page. Students not using the computer can cut a shape template from card and trace it several times onto a sheet of A4 paper. Photocopy the sheet, then have students cut the shapes out and slide, turn and flip them onto a sheet of coloured paper. Colour the Movements (Student Book p. 51) Students complete the tasks by colouring the continuation of each pattern in specific colours. (The symmetrical shapes, e.g. the pentagon, will not look different after flipping or sliding.) Provide copies of BLMs 71 and 72 ‘Triangle Shape Grid’ and ‘Tessellating Shapes’ so that students can design and colour their own patterns. Continue These Shapes (Student Book p. 52) Students may need tracing paper or card to copy the original shape so that it can be flipped, slid and turned effectively and accurately. Some shapes, e.g. the rectangle, remain the same when they are slid and flipped horizontally; students will need to use a combination of colours for these shapes to show both movements. Units 17–18 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 53).
Whole Class Share Time Have students explain the task, and the countries and flags they chose. Ask, ‘Which countries have a flag that is very difficult (or easy) to reproduce?’ Discuss what makes a design difficult or easy to reproduce. Have students explain to the class how they created their own tessellating tile. Ask them to share their designs; ask, ‘Why does the cut portion have to join the diagonal corner? Why can’t it join a corner on the same side?’ Today I learnt …
Ask students involved to explain what they did using Word and to display printed copies. Ask, ‘What have you learnt from being able to flip and rotate these shapes using Word?’ Have students display their work; check it for accuracy. Ask, ‘How could you tell when a shape had been flipped (turned, or slid)? Were there shapes that altered very little when they were rotated, flipped or slid?’ Discuss shapes that looked the same when slid and flipped (cross, smiley, rectangle, arch, rounded rectangle); ask, ‘What strategies did you use to show that the continued pattern was both a slide and a flip?’
Unit 18 Flip, Slide and Turn
77
unit
Value for Money
19
Student Book pp. 54–55
Number and patterns
BLMs 31, 73 & 74
During this week look for students who can: • • • •
round off money values using a calculator identify different combinations of money to make equal amounts select the appropriate methods to solve money problems and equations convert common fractions to decimals.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources cassette recorder, play money, dice, Inspiration 6, BLM 31 ‘Dice Roll Decimals’, BLM 73 ‘Banknotes’, BLM 74 ‘Coins’ Maths Talk Model the following vocabulary in discussion throughout the week: equations, equality, operations, change, totals, calculations, methods, word problems
Whole Class Focus — Introducing the Concept I’ve Got $20 — Change Please! Display a $20 note from BLM 73 ‘Banknotes’. Discuss how other notes and coins could be combined to have the same value. Record the possibilities on the whiteboard. Ask, ‘If I spent $3 and paid for it with a $20 note, how much change would I get?’ Use a cassette recorder to tape the answers. Discuss responses, and the mental methods students used to find the answer. Repeat, spending $9 from $20, and $5 from $20. Replay the tape and talk about the strategies suggested. Then ask, ‘If I spent $4.50, how much change will I get from $20?’ 1
1
Pizza Plus More Ask, ‘If I have 1 2 pizzas, and I get another 1 2 pizzas, and 1 then I get another 1 2 pizzas, how many pizzas do I have altogether?’ Ask students to verbalise their strategies; invite several students to draw their strategies on the whiteboard. Discuss how the strategies can be recorded 1 using decimals or fractions: 1 2 or 1.5. Pose this problem: ‘Rick had $1.50; then his mother gave him $1.25, and his brother gave him $2.75. How do you work this out when you know that 100 cents will equal a new dollar?’ Decimals Can Be Money Write amounts of money on the whiteboard as decimals, e.g. 0.2, 0.3, 0.6, 1.2. Ask, ‘How can I write these amounts in dollars and cents?’ (20c, 30c, 60c, $1.20) Encourage students to provide solutions. Model the procedure, if necessary. Write other simple amounts on the whiteboard as decimals and have students convert them into dollars and cents and add the amounts together. Once students are comfortable
78
Nelson Maths Teacher’s Resource — Book 5
with this procedure, have them work in pairs to add the decimals together first and then convert them to dollars and cents. Finders Keepers Set a scene where three students win $20 in a guessing competition. Ask, ‘Do you think this amount will divide evenly?’ Discuss responses, then ask, ‘What will help you work out the share evenly?’ Use a calculator to find the answer: $6.66 repeating. Have students work out the equation on their own calculators and highlight the recurring sixes. Discuss how you might round that share off; work with students to find the most realistic sharing of $20 among three people ($6.65, $6.65 and $6.70). Add and Multiply Write on the whiteboard: ‘A large bottle of water is $1.50’. Say, ‘Imagine that the bottle of water is in a box of a dozen bottles. How can we calculate the price of a dozen bottles?’ Take suggestions, and classify the approaches: repeated addition, double the price (1 is $1.50, 2 are $3.00, etc), multiply by 12, calculator use. After checking the methods, repeat with bottles costing $2.25 each.
Small Group Focus — Applying the Concept Focus Teaching Group • I Have Five Notes Stick $5, $10, $20 $50 and $100 notes from BLM 73 on the whiteboard. Say, ‘I have five notes in my pocket; the total is $90. What notes do I have?’ Using a guess-and-check method, work with the group to find the identities of the five notes. Repeat, with five notes equalling $45, and five notes equalling $120. • Change for $100 Draw a $100 note on the whiteboard (or use a $100 note from BLM 73). Have students use their calculators to work out the change from $100 where the total spent is $44.60. Repeat, using these amounts: $56.40, $42.80, $64.80. Discuss how you could approach the task without using a calculator. • Multiplying by Factors of 10 Pose this puzzle: ‘If a box of chocolates costs $3.30, what will ten boxes cost?’ Discuss strategies; emphasise that when you multiply by 10, you move the decimal point one place to the right and add zero. Discuss the significance of zero and its value in this case. Provide similar problems for students to work out independently.
Independent Maths Individual, pair, small group
Combinations Please Provide each small group with a large sheet of paper with $30, $20 or $10 recorded in the middle and copies of BLM 73 ‘Banknotes’ and BLM 74 ‘Coins’. Have students paste different combinations of notes and coins equal to the amount written on the paper. Students can then check each other’s combinations. This activity could also be done on the computer with Inspiration 6. Roll For Money and Round Off Have students work in small groups, with three dice per group. Students name the dice 1, 2 and 3, then roll them all at once. Dice 1 is the number in tens, Dice 2 is the value of ones, Dice 3 is the divisor. The group then use calculators to check and round off the monetary value of the equation. Have groups complete the activity 15 times. Dice Roll Decimal Give each pair BLM 31 ‘Dice Roll Decimals’, a dice and a calculator. Each player rolls the dice, records the number rolled, then converts it into a decimal, e.g. 6 = 0.6; 1 = 0.1. Each player calculates their Unit 19 Value for Money
79
total after 6 rolls; their opponent uses the calculator to check. At the end of the game, they add the totals and convert the decimal tenths into dollars and cents. Cans by the Box (Student Book p. 54) Discuss the concept of bulk packaging, and how it allows people to save money. Ensure that students have calculators to complete the page. Demonstrate the division procedure, emphasising that the amount of money is divided by the number of cans. Have students round off their calculations to the nearest 5 cents. A Pocketful of Coins (Student Book p. 55) paper for students to work out their answers.
Provide sheets of scrap
Whole Class Share Time Have each group display their work and explain the combinations of coins and notes they found for one specific monetary value. Ask the other groups to check; ask, ‘Has this group covered all possible combinations?’ Before sharing work, ask the groups, ‘What is the purpose of rounding off amounts of money? If you have an uneven dividend what can you do with money?’Then have the groups share several of the equations they rolled and the answers they came up with.
Today I did not understand …
Have the groups explain how they played the game, so that each group can check on their methods of playing and calculating. Ask, ‘What is the feeling like when you roll one or two singles on the dice? Whose fraction converted into the greatest amount of money?’ Discuss the prices and the various box sizes. Ask, ‘Which size box offered the best (worst) deal when you worked out the price of an individual can? How could you estimate the cost of each can?’ Ask students to share how they worked out the total amount of money held by each child. Ask, ‘Did the results work out the way you thought they would? What types of operations did you need to do to complete the task?’ Have selected students share the various amounts that could have been in John’s pocket. Record the combinations.
80
Nelson Maths Teacher’s Resource — Book 5
unit
20 Number and patterns
Words and Numbers Student Book pp. 56–57
BLMs 32, 75 & 76
During this week look for students who can: • identify, name, extend and create number patterns • complete and create word problems involving operations. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources cassette recorder, calculator, BLM 32 ‘Number Investigator’, BLMs 75 and 76 ‘Tables Charts’ Maths Talk Model the following vocabulary in discussion throughout the week: continue, extend, pattern, repeat, odd, even, strategies, identify, halve, double
Whole Class Focus — Introducing the Concept 1, 2, 4, 7, 11 Write on the whiteboard: 1, 2, 4, 7, 11. Ask, ‘Can you see what the pattern is?’ (Digits increase by 1, 2, 3, 4.) Tape students’ responses. Ask, ‘What strategies help us solve number problem patterns like these?’ e.g. ‘Is it even? Is it odd? Is it numbers going up? Does it look like a doubling pattern?’ Provide more number patterns for students to solve orally, e.g. 2, 4, 9, 11, 16 (+ 2, + 5). Pick a Number and Double it Have students select a number between 1 and 10, then ask them to double it. Check their original numbers and doubles. Ask, ‘What do we do in our heads when we double a number?’ Ask them to double the number again and keep doubling until they are unsure what the next number is. Invite students to share their efforts. Ask students to enter 2 × 2 = in their calculator. Then have them press = and ask what they see. (If they keep pressing =, the numbers will double.) Encourage them to see if it works with other simple multiplication equations. Follow My Problem Write this on the whiteboard, without giving any verbal instructions: ‘Start with 4, double it, add two, subtract 1. Now continue the pattern and produce the next 3 numbers.’ Have students share the next three numbers they arrived at (19, 39, 79). Discuss the strategies they used. Ask, ‘What is the number pattern produced by the next three numbers?’ Have students continue the pattern for the next three numbers (using calculators if necessary), to verify that the pattern continues. Unit 20 Words and Numbers
81
Forgotten Numbers Ask students to make up and record word problems based around 17, e.g. ‘I had 22 eggs, I dropped 5; how many do I still have?’ ‘Sylvie had 20 stickers. She sold 7, then bought another 4; how many stickers does she have?’ Think of Two Numbers Have students suggest two numbers between 1–10 and write them on the whiteboard, e.g. 6 and 7. Create an addition and subtraction equation for each pairing: 6 + 7 = 13, 7 – 6 = 1. Invite students to suggest where these patterns also exist in larger numbers, e.g. 600 + 700 = 1 300, 7 000 – 6 000 = 1 000.
Small Group Focus — Applying the Concept Focus Teaching Group • o + o = e, e + e = e, o + e = o Place those three statements on the whiteboard: o + o = e, e + e = e, o + e = o. Ask the group, ‘Do you recognise this code?’ After finding the right answer, write the statements in long form: odd number + odd number = an even number; even + even = even; odd + even = odd. Ask students to write four examples for each statement; later, have them write a sentence explaining ‘why an odd plus an even number is always odd’. Share responses. • Oddly Even Give each student BLM 32 ‘Number Investigator’. Take the 3 × tables chart (BLM 75) and have students write down the pattern: 3, 6, 9, 12, etc, on BLM 32. They should apply place value to the columns, keeping tens and ones separate. Have them look at the numbers in the ones column; ask, ‘Can you see a pattern in terms of odd and even?’ Have them look at the other tables to see if there is a distinct pattern. Repeat these steps for all the tables. • Looked at the Tables Lately? Provide tables charts (BLMs 75 and 76) and ask students to identify any obvious patterns. Ask, ‘Can you see an obvious pattern in the 5 × table?’ (The ones digits go: 5, 0, 5, 0.) Have students write down any patterns they can see. The 9 × table has many patterns, e.g. tens and ones always add to 9; the ones in the product descend as the tens ascend.Work together to record the patterns.
Independent Maths Individual, pair, small group
Produce a Pattern Ask each group to work together to create a short challenging pattern that involves a combination of operations, e.g. add 6, subtract 3. Have them record the pattern on the back of a flash card; on the front of the card they should write three counting patterns that show how the pattern works. Have groups swap their cards (face down), then solve and extend each other’s patterns. Pick a Number and Halve it Have each group select ten even numbers from 200–1000 and see how far they can halve the numbers. Ask them to write down and record what happens to each of their starting numbers (the numbers stop when they become odd numbers). The number 224 can be effectively halved four times using this rule. Have the groups see if there are any numbers that can be halved further. Find My Phone Number Have students work in pairs, with each student focusing on their phone number. Ask each student to give written clues for each digit of their phone number that involve addition, subtraction, halving, doubling, multiplication and/or division. Each clue must have at
82
Nelson Maths Teacher’s Resource — Book 5
least four instructions and start with the first digit in the phone number, e.g ‘9 divided by 3, add on 4, take away 6 and double it’. (The numbers in the phone number so far are 9 and 2.) If this activity is too challenging for some students have them include only two or three instructions. Read and Solve (Student Book p. 56) Have students read the word problems and use their knowledge of the four operations to solve them. Seeing Patterns (Student Book p. 57) Ask students to use simple number patterns to produce six more examples that continue the pattern. Units 19–20 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 58).
Whole Class Share Time Have groups share examples; see if other members of the group can identify the pattern present. Ask, ‘Was there a specific card that was hard to solve?’ Highlight the difficult patterns; discuss the strategies needed to solve them. Have groups share what they learnt from this task. Ask, ‘When you halve a number, what process are you doing? How is the process different when you are dividing mentally?’ Today I created …
Have several students read out their ‘clues’; see if other members of the class can work out the number. Then ask the whole group, ‘What have we learnt from this task?’ Have students select and read out a problem. Ask the others in the group, ‘What operations are required here?’ Have students share the problems they created and have the class decide on the operations required. Invite students to give examples of each pattern; ask, ‘What have you noticed when you add odd and even numbers?’ Encourage students to share their addition patterns.
Unit 20 Words and Numbers
83
unit
Area
21 Measurement
Student Book pp. 59–60
BLMs 67 & 77
During this week look for students who can: • measure, order and record the area of regular and irregular shapes using both informal and formal units. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources Centicubes, Unifix, trundle wheel, flash cards (or Kinder squares) calculator, 4 m × 5 m grid marked in chalk on the netball court, card, A4 paper, dictionaries, newspapers, overhead projector, overhead transparencies, Kid Pix Studio Deluxe, Word, Inspiration 6, BLM 67 ‘Centimetre Grid’, BLM 77 ‘Island Life’ Maths Talk Model the following vocabulary in discussion throughout the week: measure, estimate, compare, formal, informal, units, metres, area, centimetres, squares, comparison, comparing, sensible, accurate, inaccurate
Whole Class Focus — Introducing the Concept What is Area? ‘Area’ is not a simple concept. Find out what students know by creating a brainstorming map (or use software such as Inspiration 6) before starting the unit. Use this initial discussion to review ‘perimeter’. Encourage students to add to the map as they find out more about area. Pencil Case Guess Have students bring their pencil cases to this session. Ask students to compare pencil cases, noting similarities and obvious differences. Ask, ‘How much area does your pencil case cover? How can we find out?’ Discuss responses, then have students empty and flatten their cases, and use Centicubes and Unifix to measure how many cubes and blocks it takes to cover the area of their pencil case. Area = L × W? Take the group outside and assemble them around the edge of the basketball (or netball) court. Bring trundle wheels and metre rulers. Ask, ‘How could we measure the area of this court?’ Discuss responses. Have students measure and record the length and width of the court, then use calculators to work out the area, using the formula: length × width. (A regulation basketball court is 26 m × 14 m = 364 square metres.)
84
Nelson Maths Teacher’s Resource — Book 5
Irregular Shapes Draw the closed curve of an irregular shape on a large sheet of paper. Ask, ‘How can I measure the area of this shape when there are no straight edges or sides?’Take suggestions from students, and explore their validity.Take white flash cards (or Kinder squares) and invite students to arrange them so that the irregular shape is covered as well as it can be. Count up the number of cards used and record a statement under the shape: ‘The area of the irregular shape is ____ flash cards.’ Big, Bigger, Biggest Have students draw several closed irregular shapes on an A4 sheet of paper. Then, without too much discussion, see if students can arrange themselves in order, from shapes totalling the least area to shapes totalling the greatest area.
Small Group Focus — Applying the Concept Focus Teaching Group • How Much Area Does A4 Cover? Give each student a sheet of A4 paper and ask, ‘How many hands cover this area?’ Have students trace a closed finger handprint onto a piece of cardboard as a template. Then have them trace their template ten times, cut out the copies and put them on the original A4 sheet, aiming to cover as much area as possible. Ask, ‘What strategies do you need to use to cover as much of the A4 sheet as possible?’ • How Much Area Does My Hand Cover? Provide BLM 67 ‘Centimetre Grid’. Have students trace their handprints (with fingers closed) onto the grid. Invite students to compare the size of their handprints. Ask, ‘Whose hand covers the largest area?’ Discuss responses; ask, ‘How can we measure whose handprint is biggest?’ Lead discussion towards the idea of numbering squares. Introduce the ‘1 and 0’ method of numbering squares, depending on how much of the square is covered. If a square is half or more than half covered by the handprint, number it ‘1’. If a square is less than half or not touched at all, number it ‘0’. Have students add up and compare the number of centimetres their handprint covers. • A Square Metre Tile Use large sheets of cover paper to create a tile that is one square metre. Have students measure the length and width of the sheet. Model the dimensions on the whiteboard; emphasise that area is calculated by multiplying length by width. Provide copies of the square metre and have student find examples of one square metre in and out of the classroom. Have students find the area of the space outside (chalked on the netball court) using their one square metre and laying it down repeatedly in the space. They can mark with chalk where the ‘tile’ is layed each time. Use the formula L × W = A to find the area students measured.
Independent Maths Individual, pair, small group
My Right Foot Have students work in small groups, each with a copy of BLM 67 ‘Centimetre Grid’. Have each student trace their right foot onto the grid.Then have them put a 1 in all the squares covered by the foot, or more than half covered; and a 0 in the squares outside the foot, or less than half covered. Have them add the numbers to find out how many square centimetres each foot covers. Ask students to sequence the feet, from largest to smallest area covered.Take the largest area foot and photocopy it onto an overhead transparency for comparison. Newspaper Area Provide whole sheets of two different-sized newspapers. Have students use the sheets to find the area of objects and Unit 21 Area
85
places in and out of the classroom, using both newspapers. Name the measurement units after the newspapers and have students record their findings, e.g. ‘The table top measured 6 Ages, but 10 Herald Suns’. Using Dictionaries as Units Have students work in small groups using books of common size, such as dictionaries, to measure the area of objects. Have groups nominate five objects that can be completely covered by dictionaries, or that can have their length and width determined and the area confirmed by using a calculator and the formula L × W. Encourage students to make estimates first and to record their findings. Swimming Pool Areas (Student Book p. 59) Have students calculate the number of square tiles required to cover the floor of pools A and B.They can then design two pools of their own and calculate the area of each. Students could use BLM 67 ‘Centimetre Grid’ to design other pools, then have a partner work out the area covered. Computer Pools Using Word or Kid Pix Studio Deluxe have students design pools using a 10 cm × 10 cm grid, and calculate the area each pool covers. Students could add clip art and flood-fill their designs to make them more interesting. Measuring Area (Student Book p. 60) Have students use Centicubes to calculate the area of the each island using the scale: 1 Centicube = 1 sq km. Then have them list the areas from smallest to largest. More Islands Have students design an island using BLM 77 ‘Island Life’. Make sure they include lots of bays and inlets. Students swap with a partner and work out the area of each other’s island. This activity could be also be done on the computer, using Word or Kid Pix Studio Deluxe. Students could add clip art and flood-fill their designs. Unit 21 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 61).
Whole Class Share Time Invite students to explain the steps involved in measuring foot area. Then have them use the overhead transparency to demonstrate the difference in area between the feet in the group.
Today I discovered …
The Age unfolded measures approximately 80 cm × 60 cm; the Herald Sun is 57 cm × 41 cm. Ask, ‘Which unit is more flexible when measuring large and small areas? What problems did you have when dealing with both units?’ Ask, ‘Are dictionaries a good choice for units of measurement?’ Encourage a variety of responses; seek examples of good and bad points. Ask, ‘How did you calculate the area of each irregularly shaped pool?’ Have students share their own pool designs. Have several students compare the figures they have for the area of each island. Ask, ‘Why would there be a difference in answers when the same islands are given to everyone in the group?’ Discuss reasons for the difference in answers.
86
Nelson Maths Teacher’s Resource — Book 5
unit
22 Number and patterns
More Multiplication and Division Student Book pp. 62–63
BLMs 33 & 74
During this week look for students who can: • make the connection between division and multiplication tasks • use a variety of computation methods to solve problems • use a calculator to solve decimal problems in everyday situations. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources http://www.prongo.com/lemon/game.html, collection of 5-cent coins, small baskets or containers, stopwatch, white flash cards, dice, calculators, counters, BLM 33 ‘Half, Please’, BLM 74 ‘Coins’ Maths Talk Model the following vocabulary in discussion throughout the week: computations, strategies, divide, calculate, round off, remainders, share between, methods, approaches, solve, whole numbers
Whole Class Focus — Introducing the Concept × and ÷ Travel Together Write this equation on the whiteboard: 125 × 3 = ? Ask a student to solve the problem, then discuss the computation methods used to reach the answer. Fill in the answer: 125 × 3 = 375. Now write up 375 ÷ 3 = 125. Multiplication and division are connected and, in this example, 125, 3 and 375 are the key players. Have students make up other 3-digit × 1digit equations and their corresponding division equation, and place them on cards.They can use the cards to play ‘Concentration’ or ‘Snap’. Five on the Floor Have students sit on the floor and close their eyes. Tip eight 5c coins onto the floor, then have students open their eyes and count what is on the floor. Invite the first student with a total to put up their hand. Repeat several times using different amounts. Ask, ‘What processes do you go through in a situation like this to work out the totals?’ Record the different responses. Half-price Tickets Certain airlines sometimes offer half-price tickets to various Australian destinations. Say, ‘If a full-price ticket is $520, what will the half-price tickets cost?’ Discuss the equation and the computation 1 needed to find 2 of 520. Have students demonstrate the methods they used 1 to solve the equation. Repeat, using 2 of $330, $780 and $620. Unit 22 More Multiplication and Division
87
Luggage and Trolleys Have students sit in a circle. Place 16 counters and 4 small baskets on the floor. Say, ‘Imagine you’re at an airport.’ Select a student to place the ‘luggage’ (the counters) evenly onto the four baggage ‘trolleys’ (the baskets); time their response time with a stopwatch. Time a second student completing the same task. Repeat, with variations: change the quantities of luggage, try the game in pairs, etc. Make sure the counters are always multiples of four so there are no remainders. Ask, ‘What must you look for when you complete this task?’ Calculator Round Off Each student will need their own calculator for this task. Have students enter: 16 ÷ 5 = . The answer is 3.2. Ask, ‘What does .2 mean?’ Discuss responses; emphasise that it means 2 parts out of 10. Ask, 2 ‘Where would you round this equation to, with 10 as the remainder: 3 or 4?’ Have students explain their reasoning. Repeat these steps with: 55 ÷ 7 = 7.8571428. Ask, ‘What do we have to do with this answer before we can round off to 7 or 8?’ Discuss responses, then round the number to 7.86 and ask students to round this off to the closest whole number.
Small Group Focus — Applying the Concept Focus Teaching Group • An Even Divide Write on the whiteboard: 186 ÷ 2 = ? Say, ‘The answer will be a whole number with no remainders. How can I tell this?’Together, look at the digit in the ones column; use students’ knowledge of number patterns to work out what other numbers might divide evenly into it (2, 3, 4, 7, 8, 9). Ask, ‘Why won’t 5 divide evenly into 186?’ Discuss responses. Provide students with five 3-digit numbers; have them guess which 1-digit numbers might divide into each one. Have students record these 1-digit numbers beside the 3-digit numbers, then check their guesses with a calculator, gaining a point for each correct guess. • Dividing Big Numbers Check on the methods used to divide large numbers by a single divisor. Put the equation 132 ÷ 2 on the whiteboard and ask a student to explain how they solved the task. Revisit place value: the 1 is really 100. Ensure that all understand that 2 into 13 is really 2 into 13 tens (6 with one ten remainder). Have students verbalise the methods and question when remainders are just placed in the next column down. Have students complete some similar division equations independently. • Sharing and Rounding Off Pose this question: ‘Three friends have $100 to share. How much will they each get?’ Have a student demonstrate the problem on the whiteboard as a division task. Ask, ‘What is the one remainder? What are the three friends really going to get?’ Have students enter the problem in their calculators: 100 ÷ 3 = 33.3333333. Ask, ‘How can we round that off to dollars and cents?’ ($33.34) Discuss responses, then ask, ‘In real life, what would happen to $100 shared among three friends?’ Share responses, and record the variations.
Independent Maths Individual, pair, small group
Match the Equations (Student Book p. 62) Students solve the multiplication equations, then use them to find the solution to the division equations. Lemonade Larry Have students work in pairs to log into http://www.prongo.com/lemon/game.html and solve the money equations with Lemonade Larry. Students complete ten questions then swap
88
Nelson Maths Teacher’s Resource — Book 5
positions. Partners check each other’s score count. Students not using the computer could play ‘Five on the Floor’ (the coin activity featured in ‘Whole Class Focus’). Provide coins from BLM 74 ‘Coins’. Have students take turns to throw down different amounts of 5c, 10c and 20c ‘coins’ for their partner or other group members to calculate mentally. Half, Please Give each pair BLM 33 ‘Half, Please’ and three dice. Players roll three dice, one at a time, record the number, then work out if they can evenly halve it. If students can halve the number, they should write the answer; if they can’t halve without leaving a remainder (e.g. half of 135 is 67.5) they put an ✗. At the end of each round, students use a calculator to check each other’s calculations. The winner is the player with the most correct calculations at the end of the game. Not All Will Share Have students work in pairs with a stopwatch and a container of counters. Players take turns to grab a handful of counters, pile them on the table, then group them equally in four piles while their partner times. It’s OK if there are remainders; have students state the number of piles and any remainder, e.g. ‘There are 4 piles of 8, with 2 remainder.’ Partners then swap roles. Round Off the Hours (Student Book p. 63) Students read the travel distances and use their calculators to work out the distance travelled per hour. They then round the display off to the nearest number of kilometres per hour and rank the trips by speed, from fastest to slowest.
Whole Class Share Time Have students share their equations; ask, ‘What do you have to take care with before matching up multiplication and division equations?’
Today I learnt …
Have students share their experiences on Lemonade Larry; ask, ‘What computations go on in your brain as you work out the necessary cash?’ Discuss the importance of 5 × tables when dealing with 5c quantities. Ask students in this group to explain the rules for ‘Half, Please’. Ask, ‘What have you learnt from this activity?’ Have students share their experiences with this game. Ask, ‘What strategies did you use to divide a big pile into fours?’ Discuss responses; have several students demonstrate their technique. Have several students rank the trips in terms of kilometres per hour; check against others in the group. Ask, ‘How did you round off the number of kilometres per hour into whole numbers?’
Unit 22 More Multiplication and Division
89
unit
Everyday Numbers
23 Number and patterns
Student Book pp. 64–65
BLM 34
During this week look for students who can: • create, name and rank decimal numbers in order • solve everyday problems by selecting the appropriate computation methods • use their knowledge of numbers to complete complex addition and multiplication tasks. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources assorted fruit and vegetables, kitchen scales, cutting board, cutting knife, stopwatches, supermarket flyers, bag of apples, bag of carrots, two oranges, Word, BLM 34 ‘Oranges Eaten’ Maths Talk Model the following vocabulary in discussion throughout the week: halves, quarters, whole numbers, reaction time, average, kilogram, weight, predictions
Whole Class Focus — Introducing the Concept An Apple a Day Place a bag of apples in front of students. Tell them that at your shop, all apples are 30c each. Ask, ‘How can we work out the price of the whole bag of apples?’ Emphasise the methods of calculation, rather than the total price. Record the approaches: doubling using known number facts (2 for 60c, 4 for $1.20, etc); 30c × number of apples; using a calculator to add 0.30; repeated addition of 30c on paper. Have students record the approach they feel confident with. Weight of an Apple Select a large apple. Weigh it on the kitchen scales. Record its weight, e.g. 190 g. Make sure students understand this weight as a decimal (in kilograms), i.e. 0.19 kg. Ask, ‘If the whole apple weighs 190 g (or 0.19 kg), what will half the apple weigh?’ Listen to responses, then cut the apple in half to check estimations. Do the same for a quarter of the apple; have students record what was done.
8 4 90
Cut Up the Oranges Take a knife and cutting board and cut an orange in half. Have students name the two parts (halves), then cut the halves into quarters and have students name them again. Cut another orange into 8 quarters, so you now have 8 quarters.Write the fraction: 4 . Ask, ‘What do we call eight quarters?’ Record responses. Say, ‘One whole orange plus another 5 quarter equals five quarters. What’s another name for five quarters?’ (8) Have students make a poster showing what can be done with 8 quarters.
Nelson Maths Teacher’s Resource — Book 5
Reaction Time Provide stopwatches. Have students measure their reaction time by pressing the on/off button as quickly as possible three times and recording the times, e.g 0.78, 0.67, 0.88. Have them highlight their fastest time. Discuss how the fastest time is actually the lowest decimal number. Share students’ best times, and rank the top five fastest times on the whiteboard in order. Ask, ‘What does 0.28 seconds really mean? What do the 2 and 8 really represent?’ Weigh Apple Pairs Provide kitchen scales, and 10 apples paired and labelled A, B, C, D, E. Model how to record the weight of a pair of apples as an equation, then total the combined weight, e.g. 290 g + 185 g = 475 g. Have selected students weigh other pairs and record the equation on the As an extension, whiteboard. Encourage students to use mental strategies to work out have students use calculators to combine all the apple weight the total. Share strategies. Write the combined weight of each pair of totals and convert the grams apples on card and place it in front of each pair. Now rank the apple to kilograms. pairs from lightest to heaviest. To further develop students’ understanding of related subtraction, say, ‘If a pair of apples weigh 490 g, and one apple alone weighs 250 g, how much does the second apple weigh?’ Share strategies and solutions.
Small Group Focus — Applying the Concept Focus Teaching Group • The Missing Apple Pose this problem: ‘If two apples have a combined weight of 570 g, and one apple weighs 225 g, how much does the other apple weigh?’ Discuss methods of computation: complementary addition, counting on, subtraction. Have students calculate the answer with pen and paper. Repeat, then have students complete further problems independently. • A Kilo of Carrots Have a 1 kg bag of carrots, and count them out, one by one, e.g. 12 carrots. Write this problem on the whiteboard: ‘If 12 carrots weigh 1 kilogram, will 6 carrots weigh 500 g?’ (Write 500 g in different ways 1 during this activity: 2 kg, 0.5 kg and 500 g.) Ask, ‘How can you check?’ Discuss suggestions, e.g. weighing all the carrots in the bag and halving the amount; weighing each carrot individually then adding to get the total and halving the amount; counting out half the carrots and weighing them. Have students try all the suggestions to see if the totals remain the same. • Price of an Apple Show supermarket flyers advertising fruit prices by the kilogram. Ask, ‘If apples are $2 per kilogram, how can we find out the price of one apple?’ Discuss students’ viewpoints, then model the halving approach: $1 for 500 g, 50c for 250 g, 25c for 125 g. Then weigh 3 to 5 apples to gain an average apple weight. Have students finish this exploration, recording the steps they have taken.
Independent Maths Individual, pair, small group
Junk Mail Presentation Provide supermarket flyers and have groups prepare small posters detailing the unit prices of fruit and vegetables. For example, tomatoes might be $5.00 kg; have students use calculator or pen and paper to prepare prices for 500 g, 250 g and 100 g of tomatoes. They should record these unit prices on the advertisements. 1 000 g = 1 kg Have students work in small groups using kitchen scales, recording the weight of 12 vegetables or pieces of fruit. Make sure students record each weight in grams and as a decimal of a kilogram, e.g. 360 g = 0.36 kg. Groups then rank their food items from lightest to heaviest. Unit 23 Everyday Numbers
91
Oranges Eaten Have students work in small groups; give each student a copy of BLM 34 ‘Oranges Eaten’, and a dice to share. The game involves finding the number of orange quarters eaten during a football match. Students roll the dice three times to find the number eaten at quarter time, half time and three-quarter time. They then count up the quarters eaten, giving the total as the number of whole oranges. As an extension, students could visit the Internet and find out the top five fastest times ever run over 100 metres, and the top fastest times in 50 metres freestyle swimming, and rank them from fastest to slowest.
Swimming Times (Student Book p. 64) Students look at the times swum by the eight swimmers, then rank them in order from fastest to slowest. Have students in groups of four run 100 metres. Have them use a stopwatch to time each run and then order the times from slowest to fastest.
Restaurant Meals (Student Book p. 65) Students have to create and solve addition equations to determine which restaurant served the most meals in a two-day period. The last two problems will require students to use subtraction and addition. Computer Problems Have students make up similar problems on a theme of their own, e.g. number of bikes sold in a bike store, number of CDs sold in a music shop. Extend the time period over two, three or four days and have them record their problem on a computer using Word. Units 22–23 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 66). Answers to Question 4 will vary.
Whole Class Share Time Have several groups show their posters; ask some groups to compare unit prices for common foods, such as bananas and potatoes. Have students display their work. Ask, ‘Can you think of a fruit or vegetable that weighs more than 1 kg (1 000 g)?’ Today I worked out …
Have groups share their experiences; ask, ‘How did you count up the quarters if you rolled a series of sixes?’ Discuss how a six is really 6 quarters, 1 or 1 2 oranges. Find out which lane was the fastest in the 50 metres freestyle. Ask, ‘If fast swimmers finish so close to each other, what do you have to look for in their times?’ Discuss the tenths and hundredths of seconds in the results. Ask, ‘Which restaurant sold the most meals over the two days? Which equation caused the most difficulty? Why?’ Have students share their solutions for the last two problems.
92
Nelson Maths Teacher’s Resource — Book 5
unit
24 Measurement
Volume Student Book pp. 67-68
BLMs 35 & 78
During this week look for students who can: • investigate volume and its relationship to capacity • use various informal and formal units to calculate the volume of everyday objects • identify successful and unsuccessful units for measuring volume • make and draw Centicube models. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources 525 g, 725 g and 800 g cereal boxes; small empty tissue box; three numbered boxes; Centicubes; marbles; Unifix; Lego; counters; table-tennis balls; chalk; tennis balls; cover paper; masking tape; Duplo; clean tetra-pak drink containers; attribute blocks; overhead transparency of BLM 78; overhead projector; assorted boxes; one-litre milk cartons; digital camera; PowerPoint, BLM 35 ‘Build This Box’; BLM 78 ‘Isometric Dot Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: capacity, volume, length, width, height, cubic centimetres, rectangular prisms, cubes, 3D, three-dimensional, isometric dots
Whole Class Focus — Introducing the Concept What is Volume? Introduce the term volume. Write the word on the whiteboard and brainstorm what students know about it. Have students look up the word in maths dictionaries: ‘volume’ is the amount of space an object occupies. At the completion of the discussion, make a class poster summarising what students know about volume. (Some students will confuse volume with capacity: capacity is the amount a container can hold.) What Measures Volume? Provide a collection of tennis balls and clean tetra-pak drink containers; ask, ‘Which of these objects is the best to measure the volume of a cereal box?’ Have a student fill a 525 g cereal box with tennis balls — without altering the outer shape. Record the number of tennis balls, then have students predict how many tennis balls will fill the 725 g cereal box. Fill the box and record the amount. Repeat the process, this time placing tetra paks in the cereal boxes. Ask, ‘Which units were better for measuring volume? Why were the tetra paks better?’ Emphasise the weaknesses of a tennis ball as a unit of volume. Unit 24 Volume
93
Big Blocks vs Small Blocks Take a small tissue box (top removed) and have students neatly pack medium-size Lego blocks into it; have them record its volume in blocks. Pass around a Duplo block and a Lego block; ask students to compare the amount of space that six of each block will take up. Have students predict how many Duplo blocks will fit into the tissue box, based on its known volume in Lego blocks. Record responses, then have students fit Duplo blocks into the tissue box. Same Volume, Different Formation Pass around three structures, all with the volume of eight Centicubes. Ask, ‘Which structure has the greatest volume?’ Share students’ answers; select students to make further examples of volumes that use eight Centicubes. Ask, ‘Can a set volume, such as eight Centicubes, appear in different forms?’ How Do You Draw a Cube? Use a set of eight Centicubes to construct a prism. Pass it around the group and ask, ‘How can we draw the volume of this prism?’ Display an overhead transparency of BLM 78 ‘Isometric Dot Paper’. Model how to use 3D drawings of blocks to show volume. Discuss the blocks that are seen and not seen.
Small Group Focus — Applying the Concept Focus Teaching Group • Pick a Box Place a collection of boxes in front of the group: assorted cereal boxes, tissue boxes, shoeboxes, lunch boxes. Revise the definition of volume: ‘the amount of space something takes up’. Ask students to rank the boxes from largest volume to smallest. Emphasise that the weight of a container has nothing to do with its volume. Have students take turns.Then pose a more complex task: ranking the lunch boxes only, from smallest to largest volume. • Volume is the Amount of Space it Takes Up Provide several empty one-litre milk cartons. Ask, ‘How much volume is there inside an empty litre carton?’ Discuss ways of measuring the ‘space inside’ the carton using Centicubes; allow students to experiment with filling with Centicubes. Discuss unit size; lead students towards the idea of building rectangular prisms that are the same size as the carton base, and using them to work out the answer. • Volume = Length × Width × Height Present a rectangular prism made from 12 Centicubes. Discuss the prism shape (3D, parallel bases, rectangular sides), then remind students about the meaning of ‘volume’. Ask, ‘What is the volume of this prism?’ Select students to count the Centicubes; record responses. Introduce the idea of a ‘formula’: the volume can be worked out by multiplying the length, width and height of the prism. Ask a student to build a prism from 8 cubes, then use it to test the formula.
Independent Maths Individual, pair, small group
Measuring Volume (Student Book p. 67) Provide three numbered boxes (all different sizes) and these measuring units: Centicubes, marbles, Unifix, counters, table-tennis balls, MAB tens. Students fill the boxes, one at a time, and record the number of units. They then assess which units were the best for measuring volume. Build a Box (Then Find its Volume) Give half the pairs an A4 copy of BLM 35 ‘Build This Box’; give the other half an A3 copy. Students cut out the net, fold up the sides and glue the edges. Set them the task of finding six
94
Nelson Maths Teacher’s Resource — Book 5
different types of objects that fit neatly into the box. Provide measuring units such as Centicubes, Lego, etc. Have students record the different volume for each item, e.g. ‘The volume of this box is 28 small Lego blocks.’ Build the Volume of 16 Centicubes Give each group 16 Centicubes and have them create a rectangular prism that uses all the Centicubes. Then, using cover paper, scissors and tape, have them create a folded container that will hold exactly the volume of 16 Centicubes. Students place the 16 cubes inside the box to check the dimensions of length, height and width. Repeat, using 16 Unifix, 16 Lego pieces, 16 Duplo, etc. Volume and Formation Give each group a specific volume to display, e.g. 8, 10 or 12 Centicubes. The group’s task is to build and record as many joined structures as possible that use that number of Centicubes. Have students use the digital camera to photograph each new structure. After six structures, the group can display their volume photographs using PowerPoint. Students without computer access can record their Have students with structures on BLM 78 ‘Isometric Dot Paper’. access to the computer experiment with the Autoshapes Make the Volumes (Student Book p. 68) Provide Centicubes function in Word to view 3D shapes and draw them in so that students have accurate models to copy. Make sure they use perspective. pencil so that they can alter their drawings if necessary. Unit 24 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 69).
Whole Class Share Time Ask, ‘Which box had the greatest volume?’ Discuss the different measuring units; ask, ‘Which unit was the best for measuring volume?’ Have teams share their experiences. Compare the volume of the A4 and the A3 boxes. Ask, ‘What do you have to be really careful with when you use units for measuring volume?’ Today I really liked …
Share students’ experiences; then ask, ‘What other objects are equal to the volume of 16 Centicubes?’ Have groups share their experiences; select one group to show their PowerPoint presentation on constructions that have the same volume. Ask each group, ‘What were the easiest forms to create with the volume you were given?’ Have students display the prisms they drew. Ask, ‘What was the hardest thing about drawing 3D shapes?’
Unit 24 Volume
95
unit
Chance
25 Chance and data
Student Book pp. 70–71
BLM 36
During this week look for students who can: • identify and order and apply possible outcomes with defined terms of chance • identify and record all possible outcomes in simple chance experiments • identify situations and activities that are fair or unfair • use the vocabulary of chance. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources dice, coins, games of chance, Excel, flash cards, BLM 36 ‘Dice Roll Record Sheet’ Maths Talk Model the following vocabulary in discussion throughout the week: chance, likelihood, likely, unlikely, possible, impossible, no chance, little chance, some chance, certain, uncertain, probable, always, never, sometimes, might, maybe, even chance, one-in-two chance, 50-50 chance, guess, fair, unfair, lucky, unlucky
Whole Class Focus — Introducing the Concept An Even Chance Produce a 20c piece. Say, ‘If I toss this coin, what are the chances I will toss a head?’ List suggestions on the whiteboard, e.g. even 50 chance, 50 , 1-in-2, fair chance. Ask students to select heads or tails, and to signal their selection by putting their hands on their heads or on their ‘tails’. Toss the coin several times, then see if any students want to change their selection. Ask, ‘What conclusions have you come to?’ Review other terms of chance for possible and impossible events (see ‘Maths Talk’). Have selected students suggest sentences about themselves that relate to each chance term, e.g. possible: ‘It is possible I will have pancakes when I get home from school.’ Two-coin Toss Have two 20c coins. Say, ‘What are the possible outcomes when you toss two coins?’ List the three possibilities: HH, TT, TH. Ask students to select an outcome, as follows: HH — both hands on their head; TT — both hands on their ‘tail’; TH — one hand on their head and one on their ‘tail’. Toss the coins three times; note the results. Discuss the results, then review the definition of ‘fair chance’. Ask, ‘Was there a fair chance of getting heads or tails? Was the outcome fair? What conclusion can you draw from this coin toss?’ Discuss suggestions, e.g. ‘There might be a fair chance of tossing heads, but the outcome can be all tails.’
96
Nelson Maths Teacher’s Resource — Book 5
Balls From a Bag Place three coloured balls (or counters) into a cloth bag without the class seeing them. Two balls must be of one colour, one of another. Carry the bag around the room, inviting 15 students to remove and replace one ball. Have a student record the colours on the whiteboard. Review the results; ask, ‘What colours do you think the three balls are?’ Note the answers, then reveal the true colour of the balls. Highlight the terms ‘fair’ and ‘unfair’; ask students to identify situations where the chances of winning are unfair, e.g. ‘A Prep boy playing basketball against a Year 6 boy.’ What Chance? Present this scenario: ‘One day, someone in this class will be the Prime Minister.’ Ask, ‘Does everyone in the class have the same chance?’ Consider factors such as age, exchange students in the classroom, parents relocating overseas, the need for Australian citizenship. Present another scenario: ‘One day, someone in this room will play soccer for Australia in the World Cup.’ Discuss the chance students have, and factors that make that chance unequal (currently males only; must have soccer skills; might hate ball games). Games of Chance Have students play board games that involve rolls of the dice, such as ‘Snakes and Ladders’ and ‘Life’. Afterwards, discuss the level of skill and knowledge required to play the games well. Ask, ‘Who could roll sixes every time? Was that skill or chance?’ Emphasise that luck plays a greater part than skill in games of chance.
Small Group Focus — Applying the Concept Focus Teaching Group • Least to Most Likely Prepare four flash cards marked ‘most likely’, ‘likely’, ‘unlikely’, ‘no chance’. Draw a large mountain on poster paper. Label the base camp and summit, and stage camps one-quarter, half and 3 three-quarters of the way up the mountain. Explain how mountains are 4 climbed in stages, with at least a day for each stage. Ask students to 1 sequence the ‘chance cards’ to show the chance of climbers reaching the 2 summit in one day. (The higher the starting point, the greater the chance.) 1 4 Discuss positioning of the cards, then attach them to the poster. Ask, ‘Can you think of any everyday activity we could apply this to?’ e.g. ‘The likelihood of all my family eating in a restaurant tonight.’ • Odds or Even Produce a 20c coin. Ask, ‘What chance I can toss heads?’ Discuss the ‘odds’. Say, ‘If I’m tossing the coin once, how many chances do I have of tossing heads?’ Discuss suggestions, then record ‘1 chance’. Ask, ‘How many faces does the 20c piece have?’ Discuss, then finish the sentence: ‘1 chance in 2’. Rewrite this as ‘1 in 2’. Say, ‘These are called odds. They really mean I have one chance in two possible outcomes of tossing heads.’ Ask a series of odds-related questions that go from least probable to most probable, recording responses each time, e.g. ‘What are the chances that I can roll a six? ... roll an odd or even number? ... roll a number less than 5?’ Give each student a copy of BLM 36 ‘Dice Roll Record Sheet’ and a dice and have them complete the task. • Fair or Unfair In this series of 30 draws, only one ball is drawn from the bag, recorded and then returned. Divide the group in half; give one group a cloth bag containing three balls of two colours (e.g. 1 red, 2 blue); give the other group a cloth bag containing four balls of two colours (e.g. 2 red, 2 Unit 25 Chance
97
blue). Ask each group to record their results for 30 draws. Compare the results for each group. Ask, ‘Which bag was fair? Which bag was unfair? What conclusions can you make when a fair and unfair situation are tested 30 times?’
Independent Maths Individual, pair, small group
It Just Isn’t Fair Provide each group with flash cards labelled ‘certain’, ‘perhaps’, ‘very unlikely’, ‘most likely’, ‘some chance’ and ‘no chance’. Have students sequence the cards. After checking the sequence, ask each group to record school situations for each chance card, e.g. ‘I am certain that I am in Grade 4 this year.’ ‘Perhaps it will rain this lunchtime.’ Fast finishers may like to extend the activity to sport or holiday issues.
Two-coin Research Provide each pair with two coins. Before commencing the task ask, ‘What are the possible outcomes when you toss two coins?’ Instruct each pair to record their results for 30 tosses of two Students could record their 30 coin tosses on a table coins. At the end of the experiment, have pairs tally their results they have devised on the computer for each of the three possible outcomes and write a statement about in Word or Excel. their investigation. It’s in the Bag Give each group a cloth bag containing three balls, each a different colour. Ask students to draw two balls out of the bag each time, record their colours and replace them. They should do this 30 times, recording their results. On completion, ask the groups to prepare an Excel graph showing how many times each colour was drawn over the 30 draws. Students could graph the results of their draws on the computer, using Word or Excel.
Four Counters, One Bag! (Student Book p. 70) Provide pairs with a cloth bag, 3 black counters and 1 red counter. Have students make 40 draws, recording their results each time. Your Chance in the Pool! (Student Book p.71) Students use chance phrases to place swimmers in the correct positions. They then select four chance phrases and write each one in a sentence. Unit 25 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 72).
Whole Class Share Time Discuss with the group the way they sequenced the ‘chance’ words, then have them share some of their school ‘chance’ scenarios. Choose partners to explain their findings from the two-coin toss. Ask, ‘Did any group have an even distribution of results?’ Ask all groups, ‘What would happen if we tossed the coins 300 times instead of 30?’
Today I did not understand …
Have students discuss their results from the 30 draws. Ask, ‘Can you see any similarities in your results?’ Invite groups to compare results to find out how many times each colour was drawn. Ask, ‘Did the results show that there were three of one colour and one of the other?’ Did any group have results that showed the red counter appeared more than ten times out of 40?’ Have students share their graphs and conclusions. Ask, ‘Which terms of chance were the hardest to place in the pool? Why?’ Check to see if all students have placed the terms of chance in the same order. Ask the group, ‘What did you learn from doing this page? How is it connected to a Chance topic?’
98
Nelson Maths Teacher’s Resource — Book 5
unit
26 Number and patterns
Numbers Close Up Student Book pp. 73–74
BLMs 20, 37, 38, 39, 75 & 76
During this week look for students who can: • use their knowledge of table facts and place value to solve problems • use mental and written strategies to simplify number tasks • use the calculator to perform number tasks. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources http://www.prongo.com/games/index.html, stopwatch, calculators, white flash cards, Blu-tack, BLM 20 ‘Decimal Points and Numbers’, BLM 37 ‘Number Dominoes’, BLM 38 ‘41 Up’, BLM 39 ‘Fabulous Four’, BLMs 75 and 76 ‘Tables Charts’ Maths Talk Model the following vocabulary in discussion throughout the week: rank, lowest, highest, digits, position, exact, approximate, rounding off, multiples, recall, facts
Whole Class Focus — Introducing the Concept Skip Counting Select two students to write on the whiteboard, choosing their own starting numbers between 1–10. Ask the class to suggest a number to count by, e.g. 2, 3, 4, 5, 10. The students at the whiteboard then have to write the next ten numbers from their starting number, in sequence. Phone Number Final 4 Ask four students to provide the last four digits of their home phone numbers. Write the 4-digit numbers on the whiteboard; ask students to rank them in order, from lowest to highest. Focus on the highest ranked 4-digit number; ask, ‘Can we make this number greater by rearranging the position of the digits?’ Look at each number in turn, and ask students to rewrite the digits to make the largest number they can. Alternatively, have students make their 4-digit numbers using number cards 0 to 9 (from BLM 20).These can be Blu-tacked to the whiteboard and rearranged accordingly. How Fast Are You? Use a stopwatch to time students as they record their 2 ×, 3 ×, 4 ×, 5 × and 10 × tables. You could make this more competitive by having students record the tables on the whiteboard; alternatively, students could just record the answers for designated tables. Unit 26 Numbers Close Up
99
Close or Not Close Have students enter this equation in their calculators: 17 ÷ 3. Write the equation and its answer (5.66666) on the whiteboard. Ask, ‘What is the exact answer to this equation? And what is an approximate answer?’ Put these possible answers on the whiteboard: 5, 5.66, 5.67, 5.7, 6. Highlight the merits of each possible answer and the context where each answer would be ‘correct’. Create a number line on the whiteboard showing all five answers. Ask, ‘If we want an answer to two decimal places, what is the real answer?’ (5.67) What Goes Together to Make One? This activity builds confidence with automatic facts and reminds students that numbers can be made in very different ways. Write on the whiteboard: 10, 20, 30. Select one of the numbers (e.g. 20) and ask, ‘What addition equations can you think of that equal 20?’ Record replies, e.g. 14 + 6, 11 + 9, 15 + 5. Repeat these steps for 10 and 30, creating a set of addition equations for all three numbers. Give students BLM 37 ‘Number Dominoes’ and have them create dominoes where one half of the domino has an equation that equals 10, 20 or 30, and the other half features a whole number not represented by that equation. Use the cards to play dominoes with the group.
Small Group Focus — Applying the Concept Focus Teaching Group • Factor Trees Draw a tree on the whiteboard. Write on its trunk: 24. Ask, ‘What numbers go evenly into 24?’ Model factors by placing numbers such as 3 and 8 in the branches of the tree. Repeat the activity with numbers such as 20, 32 and 48. Have students make their own factor tree for 56. • Multiplication Pairs Write on the whiteboard: 32. Ask students to write pairs of multiplication equations based on 32, e.g. 8 × 4 and 4 × 8. Have them write the equation pairs on either side of a flash card, and work in groups to find all the pairs of multiplication equations they can for 18, 32, 48 and 100. • 24: the Whole Story Have the group write 24 in the middle of a large sheet of paper. Ask, ‘What multiplication equations can we make that equal 24?’ List the facts, e.g. 6 × 4, 8 × 3, and make sure the commutative properties of 24 are understood, e.g. 3 × 8 and 8 × 3.Then create two division equations with each pair of multiplication facts. Ask, ‘What other ways can we show our knowledge of 24?’ e.g. double 12, halve 48. Have students complete the poster. As an independent activity students could create posters for 32, 40, 48, etc.
Independent Maths Individual, pair, small group
41 Up Give each pair a dice and a copy of BLM 38 ‘41 Up’. Students roll the dice twice: the first number is their starting point; the second number is the number they will count by. They mark the next 10 numbers in the pattern on the chart, using a coloured pencil, then write the numbers in the table. Make sure they use a different colour for each turn. The aim of the game is to reach 41; not all skip patterns will reach this. Partners then check each other’s patterns, count the squares crossed, and count the patterns that reached 41. Fabulous Four Give each group four dice and a copy each of BLM 39 ‘Fabulous Four’. Players take turns to roll all four dice, then make the highest and lowest numbers they can with the digits rolled. When each player has created their numbers, the dice are rolled again.
100
Nelson Maths Teacher’s Resource — Book 5
Prongo.com/Batter’s Up Baseball Have students access http://www.prongo.com/games/index.html. Instruct students how to play the single game where multiplication tables are used. Tables Race Copy BLMs 75 and 76. White-out the answers for each set of tables, keeping the sheets as masters. Photocopy these sheets a number of times and cut them into table strips. Give each pair of students three random table strips. Have one student in each pair use a stopwatch to time how long it takes their partner to complete one table strip. They can write the time at the base of the strip. Pairs then swap roles. The aim of the activity is for students to improve their table times over three tries. Repeat this activity regularly. Calculator Accuracy (Student Book p. 73) Have students use a calculator to work through each equation and determine whether it is correct or not. If the calculation is correct they colour the green square; if within five whole numbers of being correct, the yellow square; and if more than five whole numbers from the answer, the red square. Making Equations Easier (Student Book p. 74) Ask students to approach each stepping stone and join two numbers together to simplify the equations, following the example.
Whole Class Share Time Select a student to explain how ‘41 Up’ works. Ask, ‘Did anyone actually reach 41 in their 10 numbers?’ After discussion, ask, ‘Why do you think the game is called “41 Up”?’
Today I discovered …
Have students in each group check their answers to ensure they recorded the highest and lowest 4-digit numbers possible. Ask, ‘What was the highest number you could make with a 6-sided dice? And if you were using a 9-sided dice: what would be the biggest number possible?’ Check on students’ progress; ask, ‘Why do you think the makers of Batter’s Up Baseball give you options instead of asking for an answer?’ Ask students who completed ‘Tables Race’ if their table times improved by the third try. Have students check their own calculations. Ask students to nominate which colour they applied to each equation. For each boulder, ask, ‘What two numbers did you join to make the equation simpler?’ Responses will vary; encourage students to explain their approach if it varies from the expected response.
Unit 26 Numbers Close Up
101
unit
Numbers Beware!
27 Number and patterns
Student Book pp. 75–76
BLMs 40, 41, 42 & 79
During this week look for students who can: • use their knowledge of place value to round off and order numbers • use mental and written methods to simplify number tasks • skip count by 2, 3, 4, 5, 6 from any given number. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources strips of cover paper, cassette recorder, supermarket dockets, coloured whiteboard markers, flash cards, stopwatch, dice, BLM 40 ‘Hot Numbers’, BLM 41 ‘Are You Ready to Count On?’, BLM 42 ‘MAD Cards’, BLM 79 ‘5digit Number Expander’ Maths Talk Model the following vocabulary in discussion throughout the week: round up, round down, round off, extended notation, value, starting point, count on, largest, smallest, arrange, strategies, approaches
Whole Class Focus — Introducing the Concept Extend These Numbers Write on the whiteboard: 8 921. Ask a student to extend the number into 8 thousands, 9 hundreds, 2 tens and 1 ones. Make a number expander from BLM 79 ‘5-digit Number Expander’, and write 8, 9, 2, 1 on the appropriate folds. Ask, ‘What is the value of the 9 in this number?’ Repeat with 5-digit numbers, then have students make up their own number expanders and use them for extending 5-digit numbers. Pick a Number Have students select a number between 1– 20 and write it on the whiteboard. Invite other students to count on from that number by 2, 3, 4, 5 and 6. They should record the next five responses on the whiteboard using a different coloured pen. Have other students check their accuracy. Repeat, adding 100 to the starting number and selecting another group to skip count from that point. To the 5, to the 10 Write on the whiteboard: $3.36. Ask, ‘If this was the price of an item in a shop, how much would you actually pay at the cash register?’ Discuss methods and strategies for rounding up and down to the nearest five cents.Then have students round $3.36 to the nearest ten cents. Explain It Out Loud CDs are expensive items. Ask, ‘How could you work out the cost of nine CDs at $27 each?’ Place the emphasis on oral strategies for solving word problems; use a cassette recorder to tape students’
102
Nelson Maths Teacher’s Resource — Book 5
responses. Discuss common approaches, e.g. ‘9 twos are 18, so 9 twenties are 180; 9 sevens are 63, that means 63 and 180 is 243.’ Repeat, using similar amounts. Discuss the strategies students used. Popular 36 Have students write 36 in the middle of an A4 sheet of paper. Ask, ‘What multiplication equations equal 36?’ Model the task on the whiteboard, recording equations such as 9 × 4, 4 × 9, 3 × 12, 6 × 6. Repeat the task, searching for division equations that begin with 36. Record the responses, e.g. 36 ÷ 4 = 9, 36 ÷ 12 = 3. Then have students circle the division and the multiplication equations that are directly related. Ask, ‘What aspects of these equations link them together?’ Repeat, using 60, 54 and 72.
Small Group Focus — Applying the Concept Focus Teaching Group • Hop to it Numbers Write these numbers on flash cards: 1 787, 2 817, 3 928, 4 859, 5 028, 6 178, 7 133. Have seven students take the cards; ask them to order themselves from smallest to largest, without talking. Use a stopwatch to time them as they do this. Ask, ‘What place-value aspect of the numbers gives you the greatest sense of order?’ After discussing the value of the digit in the thousands place, repeat the task with sticky labels over the digits in the thousands place. Ask, ‘Which place did you use this time to order yourselves?’ Discuss responses. Record other numbers on the whiteboard and have students work independently to record their order from smallest to largest. • Hot Hundreds Cut out these numbers from BLM 40 ‘Hot Numbers’: 2 817, 2 783, 2 659, 2 568, 2 419, 2 399. Shuffle the cards and give them to six students. Have the students — without speaking — place themselves in order from largest to smallest number. Discuss the order the students have arrived at. Ask, ‘How did you decide on the order? What strategies did you use?’ Invite responses, then ask, ‘Can the hundreds column always help you to order 4-digit numbers?’ Have the students discuss their opinions on ordering numbers. Record other 4-digit numbers on the whiteboard and have students record their order from smallest to largest independently. • Big Numbers, Close Together Cut out the remaining numbers from BLM 40 ‘Hot Numbers’: 2 222, 2 220, 2 202, 2 200, 2 022, 2 220. Go through each card to familiarise students with the numbers. Ask a group of students to order the cards from smallest to largest — without talking. Note the strategies used; when they are ordered correctly, discuss the students’ approach. Ask, ‘Why did you think I selected those six numbers?’ Discuss the strategy of looking beyond the first digit to order a series of numbers. Have students discuss their opinions on ordering numbers. Record other numbers on the whiteboard and have students record their order from smallest to largest independently.
Independent Maths Individual, pair, small group
Big Numbers (Student Book p. 75) Explain each task on the page so that students can complete the set tasks. Highlight the relevance of place value in Question 4, especially when finding the value of 7 in a number such as 5717. Count On: Are You Ready? Have students work in threes. Give each group a dice and two copies of BLM 41 ‘Are You Ready to Count On?’ Two players roll the dice to establish their starting number, which they record. The third player is the judge. The judge rolls the dice to establish the Unit 27 Numbers Beware!
103
numbers the players will count on by.The players record the digits rolled in the ‘Count on by’ column. After both players complete their counting tasks, the judge checks the results, then rolls the dice again. Round Off the Money Have students work in small groups. Provide the collection of supermarket dockets and ask students to select ten items from one docket. Have students record on paper the actual price of each item in one column and the rounded-off price in the next column. Students then work out if you pay less or more when individual prices are rounded off rather than the total. Solving Money Problems (Student Book p. 76) Have students read through Question 1a, where four CDs are purchased.Tell students to model their explanations on this example, then have them solve the rest of the problems without calculators. MAD Cards Give copies of BLM 42 ‘MAD Cards’ to each group. Have students prepare cards featuring pairs of multiplication and division equations that have direct relationships to each other, e.g. 4 × 12, 48 ÷ 4; 18 ÷ 3, 6 × 3; 27÷ 9, 3 × 9. They should write one equation on each card. Then have them use the cards to play ‘Snap’, ‘Concentration’ or dominoes. Emphasise that the connection between cards is the relationship between equations, not the answer. Units 26–27 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 77).
Whole Class Share Time Ask, ‘What have you been doing with numbers in this activity?’ After explanations, have a student extend 10 001, for example, to the whole class. Have students explain their game to the group; pose the question, ‘What numbers do you hope to avoid when you are counting on?’ Today I really liked …
Have several students explain the task. Discuss whether consumers pay more or less when individual items are rounded up or down. Ask, ‘Why do shops round up and down to the nearest five cents? Are we lucky that shops only round off the totals?’ Ask, ‘Why are we explaining how we reached the answers, rather than writing down the equations?’ Ask students to explain how they set up the game. Ask, ‘Why don’t you write the answers on the MAD cards?’ Have students demonstrate a brief version of the game.
104
Nelson Maths Teacher’s Resource — Book 5
unit
28
Capacity Student Book pp. 78–80
Measurement
BLMs 43 & 65
During this week look for students who can: • • • •
make predictions about capacity make connections between function and the use of litres or millilitres use containers of various units to conduct capacity experiments identify the relationship between capacity and volume.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources collection of plastic bottles (250 mL, 375 mL, 500 mL, 600 mL, 1 litre, 1.25 mL, 2 litre), assorted medicine cups, eye dropper, teaspoons, measuring cups and water trough, wet area, buckets, Excel, maths dictionaries, BLM 43 ‘Investigating Millilitres’, BLM 65 ‘My Graph’ Maths Talk Model the following vocabulary in discussion throughout the week: litres, millilitres, estimate, measure, suitable, unsuitable, accurate, dosage, capacity, volume, occupies
Whole Class Focus — Introducing the Concept What Do We Know About Capacity? Conduct a brainstorming session to establish students’ pre-existing knowledge of capacity. Ask, ‘What do we know about capacity?’ Accept answers that don’t have anything to do with measurement of containers, e.g. ‘the capacity of the MCG is 95 000 people.’ Emphasise the difference between volume and capacity: volume is the amount of space an item takes up; capacity is the amount a container can hold, i.e. a 250 mL can of drink holds 250 mL of liquid. Have students check a maths dictionary for both definitions. Include in the brainstorming how capacity is measured: litres, millilitres, cups, caps, containers, etc. Also include the abbreviations mL and L. How Many? Cover the labels on a 1 litre container and a 250 millilitre fruit drink. Present both containers. Have students predict how many small containers it will take to fill the big one. Record the predictions, then have students use the smaller container to fill the larger one with water. Discuss the amount each container holds. Ask ‘If the big bottle holds 1 litre, how much does the small container hold? What fraction of 1 litre does the small container contain?’ Unit 28 Capacity
105
10 mL is Not Much Provide water, a collection of medicine cups, teaspoons and an eye dropper. Have students cover the markings on the medicine cups and estimate what 10 mL looks like. Then have them accurately measure 10 mL, and carefully spill it onto paper. Encourage them to see if they can spread the 10 mL all over the paper. Have students use an eye dropper to collect 10 mL. Ask, ‘How much do you think a teaspoon will hold?’ (Generally 5 mL.) Add two teaspoons of water to a measuring cup and see if this is accurate. Set this challenge: ‘How many lots of 10 mL will it take to fill a pop-top drink bottle?’ Litres: When Do We Use Them? Give each student a piece of A4 card so they can prepare a poster. Conduct a brainstorming session on the question: ‘Where do we use litres?’ Have students record in pictures and words situations where we use litres: buying petrol, washing machine loads, large soft drink bottles, milk containers, swimming pools, liquid chlorine, lawn mower fuel, oil, etc. Have students display their posters; ask, ‘Why is the volume of some liquids measured in litres?’ Discuss responses; emphasise that large amounts of liquid, e.g. petrol and water, are easier to measure in litres. (This activity will take longer than the session time.) Millilitres: When Do We Use Them? Discuss and review where litres are used in everyday situations. Brainstorm situations where millilitres are used: medicine, eye drops, drinks, shampoos, aftershave, perfume, sunblock. Have student make a poster about everyday mL usage. Display the posters; ask, ‘If millilitres are so useful, why don’t liquids such as shampoo come in one litre containers?’ Discuss responses, emphasising portability and practicality: small containers are for liquids used in small amounts. (This activity will take longer than the session time.)
Small Group Focus — Applying the Concept Focus Teaching Group • Guess How Much of a Litre Revisit the litre. Write on the whiteboard: ‘1 L = 1 000 mL.’ Ask, ‘What will half a litre be?’ Have a 500 mL bottle to show (e.g. a mineral water bottle). Ask, ‘Which measure is more suitable for personal drinking?’ Discuss the size and suitability of drink bottles. Pass the empty litre bottle around; have students stick named labels on the bottle to indicate where they think half a litre will come up to. Fill the 500 mL bottle with water and pour it into the one litre bottle; note down whose estimate was closest. Now ask selected students to half fill an unmarked litre bottle; (use a measuring cup) to see who was closest. • Small into Big Provide water and unlabelled 1 L and 250 mL containers. Present an unlabelled 250 mL pop-top container; ask, ‘How many small bottles will it take to fill a 1 L bottle?’ Have students make predictions, then select a student to fill the litre bottle. Check and discuss estimates. Repeat, using 750 mL and 2 L bottles. Have students record their discoveries. • Let’s Make Some Equations Provide a collection of 500 mL, 750 mL, 250 mL and 1 L containers. Have students make equations using just the bottles, e.g. 4 × 250 mL bottles = 1 L; 500 mL + 500 mL = 1 L. Students can then record their 3D equations on paper.
106
Nelson Maths Teacher’s Resource — Book 5
Independent Maths Individual, pair, small group
Three Attempts Please Have students work in small groups. Provide an opaque 600 mL container. Have students attempt to fill half the container by estimation alone. They check their estimate by pouring the water back into a measuring jug and noting how close they were to 300 mL. Provide clean 600 mL milk containers; ask each student to repeat the task ten times then graph their results.The group should analyse each member’s results to see if their estimates became more accurate. A Millilitre Investigation Have students work in small groups. Place twelve 250 mL drink containers around the classroom, each containing a different amount of water. Label the bottles from A to L. Give each group a measuring cup and BLM 43 ‘Investigating Millilitres’. Students’ aim is to estimate the capacity of each container, measure the capacity, record the details, then pour the water back in its original container without spilling! Each group can record their findings on an Excel spreadsheet where ‘Bottle A’ to ‘Bottle L’ is placed in Column 1 and the number of mL in Column 2. Students without computer access can record details on BLM 65 ‘My Graph’. Millilitres for Medicine (Student Book p. 78) Have students read the instructions and work out the different dosages required. When and Where: L or mL? (Student Book p. 79) Students are to draw and name situations where millilitres and litres are used. Graphing Millilitres (Student Book p. 80) on the graph to answer the questions.
Students use the information
Unit 28 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 81).
Whole Class Share Time Have groups share their findings. Ask, ‘With a non-transparent container, how do you guess what half the container is?’ Today I found out …
Ask students what they have learnt from this activity. Have groups compare the results and display their graphs. Have students share some of their answers about doses of medicine. Ask, ‘Why do different ages have different dosages?’ Have students display their work; ask, ‘Which is easier to find: items measured in mL, or items measured in litres?’ Encourage students to share their thoughts on gaining information from graphs. Ask, ‘Was it difficult to calculate the exact measurements of any of the bottles?’
Unit 28 Capacity
107
unit
Fractions as Operators
29 Number and patterns
Student Book pp. 82–83
BLMs 17, 18 & 68
During this week look for students who can: • work with fractions to create and solve word problems • use fractions as an operator when dealing with amounts, length and groups of objects • identify and order fractions according to size. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources 24 small chocolate bars (e.g. Crunchie), calculator, 80 cm and 120 cm lengths of coloured stripping, stopwatch, flash cards, counters, Excel, Word, Kid Pix Studio Deluxe, BLM 17 ‘Fraction Wall’, BLM 18 ‘Build Your Own Fraction Wall’, BLM 68 ‘Fraction Cards’ Maths Talk Model the following vocabulary in discussion throughout the week: numerator, denominator, share, split, divide, distribute, evenly, fraction, part of, greater than, less than, equal to, order, rank
Whole Class Focus — Introducing the Concept More is Less Place 20 Unifix in a pile; have one student count them. Ask another student to divide them in half and record the matching 1 equation: 2 of 20 = 10.
Jumble the cubes together; ask another student to divide them into 10 equal 1 piles. Ask, ‘What equation have we created?’ ( 10 of 20 = 10) Record the equation, then ask, ‘How come we get less when objects are split into tenths than when they are split into halves?’ Discuss, emphasising that 10 is bigger than 2 on the number scale. Have students make statements identifying the denominator as a factor of division, e.g. ‘The denominator tells you how 1 1 many piles to divide into: 2 of 20 means 2 piles. 4 of 20 means 4 piles.’ What’s in a Line? Provide pre-cut 120 cm lengths of stripping in different colours. Have students fold the stripping in half. Ask, ‘What have you created now?’ Record responses, e.g. 2 halves, 2 equal lengths. Ask students to fold one of the halves in half again; ask again, ‘What have you created now?’ Emphasise that half of a half is a quarter. Have students carefully cut off one quarter piece, swap it for one of another colour and tape it back on
108
Nelson Maths Teacher’s Resource — Book 5
3
with clear tape. Now they will have 4 in one colour and students make statements about what they have done.
1 4
in another. Have
Fractions as Words Write this word problem on the whiteboard: ‘A bag of Crunchie bars was opened and 24 Crunchies were counted out.They were to be placed in 4 equal bags. How many must go in each bag?’ Ask students to read the problem; ask, ‘Who can see what we have to do here?’ Listen to responses and record what actions must take place. Ask students to identify the key words: placed, equal, each; list other words that occur in fractional word problems, e.g. share, distribute and divide. Have students create their own fraction word problems about the 24 Crunchie bars. Word Problems Work with students to create word problems about a packet of 24 Crunchie bars, e.g. ‘Sean opened the bag of 24 Crunchies and 1 3 of them fell out. How many were left?’ Encourage students to be as creative and humorous as possible. At the end of the task, compile a list of the most challenging fraction word problems, then have students solve them. What Are We Really Doing? Write this equation on the whiteboard: 1 1 2 of 12. Ask, ‘What process are we really doing when we say 2 of 12?’ Invite responses, emphasising the links between division and fractions and of. 1 Point to the equation again and ask, ‘As a division equation, what is 2 of 12?’
Small Group Focus — Applying the Concept Focus Teaching Group • Bigger Fractions Provide a container of Unifix. Sit the group in a circle 1 1 and place 12 Unifix in a pile. Write on flash cards: ‘ 3 of 12’ and ‘ 4 of 12’; 1 place the cards near the Unifix. Ask, ‘What do we have to do to show 3 of 12 blocks?’ Have a student show how the group is split into thirds. Fill in the 1 card so it reads ‘ 3 of 12 = 4’.
Put the Unifix back in a pile, then have a student show how to divide the 1 group into quarters. Fill in the card: ‘ 4 of 12 = 3’. Say, ‘From this example, what can you tell about splitting groups of objects into thirds and quarters?’ Have students make statements about the fractions, e.g. ‘A third is more than a quarter.’ Discuss the statements, then ask, ‘If your friend had 24 1 1 Easter eggs, would you rather eat 3 or 4 of them?’ Emphasise that the higher the denominator, the less you get. • What’s Half of a Half? Provide 80 cm lengths of coloured stripping. Have students fold the stripping to create two halves, then take one half and fold it into quarters, then into eighths. Have students label the fractions with pen and display their work. • Shuffle a Fraction Have students cut cards from BLM 68 ‘Fraction Cards’. Have on hand a stopwatch and a completed copy of BLM 17 ‘Fraction Wall’. Shuffle the cards, select four and place them face down. Time how long it takes a student to turn the fractions over and place them in order, from smallest to largest. They can refer to the Fraction Wall if needed; when timing has stopped, others can check the fraction order. Repeat several times. Unit 29 Fractions as Operators
109
Independent Maths Individual, pair, small group
How Many in Our Class? Have students work in pairs, using the number of students in the class to create a poster entitled ‘Fractions in Our Class’. 1 4 Every number has its fractions, e.g. 25 students: 5 of 25 = 5, 5 of 25 = 20, etc. How they present the fractional data is up to each group. Fractions with Counters Give each group 50 counters. Ask them to create fractions about the 50 counters. One member of the group records 1 1 the fractions as they are created, e.g. 5 of 50 = 10, 10 of 50 = 5, etc. Computer Fractions This activity could also be presented on the computer using graphing software, Kid Pix Studio Deluxe, Excel or Word. Students could make a table, pie chart or grid with 25/50/100 cells (or rows or columns, 1 depending on their level of understanding). They then shade or flood-fill 5 , 1 for example, to indicate the fraction, and write below, 5 of 25 = 5. Fraction Problems (Student Book p. 82) Have students read through the problems. Each problem requires a fraction equation and a drawing. Fractions of the Road (Student Book p. 83) Students require rulers and a calculator to find a fraction of each road. In Question 5, students are required to put all the fractions on one road. Fraction Wall, Money and a Calculator Have students work in small groups with a calculator and a copy each of BLM 17 ‘Fraction Wall’. Have students write an amount of money on the top line of the wall, e.g. $400. 1 1 They divide the amount by 2 to find 2 ($200), and by 3 to find 3 ($133.33), etc. Complete the task by rounding off difficult amounts. Computer Wall The above activity could also be performed on the computer using Word. First, have students follow the procedure on BLM 18 to make a fraction wall, then have them divide an amount of money into halves, thirds, quarters, etc. Unit 29 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 84).
Whole Class Share Time Have several groups share their posters; discuss the class fractions they created. Ask, ‘What is the most complex fraction you were able to create? Why is it complex?’ Today I discovered …
Have groups explain what they did. Have them share some of their ‘50 fractions’. Ask ‘Why were each group given the same number of counters to start with?’ Share responses; ask students what they learnt from this activity. Have students share their work; ask how they have shown selected fractions. Ask, ‘What clues do you look for when dealing with fraction word problems?’ 1
Ask, ‘What steps were required to find where 2 was situated on the road?’ Have students compare their ✗s to check their accuracy. Have selected groups share their ‘fraction money walls’; other groups can check the fractions using calculators.
110
Nelson Maths Teacher’s Resource — Book 5
unit
30
Location Student Book pp. 85–86
Space
BLMs 67 & 80
During this week look for students who can: • • • •
use grid references to locate specific venues use cardinal compass points to plot pathways plan and draw locations from a bird’s-eye view use and understand turns in terms of degrees.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources cassette recorder, street directories, atlases, maps, drawings of the school, maps of Australia, skateboards, Word, Excel, BLM 67 ‘Centimetre Grid’, BLM 80 ‘Grid Coordinates’ Maths Talk Model the following vocabulary in discussion throughout the week: degrees, bird’s-eye view, north, south, east, west, coordinates, location, direction, position, near, grid, route, compass, cardinal points, compass rose, path
Whole Class Focus — Introducing the Concept Like 360° Wow! Introduce the concept of a circle being divided into degrees. Ask, ‘What does “doing a 360” mean?’ Discuss examples, e.g. turning full circle on a boogie board or skateboard. Ask, ‘Why do you think it’s called a 360?’ Introduce the idea of a circle being divided up into 360 degrees. Ask, ‘If a 360° is a full circle, what would a 180° be?’ Draw a circle on the whiteboard and divide it into quarters. Ask, ‘If a full turn is 360°, then how many degrees is a quarter turn?’ ‘How many degrees is a three-quarter turn?’ Have all students face the front and close their eyes. Agree that the front of the classroom is 0° (and 360°). Say, ‘Turn right 90°.’ Then, when completed, ‘Turn right another 90°.’ Repeat, nominating and varying the number of degrees, having students turn always to the right. I’m New Here Discuss the experience of being new in school. Ask, ‘If you had to give directions to a new student so they could get to the office, what directions would you give?’ Tape several students’ instructions using a cassette recorder. Play back the tape to the class; point out and record the ‘location language’ used, e.g. straight ahead, down, go outside, turn right. Bird’s-eye View Ask, ‘What does it mean to have a bird’s-eye view?’ Ask students to pretend they are sitting on the roof of the classroom looking down. Work together to make a bird’s-eye plan of the classroom on the whiteboard. Unit 30 Location
111
Grids Like Us Provide a map of Australia with grids and coordinates on it (or have students work with atlases). Use the map to revise the use of letter and number coordinates, and the order they are written. Make a sign for the class: ‘When reading coordinates, remember: letter first, then number!’ Select a city and ask students to find where it is on the map. Do this several times, then write the coordinates of a specific city and have students use the grid to locate it. North is North Use a compass to show where due north is. Place a large sheet of butchers’ paper on the floor; draw an arrow pointing north on the paper. Ask, ‘If we have located north, where are the other three main compass points?’ Write the cardinal compass points on the whiteboard; encourage students to state where they think the compass points are, and discuss their reasons, e.g. ‘The sun sets in the west, so west must be in the direction of the park.’
Small Group Focus — Applying the Concept Focus Teaching Group • Never Eat Soggy Weetbix! Draw a compass rose on the whiteboard, minus the cardinal points. Blu-tack a map of Australia next to the rose, with all the states shown and named. Ask, ‘How does the map of Australia help of us work out cardinal compass points?’ Highlight those states with compass points in their names, e.g. Western Australia. Recite the compass mnemonic: Never Eat Soggy Weetbix. Ask, ‘Can you make up a another sentence to remember the compass points?’ • My School Have students open the street directory to the map that features the school. Give the grid reference for the school and see if students can find it. Ask students who live near the school, ‘What are the coordinates of your street?’When they have found their street, have them trace the route they take to school, using the compass rose to name each different direction they take. Select landmarks around the neighbourhood (e.g. shops, parks, churches, etc), and have students work out which compass direction the landmarks are in from the school. Have students work independently to record how they get from their home (or school) to another location on the same map. • My Map Have students turn to a map of Australia in the atlas. Have them discuss the features of the continent, using their hands as measurement 1 units, e.g. ‘Australia is the width of 1 2 handspans’, ‘Queensland is as wide as the length of my fourth finger.’ Discuss other ways of approximating the size of Australia and its states.Then, using only the atlas page as reference, have students copy the map of Australia on A4 paper — without tracing!
Independent Maths Individual, pair, small group
112
Follow Me Please! Have partners sit back-to-back, each with a copy of BLM 67 ‘Centimetre Grid’. Students take turns to be the ‘leader’. The leader must give 10 instructions, starting in the bottom left-hand corner of their grid, drawing the path on their own sheet as they go, e.g. ‘Go north for 11 squares, turn right 90° and move 6 squares, etc. After the 10 instructions, the leader and the follower compare their paths, then reverse positions. Encourage vocabulary associated with location including 90° and 180° left and right. Computer Follow Me This activity could also be done with two students sitting side by side using computers. Have them make a 10 × 10 or 20 × 20 grid in Word; the leader then provides instructions as they both track their
Nelson Maths Teacher’s Resource — Book 5
way across their individual grids. Have students put an ‘✗’ in their cell after 10 instructions, then compare positions. Partner Guide Me Have students work with a partner; each pair will need a street directory map showing the school and surroundings. Have each student plan a trip from school to a nearby location (e.g. a street, park or shopping centre) that involves ten instructions. The instructions can only include street names and ‘turn right’, ‘turn left’, ‘go straight ahead’ and ‘stop’. After completing the instructions, partners sit back-to-back, and take turns to talk their partner to the destination. Bird’s-eye View of a Bedroom Give each student BLM 67 ‘Centimetre Grid’ and have them work individually to prepare a bird’s-eye view of their bedroom. Before starting, discuss the items to be included: bed, table, windows, wardrobe, door, rug, etc. Ask, ‘What would the top of a wardrobe look like? What about the top of a lamp?’ Secret Message (Student Book p. 85) Students use the grid coordinates to solve the puzzle. They can then make up their own puzzle using BLM 80 ‘Grid Coordinates’ for a friend to solve. Students could also produce their own puzzles on the computer using Word or Excel. Action Land! (Student Book p. 86) Before letting students complete the task, revise the concept of ‘to’ and ‘from’ in terms of cardinal compass points. Ask, ‘If you fly from Queensland to Melbourne, what direction are you travelling?’ Unit 30 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 87).
Whole Class Share Time Ask partners, ‘Which was the hardest position: leader or follower? Why?’ Check with other groups to see where most incorrect positioning occurred. Draw up a chart with three columns labelled ‘Plus’, ‘Minus’ and ‘Interesting’ and record a PMI about the positive and negative aspects of being a follower and a leader.
Today I created …
Discuss the impact of having only ten instructions. Ask questions such as, ‘Who experienced trouble guiding their partner? If you could have more instructions, what would you include?’ Discuss the bird’s-eye view drawings. Ask, ‘Which features were difficult to draw from above? What are the key elements to remember when drawing a view from above?’ Have students show their responses; check for errors, then ask, ‘What do you have to remember when dealing with letter/number coordinates?’ Select a student to describe how they navigated through ‘Action Land’. Then ask, ‘What was difficult about completing a task such as this?’
Unit 30 Location
113
unit
Mass
31 Measurement
Student Book pp. 88–89
BLMs 44 & 65
During this week look for students who can: • estimate the mass of items in grams and kilograms • use and apply the appropriate mass units to measure objects. When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources bathroom scales; pan scales and weights; kitchen scales; Excel; Word; unopened 725 g box of breakfast cereal; vegetables; 1 kg bag of sugar; 2 kg bag of sugar; a collection of 24-, 48- and 96-page exercise books; BLM 44 ‘Weight of Eight’; BLM 65 ‘My Graph’ Maths Talk Model the following vocabulary in discussion throughout the week: gram, kilogram, estimate, mass, measure, balance scales, difference, more, less
Whole Class Focus — Introducing the Concept How Heavy? Provide a pan balance. Have students choose two items in the classroom that are light and close to each other in mass. Select students to stand in front of the group and predict, by hefting, which item is heavier, e.g. chalk or the pen lid? Then have them use a pan balance to see which item is heavier. Keep a tally on the whiteboard of Correct and Incorrect Guesses. Above and Below 500 g Prepare headings on two posters: Classroom Objects Below 500 g, and Classroom Objects Above 500 g. Have students collect classroom items and weigh them on kitchen scales to find out if they weigh less than or more than 500 g. They then select the appropriate poster and either write about or draw the item. Ask, ‘What does 500 g feel like?’ Weigh Eight Provide bathroom scales and kitchen scales. Tell students the aim of this task is to collect eight objects that when weighed total 10 kg. Select eight students to collect a classroom object each. After students have collected their objects, ask the class to estimate the total weight. Use the bathroom scales and/or kitchen scales to weigh each object and record its weight in kilograms on the whiteboard, e.g. 2.3 kg. Total the individual amounts (using a calculator or pen and paper calculations). Ask, ‘How close was our estimate?’ Round off the total to the nearest kilogram. Repeat the task. Ask, ‘Was our estimate closer this time?’
114
Nelson Maths Teacher’s Resource — Book 5
Pencil Case Dilemma Have five students volunteer their pencil cases for this task. The aim of this activity is to rank the pencil cases in order, from heaviest to lightest. Encourage students to estimate the order, then arrange the pencil cases in that order. When the group is happy, weigh each pencil case and record its mass. Compare the results with the students’ estimate. Mystery Masses Provide a selection of grocery items. Put a sticker over the printed mass on each item, then have students guess whether the item would have its mass calculated in kilograms or in grams. Discuss students’ guesses.
Small Group Focus — Applying the Concept Focus Teaching Group • Using a Pan Balance and a Kitchen Scale Use kitchen scales to weigh a collection of items from around the room, as well as full cans, cereal packets, etc. Record the mass of each object weighed. Ask, ‘Can we expect the same degree of accuracy when we use the pan balance? Why not?’ Have students weigh the same objects using pan balances and note down any obvious differences. • Gross and Net Weight Provide a large unopened box of breakfast cereal. Pass it around the group; have students note down the weight of the product. Remind students that the measurement on the outside of the box is net weight: this is the weight of the cereal only, and doesn’t include the box and packaging. Take the cereal bag out of the box and pass both around the group. A 725 g cereal box actually weighs about 820 g. Have students predict what the weight of the box will be. Have students apply net weight and gross weight to classroom objects. Take classroom containers, fill them with different amounts of Centicubes, then have students record the gross and net weight for each container. • Getting the Balance Right Take items from around the class and use the pan balance to weigh them. Pan balances require a sense of estimation to make their measurements accurate. Have the group weigh a selection of 24-page exercise books and record the mass of each. Exercise books have a different mass according to their number of pages. Then, using the mass of the 24-page books as a guide, predict the mass of 48- and 96-page books; weigh the books to find the exact mass. Ask, ‘Why would some books weigh more than others?’ List responses.
Independent Maths Individual, pair, small group
Incredibly Close Have students work in small groups. Give each group a manufactured mass of either 100 g, 500 g or 1 kg. Have students find and record classroom items that are very close (+ or – 10 g) to the designated mass. They will need to alternate between hefting the mass and hefting the classroom item to maintain a true idea of their designated mass.Then have students weigh the classroom items to check their mass. These Equal 500 g Have groups select classroom items whose combined mass is about 500 g. Have them create an equation on cover paper for each combination. Each equation must begin: 500 g = ... ; students can draw or name the objects to complete each equation. Have groups check each other’s combinations to ensure accuracy. Repeat this task with combined items that equal 100 g. Unit 31 Mass
115
How Much Do They Weigh? Have students work in small groups. Provide each group with a set of bathroom scales and kitchen scales, and a copy of BLM 44 ‘Weight of Eight’ for each student in the group. Have students find eight objects that when weighed, total exactly 10 kg and 5kg. Students record each object and its individual weight on the BLM. Point out that the total weight of the objects should weigh exactly 10 kg and 5 kg; therefore they will need to experiment with a number of objects to get an exact measurement (these can be recorded in the extra spaces on the tables). If students are having difficulty totalling exactly 10 kg or 5 kg, have them total a weight as close as they can to the desired amount. Weighing Fruit and Vegetables (Student Book p. 88) Provide a selection of 10 vegetables or pieces of fruit. Have students estimate and record the mass of each vegetable or fruit.They then weigh the vegetable or fruit and record its actual mass. Students can show their results on BLM 65 ‘My Graph’, or use Excel or Word on the computer. Kilogram or Gram? (Student Book p. 89) Have students look at each object drawn and decide whether its mass would be measured in grams or kilograms.They then answer the questions based on the illustrations. Unit 31 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 90).
Whole Class Share Time Survey the group to see if any two different items had the same mass. Use a kitchen scale in front of the group to check the items. Ask, ‘Did this activity become easier once you realised the mass of certain objects around the room?’ Check students’ work and display the posters. Select one poster and check the equations to see if the items have a combined mass of 500 g. Ask, ‘What part of this weighing task did you find the hardest? Why?’
Today I had problems with …
Have students share their findings. Ask, ‘What was difficult about this task? Was it easier to find eight objects that totalled 10 kg or was it easier to find eight objects that totalled 5 kg? Did anyone actually total 10 kg or 5 kg? Who totalled the closest amount to 10 kg or 5 kg? Did you estimates become more accurate as you weighed more and more objects?’ Have students share their work; discuss the fact that many fruit and vegetables are 90% water. Ask, ‘What were the heaviest vegetables and pieces of fruit? Why do you think they were the heaviest?’ Have students share their work; ask, ‘Is there any object on the page that you were not too sure about?’ Discuss where gram measurement ends and kilogram measurement starts, then invite students to share some of their mass estimates and combinations from Question 3.
116
Nelson Maths Teacher’s Resource — Book 5
unit
32
Multiplication and Decimals Student Book pp. 91–92
Number and patterns
BLMs 45, 46, 73 & 74
During this week look for students who can: • • • •
multiply single-digit numbers by factors of 10 round off answers on a calculator use fractions as operators apply decimals to everyday situations.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources calculators, wall marked in cm for measuring reach, chalk, 24 wall magnets, dice, plastic coins, cloth bag, BLM 45 ‘Multiple Race’, BLM 46 ‘Round Off ’, BLM 73 ‘Banknotes’, BLM 74 ‘Coins’ Maths Talk Model the following vocabulary in discussion throughout the week: divisor, tens, ones, rounding off, factor, decimals, currency
Whole Class Focus — Introducing the Concept I See a Pattern Write on the whiteboard: 5 × 7, 5 × 70. Ask, ‘Can someone solve the first equation?’ After a solution, point to the second equation; ask, ‘How is the second equation similar?’ Discuss responses, emphasising that 70 has a factor of 10. Remind students what the factors of 10 are; have them record these. Ask, ‘If we are multiplying by a factor of 10, what do you think the answer will be?’ Repeat the process, using 9 × 5 and 9 × 50; 3 × 4 and 3 × 40. After completing these equations, ask, ‘Can you see a pattern?’ Have students record the pattern; after hearing their explanations, make a group statement about what to do when you multiply a single digit number by a factor of 10. Round It Off Write these equations on the whiteboard: 54 ÷ 5, 16 ÷ 4, 21 ÷ 6, 33 ÷10 and 17 ÷ 2. Have students enter the equations into their calculators, one at a time. Discuss the answers and what they round to. When they get to 17 ÷ 2 = 8.5, ask, ‘What would you round this number to if you wanted a whole number as the answer?’ Discuss the concept of 0.5 and above rounding up, and below 0.5 rounding down. Money By Any Other Name Provide ‘banknotes’ and ‘coins’ from BLMs 73 and 74. Ask, ‘How do we record all the notes and coins in our system using decimal notation?’ Discuss responses, e.g. ‘A $100 note is recorded as $100.00.’ Have students record all the currency in decimal form, from Unit 32 Multiplication and Decimals
117
$100.00 to $0.05. After completion, ask, ‘If you had one of each form of currency, how much money would you have?’ How High Can You Reach? Prepare a wall showing height in centimetres. Have each student stretch as high as they can with both feet on the ground; record with chalk where they touch. Have each student record the results for the whole group. Model an example on the whiteboard, e.g. 118 cm. Ask, ‘How many centimetres in a metre?’ Record the answer, then ask, ‘If I want to show 118 cm as a decimal measurement of a metre, what would it be?’ Extend the discussion: ‘If an item cost 118 cents, how do we show that as part of a dollar?’ Emphasise the connection, then have students convert the centimetre measurements into metres. Magnet Fractions Place 24 magnets on the whiteboard; select a student 1 to find the total. Record on the whiteboard: 2 of 24; ask a student to show you half of the 24 magnets. Have students model the activity on paper. 1 1 1 1 Repeat for 4 of 24, 3 of 24, 6 of 24 and 8 of 24. Ask, ‘Do you see any patterns or connections between the fraction, the number of magnets and the number 24?’ Explore the many options.
Small Group Focus — Applying the Concept Focus Teaching Group • $100 between 3? Have students write the following sentence: ‘$100 is shared between three friends. How much will each person receive?’ Discuss methods of working out the answer: mentally, written or using a calculator. Have students enter 100 ÷ 3 = into their calculator. Ask, ‘With an answer like 33.33333 what do we do?’ Discuss methods of rounding off and up. Ask, ‘With three people, can they really get an even share of $100? Students then plan how $100 could be divided unevenly between 3, with each person getting nearly the same amount. Ask them to produce ten different variations.They could then do the same with hundred dollar amounts from $200 to $1 000, each time dividing by three. • 4 into 50? Have students enter 50 ÷ 4 into a calculator. Before they hit the equals button, ask, ‘What do you think the answer will be?’ Note predictions, then have them find out. Record the answer next to the predictions: 12.5. Ask, ‘What do we do with an answer like 12.5?’ Discuss rounding 12.5 up to 13. Repeat, sharing 50 among 3, 6, 7 and 9. Discuss students’ answers, then have them work independently dividing 50 by numbers from 10 to 20. They should record the answers in two columns: ‘Numbers that need rounding’; and ‘Numbers that divide evenly’. • 17 Showbags Have students draw 17 showbags. Ask, ‘How would you share the 17 showbags between two friends?’ Discuss how this could be solved: the visual model, division, mental computation or the use of a calculator. Have students enter 17 ÷ 2 into their calculators; discuss whether 8.5 should be rounded up or down. Have students examine 17 as a number, then write a paragraph about why 17 is not a good number of showbags for any family. (The paragraph should show the unsuitability of 17 as a number to divide.)
Independent Maths Individual, pair, small group
118
Multiplying by Factors of 10 Give each group two dice and BLM 45 ‘Multiple Race’. The aim is to be the first player to reach 1 000. Players roll the 2 dice. They record the number on Dice 1; it will be the first digit in the equation. The number on Dice 2 is multiplied by 10 before being recorded,
Nelson Maths Teacher’s Resource — Book 5
e.g. 6 becomes 60.The numbers are then multiplied and the total recorded. Students keep a running total throughout the game. If the game is completed quickly, provide more copies of BLM 45. Just Round it Off Give each pair three dice and a copy each of BLM 46 ‘Round Off ’. Students roll the three dice, then record the number rolled on Dice 1 in the tens column; Dice 2 in the ones column; Dice 3 as the divisor. They then complete the equation and round off the answer to the nearest whole number. After 10 rolls each, players swap and check each other’s answers. Grab Three Coins Have students work in pairs. Provide a set of plastic coins inside a cloth bag. Players take turns to remove three coins and record them, e.g. 50c, $1, 20c; they then record them as decimals and find the total: $0.50 + $1.00 + $0.20 = $1.70. The coins are then returned to the bag. The player with the highest total after ten grabs is the winner. Standing Jump (Student Book p. 91) Students have to convert each standing jump from centimetres to metres. Emphasise that 111 cm is recorded as 1.11 m. After converting the jumps, students rank the jumps in order from biggest to smallest and use the table to answer the questions. Cherries for My Friends (Student Book p. 92) Students are given the fraction of cherries eaten from identical bags of 36 cherries. Have them use the fraction to find the number eaten and the fraction remaining.They then use the table to answer the questions.
Whole Class Share Time Ask the players of ‘Multiple Race’ to explain the rules and procedures of this game. Ask, ‘What did you learn from playing this game?’ Have student share their responses, then ask, ‘When you were rolling the dice, what numbers were you looking for?’ Ask the players of ‘Round Off ’, ‘Was there anyone who rolled ten equations without having to round up or down?’ Investigate the divisors 1–6 and how they round off. Today I found out …
Ask players to calculate the money difference between each pair. Then ask, ‘How did you calculate the ongoing total for each player?’ Have students share their responses, then ask, ‘How do we show 5c as a decimal?’ Discuss the activity, then ask, ‘Why would we want to convert measurements into metres?’ Discuss suggestions, then ask, ‘Is it easier to picture distances as centimetres, or as parts of a metre?’ Have students explain how they calculated how many cherries were eaten from each bag. Ask, ‘Why do you think 36 was selected as the amount of cherries in each bag?’
Unit 32 Multiplication and Decimals
119
unit
More About Decimals
33
Student Book pp. 93–95
Number and patterns
BLMs 47, 48, 65 & 69
During this week look for students who can: • • • • •
read, write and say decimals compare, order and round off decimals calculate the average and range using decimals choose appropriate methods to calculate problems display knowledge of decimals.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources Excel, calculators, FM radio frequencies, BLM 47 ‘Average Maximum Temperatures’, BLM 48 ‘Temperatures: Up and Down’, BLM 65 ‘My Graph’, BLM 69 ‘Hundreds,Tens, Ones,Tenths & Hundredths Chart’ Maths Talk Model the following vocabulary in discussion throughout the week: range, decimal, round off, seasons, methods, strategies, rank, compare, order
Whole Class Focus — Introducing the Concept Order These Temperatures Write these temperatures on the whiteboard: 24.1, 25.5, 25.6, 27.4, 29.1, 20.2, 23.5, 26.3. Ask,‘How could we order these temperatures?’ Record suggestions. Draw a number line on the whiteboard, from 20°C to 30°C. Ask one student at a time to record a temperature on the number line. Hottest to Coldest Provide BLM 47 ‘Average Maximum Temperatures’. Have students locate the hottest and coldest average temperatures for Melbourne: 25.8°C in January and 13.4°C in July. Introduce range to describe the difference between lowest and highest temperatures. Ask, ‘How can we find the range of temperature in Melbourne?’ Discuss responses. Write 25.8 and 13.4 on the whiteboard, and demonstrate how to do a subtraction equation involving decimals. Ask, ‘How could we work out Ensure students the average maximum temperature for Melbourne for the year?’ After understand the terms ‘maximum’, ‘range’ and ‘average’. discussion, instruct students to find the average by adding the temperatures for the year and dividing by 12. What’s the Difference? Provide BLM 47 ‘Average Maximum Temperatures’. Look at the Melbourne temperatures for February and March (25.8, 23.8). Ask, ‘What symbol could we use to show whether the temperature went down (or up)?’ Record suggested symbols; use these to show the difference between temperatures for April-December.
120
Nelson Maths Teacher’s Resource — Book 5
What to Do with Temperatures Say, ‘We often hear that the top temperature of the day was 28°C, when it might have actually been 27.6°C. Why would reporters do this?’ Discuss responses, then ask, ‘How do you round off decimal numbers?’ Draw a number line ranging from 10–30 and write these decimals on it: 23.3, 28.5, 27.1, 25.9, 19.6, 22.4. Have students round off each decimal to the closest whole number and rewrite the number line in order.
25.6 – 19.9 June in Darwin June in Hobart
31.2 – 11.9
Subtraction with Decimals Show the connection between subtraction with 2- and 3-digit numbers, and subtraction with decimals. Record and complete this equation (as seen in margin). Emphasise that the decimal point doesn’t change the right-to-left processing; everything remains the same, including renaming and the decimal point in the same place. Pick a month from BLM 47 and model how to subtract the temperatures. (See margin for example.) Have students select a month and two cities to create their own equation.
Small Group Focus — Applying the Concept Focus Teaching Group • Adding and Subtracting Decimals Subtraction and addition of numbers with decimals is no different from the standard operations, except the value of the digits changes because of the position of the decimal point. Write on the whiteboard: 293 and 217. Have a student add decimal points to show tenths: 29.3 and 21.7. Ask, ‘What has the decimal point done to the value of those 3-digit numbers?’ Emphasise that the numbers have gone from approximately 300 and 220 to 29 and 22. Have students display their understanding by modelling further subtraction and addition equations on the whiteboard. • Where Do Numbers Appear? Provide a radio guide; write the FM radio frequencies on the whiteboard in random order. Have students order the frequencies, then have them suggest the increments needed on a number line to show all the frequencies. Draw the number line, making sure there is enough space to show stations that are close together, such as MIX 101.1 and FOX 101.9. Ask, ‘When you are ordering decimal numbers, what do you do first to rank them?’ Emphasise looking at the whole number first. • Autumn and Spring Provide copies of BLM 47 ‘Average Maximum Temperatures’. Have students identify spring and autumn. Select a season and a city, and record the temperatures, e.g. autumn in Canberra: 24.7°C, 20.1°C, 15.8°C. Ask, ‘If we wanted to find the average maximum temperature in Canberra in autumn, how could we work it out?’ Discuss suggestions, then model adding up the temperatures and dividing by three. Ask, ‘Why do we divide the total temperature by three?’ Have students work out the average autumn temperatures for other capital cities.
Independent Maths Individual, pair, small group
Order the Temperatures Have students work in pairs with BLM 47 ‘Average Maximum Temperatures’ and Excel. Have pairs select a city and list the months and temperatures in order. They then transfer the data to Excel, recording the months in order from coldest to hottest in Column A, and the decimal temperatures in Column B. They select a column graph from Chart Wizard and name the graph. Students without computer access can replicate the task using BLM 65 ‘My Graph’. Unit 33 More About Decimals
121
Hot and Cold Cities (Student Book p. 93) Have pairs of students use BLM 47 ‘Average Maximum Temperatures’ to complete Student Book p. 93. Ask students to locate the highest and lowest average temperatures for each capital city, and use those to work out each city’s ‘range’. Then have students find each city’s average temperature over the year and order the capital cities from highest to lowest. The Change between Months Have students work in pairs using BLM 47 ‘Average Maximum Temperatures’ and BLM 48 ‘Temperatures: Up and Down’. Each pair select two cities and record the maximum average temperatures over 12 months. In the third column, they use a symbol to represent the temperature difference compared with the previous month. (January will need to be compared with December.) Temperature Graph (Student Book p. 94) Using BLM 47 ‘Average Maximum Temperatures’, have students select a city, round off the temperatures for each month, then display the rounded-off temperatures as a graph (using Excel or BLM 65 ‘My Graph’). The colours for each month should be the same. Temperature Equations (Student Book p. 95) Have students use BLM 47 with this Student Book page to create and solve subtraction equations based on the differences in temperatures between cities and seasons. Have students do their working out on copies of BLM 69 ‘Hundreds, Tens, Ones, Tenths & Hundredths Chart’. Units 32–33 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 96).
Whole Class Share Time Have several students compare their Excel graphs. Ask, ‘Are there any patterns between graphs regarding warmer and cooler months?’ Discuss responses, then check that temperatures in the graphs are correctly ordered. Have students share their information on each city’s range and average temperatures. Ask, ‘How would you explain this task to a new student?’ Today I worked out …
Check if any groups found cities where the temperatures were similar (or very different). Have groups compare the order of their temperature symbols. Have students display their graphs, encouraging observations from the class. Revise rounding off with decimals; ask, ‘Why do the graphs look similar when the cities have very different climate conditions?’ Have students share some of their temperature equations. Ask, ‘Is there anything you do differently when you subtract with decimals?’ Select students to demonstrate how they worked out their decimal subtraction equations.
122
Nelson Maths Teacher’s Resource — Book 5
unit
34
3D Objects
Space
Student Book pp. 97–98
BLMs 49, 50, 51, 52, 53, 54, 55, 56 & 78
During this week look for students who can: • • • •
recognise, name, describe and construct simple 3D shapes use rulers or computer software to draw lines, shapes and angles construct recognisable objects using combinations of shapes identify the important features of 3D objects.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources set of classroom solids, a collection of boxes and Blu-tack, packaging, cereal boxes, tissue boxes, collection of 6-sided dice, magazines, MicroWorlds and Kid Pix Studio Deluxe, Word, scanner, BLM 49 ‘3D Objects’, BLM 50 ‘Square Pyramid Net’, BLM 51 ‘Triangular Pyramid Net’, BLM 52 ‘Triangular Prism Net’, BLM 53 ‘Cube Net’, BLM 54 ‘Rectangular Prism Net’, BLM 55 ‘Octahedron Net’, BLM 56 ‘Pentagonal Prism Net’, BLM 78 ‘Isometric Dot Paper’ Maths Talk Model the following vocabulary in discussion throughout the week: net, solid figures, objects, solids, face, edge, corner, vertex, vertices, cube, cylinder, prism, cone, sphere, hemisphere, triangular pyramid, attributes, features
Whole Class Focus — Introducing the Concept About 3D Shapes Write ‘three-dimensional’ and ‘3D’ on the whiteboard. Ask, ‘What do we mean by 3D? What are the three dimensions?’ Record responses. Using a set of solids and BLM 49 ‘3D Objects’, work together to name and tag the 3D shapes. On a large sheet of paper, brainstorm where students have seen 3D shapes in everyday life. Use only one colour so that further examples can be added later in the unit, using another colour. What is a Net? Ask, ‘What does the term net make you think of?’ Display an empty cereal or tissue box; undo the ends and sides and demonstrate what a net is. Pass the net around the class, pointing out the joins and sections that are scored for folding. Blu-tack the box net to the wall and, after handing out card, have students attempt to copy the net. (This activity may be carried through to Independent Maths.) Faces Ask, ‘When we say a “face”, what do we mean?’. Some students might say a model is the ‘face’ of fashion, or that Cathy Freeman is the ‘face’ of Australian athletics. Ask, ‘What do you think is the face of a 3D solid?’ Discuss responses; emphasise that the ‘face’ is the surface of a 3D object. Unit 34 3D Objects
123
Provide a set of classroom solid shapes; hand them around one at a time. Ask questions related to each shape, e.g. ‘How many faces can you identify on this cube?’ or ‘How many faces does this sphere have?’ Have students demonstrate the faces present on each 3D object. Make a chart recording the number of faces on each 3D object; students could decorate the chart with pictures of faces cut from magazines. Edges and Corners Provide a collection of 6-sided dice. Make sure all students have a dice to touch and turn over in their hands. Ask, ‘Can you hold the dice by only touching the corners?’ Have students demonstrate this; ask, ‘What are the corners like?’ Discuss responses, e.g. pointy, sharp, etc. Explain how 3D solids are classified by the number of edges they have. Ask, ‘How many corners does a dice (or cube) have?’ Hand around other 3D solids so that students can feel the number of edges they have. Introduce the words ‘vertex’ for ‘corner’ and ‘vertices’ for ‘corners’, although students should still feel comfortable calling them corners. They’re Everywhere! Split the class into groups and allocate one solid shape to each group. Provide magazines and the name tags from BLM 49 ‘3D Objects’. Have students search through magazines to find examples of ‘their’ solid. Have them cut out the pictures and use them to create a poster for each solid. (Some solids, e.g. octagonal pyramids, will be difficult to find. You could have students find pictures of 3D solids first, then allocate each picture to a group making a poster for that shape.)
Small Group Focus — Applying the Concept Focus Teaching Group • Investigating Faces, Vertices and Edges Create a characteristics profile for each basic 3D shape: cube, rectangular prism, triangular prism, cylinder, cone, sphere, square pyramid, triangular pyramid. The profile should include the number of faces, vertices and edges each shape has. Have students then draw three 3D shapes, labelling the edges, faces and vertices on each shape. • Pyramids and Prisms Provide models of a square pyramid, a triangular pyramid and a triangular prism. Work together to find the differences between the three shapes. Pose questions such as, ‘Do these solids have anything in common? What is unique about each solid shape?’ Provide copies of BLMs 50, 51 and 52 (‘Square Pyramid Net’, ‘Triangular Pyramid Net’, ‘Triangular Prism Net’) for students to complete independently. They could then write a description of the three shapes. • Prisms and Pyramids Have a collection of prisms and pyramids on hand; let the group observe their similarities and differences without prompting. Draw a large two-circle Venn Diagram; label one circle Prisms and the other Pyramids. Work together to look for unique and shared attributes, and list these in the circles. Focus on attributes such as the number of faces, edges and vertices. Have students write their own definition of a difference between the two solids, e.g. ‘The base of a prism is always rectangular.’
Independent Maths Individual, pair, small group
124
3D Drawings Have students work in pairs. Provide BLM 78 ‘Isometric Dot Paper’ and ask students to use the dots to create 3D objects. Have them draw or rule these solids: cube, rectangular prism, square pyramid, triangular prism. After completing the tasks, students could replicate their
Nelson Maths Teacher’s Resource — Book 5
structures using MicroWorlds or Kid Pix Studio Deluxe. The isometric dot paper can be scanned in as an import picture. Alternatively, students can draw and colour 3D shapes using the Draw and/or Autoshapes function of Word. Photocopy Nets Provide each pair with three copies of BLM 53 ‘Cube Net’; make sure each BLM is at a different size so that students can compare their completed cubes. Keep one BLM at 100%; make the others 110% and 120%. Have students cut out and complete the cubes, then make comparisons about the size of their faces and the lengths of the edges. Cubes on Computer Have students work in pairs using Kid Pix Studio Deluxe or MicroWorlds to create coloured cubes, using text boxes for ‘face’, ‘vertex’ and ‘edge’ to show their understanding of 3D shapes. Students without computer access can do the same by creating a cube on BLM 78 ‘Isometric Dot Paper’ and labelling the features. If time allows, have students create and label further 3D shapes. Faces, Edges and Vertices (Student Book p. 97) Provide a set of solid shapes. Have students use the models to complete the table.Time permitting, have students make their own models of 3D shapes using classroom construction materials or the nets on BLMs 50–56. Where Do We See Them? (Student Book p. 98) Students are to name the solid shapes and record three situations in everyday life where these solids can be seen. Unit 34 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 99).
Whole Class Share Time Have students present the solids they created on isometric paper. Any tasks completed on computer software can also be displayed. Ask, ‘Which are the easy 3D solids to draw? Which are the difficult ones?’
Today I discovered …
Have students display their cubes; note their different sizes. Ask, ‘Did you notice anything different when you constructed the same cube in three different sizes? Make comparisons about the length of the edges. Select pairs to show their presentations on Kid Pix Studio Deluxe or MicroWorlds. Ask the other group members, ‘Have they named the faces, edges and vertices correctly?’ Have students use 3D models to demonstrate how they worked out the number of faces, edges and vertices in a specific shape. Discuss the everyday 3D shapes. Ask, ‘What are the names of the solids featured and where do we see them in everyday situations’?
Unit 34 3D Objects
125
unit
Revision
35
Student Book pp. 100–102
Number and patterns
BLMs 57, 58 & 81
Measurement Chance and data
During this week look for students who can: • • • •
round off money to the nearest five cents, ten cents and dollar estimate short periods of time plan timetables experiment with fair and unfair chance activities.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources coloured counters, cloth bags, Maths dictionaries, coloured dice, supermarket flyers, flash cards, Unifix, packets of cards, phonebooks, BLM 57 ‘Chance Spinners’, BLM 58 ‘Chance Words’, BLM 81 ‘My Timetable’ Maths Talk Model the following vocabulary in discussion throughout the week: probability, draw, actual, predict, prediction, possible, fair, unfair, 50-50 chance, even, likely, unlikely, probability, possible, least possible
Whole Class Focus — Introducing the Concept Your Day in a Sequence Give each student a copy of BLM 81 ‘My Timetable’; ask them to pick their favourite school day, then record their personal timetable for that day. They should include activities at home and school, and record times with each task, e.g. ‘Wake up at 7:00 am.’ Have several students read their full schedules. Ask one student to place their times on the whiteboard in random order and then read their events only. Have the other students predict the time each event occurred. Money Now and Then Revisit the coins of the current Australian decimal system; compare the coins to the system prior to the removal of 1c and 2c coins. Ask, ‘What did the removal of 1c and 2c coins mean for our currency?’ Present examples of supermarket junk mail. Ask, ‘If 1c and 2c coins are gone from circulation, how do we pay for an item that costs $1.43?’ Discuss methods of rounding up and down to the nearest 5c, then have students brainstorm 15 prices and round them off. Even and Uneven Chance Toss a coin and ask students to predict whether it will be heads or tails. Record the possible ways of showing a 5050 chance.Then toss two coins and record the possibilities: HH, HT,TT. Ask, 1 ‘How do we record a one-in-three chance for two coins to show TT?’ ( 3 , 1 in 3, every third turn, 33%.) Repeat the activity, using even and uneven
126
Nelson Maths Teacher’s Resource — Book 5
number of coloured counters in a cloth bag. Record the fractions of uneven numbers of counters to show their probability of being drawn from the bag. Rounding Off the Dice Roll Provide three dice of different colours; allocate a different place value to each: hundreds, tens, ones. Roll each dice ten times and have students record the 3-digit numbers. Discuss methods of rounding off each number to the nearest five, ten and hundred. Make three columns (H, T, O) and round off each rolled number. Have students use calculators to add up real totals of the ten numbers and the rounded off totals. Ask, ‘What purpose does rounding off play in mathematics?’ How Long is a Minute? Ask, ‘How long is a minute?’ Ask students to count silently to themselves and put their hands up when they think 60 seconds has passed; time with a stopwatch. Repeat the task, then ask, ‘What methods help us count to 60 seconds without using a watch?’ Discuss answers. Ask students to write their full name, then ask, ‘How many times do you think you can write your full name neatly in 60 seconds?’ Survey, then test predictions. Allow students to change their predictions, then repeat the task.
Small Group Focus — Applying the Concept Focus Teaching Group • Fair or Unfair Place 2 red, 2 blue and 2 green counters in a bag. Ask, ‘Why does each colour have a fair chance of being drawn from the bag?’ Discuss responses, then ask, ‘Can you change the combination of colours so that one colour has a strong chance, the next colour a fair chance and the third colour little chance?’ Change the colour combination according to suggestions and make ten draws. Adjust the combinations and repeat again, if needed. Highlight the changes made; brainstorm other words that illustrate likelihood. Have students work independently to make posters summarising the information they found out. • What is Likely? Toss a coin ten times and have students record the results. Ask, ‘What chance did each toss have of being a head?’ Discuss synonyms for ‘50-50’ and record them on the whiteboard. Say, ‘If you were to toss a coin 50 times and you had a 50-50 chance of tossing heads, what would the results be?’ Give each student a coin; ask them to toss the coin 50 times and record the results. Discuss the results and compare them with students’ predictions. Have students suggest other times when they have had a 50-50 chance of success. Record these on the whiteboard. Ask, ‘Why do we say a 50-50 chance? Is it the same as a one-in-two chance?’ • Place Them in Order Pose this scenario: ‘One day, someone in this class will be Prime Minister of Australia.’ Brainstorm words that reflect that chance, e.g. likely, possible, unlikely, strong chance, etc. After reviewing the list, place each option on a flashcard and ask students to rank the options from least possible to most possible, rearranging the cards to match. • What Chance? Provide copies of BLMs 57 ‘Chance Spinners’ and 58 ‘Chance Words’. Have students select a chance card and design a spinner to match, e.g. a spinner to match ‘50-50 chance’ would have each half coloured a different colour. Emphasise that spinners should show a 1-in-2 chance, 1in-4, etc, of landing on a specific colour. Octagonal spinners are for more confident students. Unit 35 Revision
127
Independent Maths Individual, pair, small group
An Excursion to the Zoo Ask each group to make a timetable or itinerary for a day at the zoo. Discuss events to be included and record these on the whiteboard: travel to and from the zoo, lunch, morning tea, walking around the zoo, arrival at and departure from school, a lesson at the zoo. Have each group create their timetable on an enlarged copy of BLM 81 ‘My Timetable’. Junk Mail Round-off Provide each group with supermarket flyers and a large sheet of paper. Ask groups to cut out and glue pictures of 15 shopping items on the paper; they should write the price beside each item, then add the prices to find the total.Then have groups round off the price of each item to the nearest five cents and find the total. Compare and discuss the two different totals. What Sort of Chance? (Student Book p. 100) Give each student a cloth bag and 10 counters (4 blue, 3 red, 2 yellow, 1 green). Have students record the chance of drawing each colour as a fraction, then make 20 draws. They then convert their predictions from tenths to twentieths and compare them with the results. Shopping Round-up (Student Book p. 101) This activity involves adding and rounding prices to the nearest 5 cents, 10 cents and dollar, then using the table to answer questions. Students can use calculators to add up their totals. How Long Will it Take? (Student Book p. 102) Have students work in pairs, estimating the time it will take them to complete the nine activities, then using a stopwatch to record the actual time. Unit 35 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 103).
Whole Class Share Time Have several groups read their zoo timetables; ask other groups to identify any problems or time concerns they have with the timetables. Discuss the posters. Ask, ‘Of the 15 items on your poster, how many were rounded up, and how many were rounded down?’ Discuss the numbers of items rounded up and down. Ask, ‘Are buyers getting better value when each shopping item is rounded off?’ Today I found out …
Have students share their experiences. Discuss any results that deviate from the recorded probabilities. Ask, ‘How many draws do you think we would have to do to show the real chance of drawing each colour?’ Check the actual total of the shopping items. Ask, ‘What were the totals when items were rounded to the nearest 5 cents, 10 cents and dollar?’ Discuss the totals, then ask, ‘What have you learnt about rounding off ?’ Compare students’ estimated times for the ten tasks; discuss any obvious discrepancies before checking the actual times. Ask, ‘What tasks were the easiest to predict? Why?’
128
Nelson Maths Teacher’s Resource — Book 5
unit
36 Number and patterns
Solving Problems Student Book pp. 104–106
During this week look for students who can: • make mental and written computations using money • choose the appropriate method (written or mental) to complete calculations • use two operations to solve a problem • round off calculator displays to achieve a required result.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources calculators, 500 mL bottle, disposable cups, measuring cups Maths Talk Model the following vocabulary in discussion throughout the week: BODMAS, methods, equation, pattern, repeated addition, extend
Whole Class Focus — Introducing the Concept What’s Wrong with This Equation? Write this incorrect equation on the whiteboard: 21 + 9 ÷ 3 = 10. Ask, ‘Do you think this is the correct answer?’ Have students discuss the equation in terms of order of operations. Introduce BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction). Ask, ‘If we follow BODMAS, what is the answer?’ Have students work through the BODMAS process to calculate the answer (24). Remind students that if brackets appear in an equation they are calculated first, then division or multiplication as they occur reading from left to right; followed by addition or subtraction as they occur reading from left to right. What is 12th in This Pattern? Have students enter 1 + 4 = on their calculators. Ask, ‘What has come up on the display?’ Have students predict what the 12th number in this sequence will be if they continue to press the = button. Record responses, then have students press the = button 11 times. Students can then work individually to complete their own calculator counting patterns. 500 mL and Six Drinkers Provide drinking cups, measuring cups and a 500 mL bottle of water. Ask students what they know about 500 mL, e.g. ‘500 1 1 mL is 2 a litre’, ‘500 mL is 4 of 2 litres.’ Ask, ‘If we had to divide 500 mL of water evenly between 5 drinkers, how much would each get?’ Record responses, then ask, ‘If we want to share 500 mL between six people, what Unit 36 Solving Problems
129
operation do we need to do?’ Have students act out the division using drinking cups, measuring cups and the 500 mL bottle of water. Estimate and Calculate Write on the whiteboard: $2.45 + $3.95 + $4.50. Ask students to estimate what the answer might be: $2 + $4 + $5 = $11. Have students use pen and paper to find the real answer and check how far from the estimation it is. Encourage students to suggest other money addition problems that involve estimating before finding the exact answer. Two Ways to Reach an Answer Write this scenario on the whiteboard: ‘Anne received $5.70 per hour for 3 hours of collecting paper for recycling’. Ask, ‘How can we work out how much Anne earned altogether?’ Listen to the responses, and discuss different methods of finding a solution: calculator, pen and paper, mental calculation. Model repeated addition ($5.70 + $5.70 + $5.70) as well as multiplication ($5.70 × 3). Ask, ‘Which method do you prefer?’
Small Group Focus — Applying the Concept Focus Teaching Group • Working with Brackets Ask, ‘What do you do when an equation has a bracket?’ Listen to students’ responses, then write this equation on the whiteboard and use it to model: (5 + 3) × 2. Work through a number of examples with and without brackets, reinforcing order of operations.’ Have students complete similar equations independently. BO
Brackets, Of
DM
÷ or × in the order they occur reading left to right
AS
+ or – in the order they occur reading left to right
• Add or Subtract and Multiply and Divide Write these equations on the whiteboard: 16 – 8 + 7 = 1; 16 – 8 + 7 = 15.Without comment, have students read the equations; ask, ‘Are they both correct?’ Discuss the concept of groupings (+ and –; ÷ and ×) in relation to BODMAS, e.g. in 16 – 8 + 7, we calculate subtraction first, as we are reading from left to right, e.g. 10 – 6 + 7 = 11, 12 ÷ 3 × 3 = 12. Encourage students to work independently to make their own equations using groupings and reading from left to right. • BODMAS Have students make a BODMAS poster for classroom display. Ask, ‘While BODMAS gives us rules when dealing with equations, why are they listed in this order?’ Discuss operations and the connections between addition and subtraction, and between multiplication and division. Ask, ‘What do you do when addition and subtraction appear together? Or multiplication and division?’ Discuss responses, emphasising working from left to right. Ensure this understanding is displayed in the poster.
Independent Maths Individual, pair, small group
Two Operations to Make 9 Have students work in small groups using two operations to make 9, e.g. 16 + 4 – 11 = 9. Their target is to make nine different equations.They can combine addition, subtraction, multiplication and division, but they must remember BODMAS. A Stuck Cash Register Have students work in pairs. Present this scenario: ‘A shop’s cash register is stuck; it keeps recording purchases of $2.55.’ Have students enter into their calculators: $2.55 + $2.55 = . Ask them to record the total for the next 50 presses of the = button. Ask, ‘When the cash register stopped, what was the total?’
130
Nelson Maths Teacher’s Resource — Book 5
Buy and Divide (Student Book p. 104) Students complete the activities, drawing the pizzas and drinks, and describing what they did to reach a solution. Match-up the Money (Student Book p. 105) Students need to match the amounts spent with a total. Encourage more able students to estimate the total for each equation before they use pen and paper to work out an accurate total. Have students make some problems of their own where the added total is $72.60. Daily Pay (Student Book p. 106) Discuss the activity and the computation methods (mental, written, calculator) that could be used to work out which child received the most pay for the week.
Whole Class Share Time Check students’ answers; ensure they have a sound understanding of BODMAS. Ask selected students to present their nine equations that make 9. Have students explain the task; check how they used a calculator to add to $2.55. Have students check their answers at 10 ×, 30 × and 50 × $2.55. Ask, ‘What does the calculator do to create this pattern?’ Today I discovered …
Have students share their experiences with this task. Select a student to verbalise the pizza-sharing activity. Have students share their work. Encourage those students who used estimation to share their strategies. Ask, ‘What do you have to be careful with when you are adding amounts with decimal points?’ Have selected students share their different ways of spending $72.60. Check students’ answers; ask, ‘What methods did you use to work out how much pay each child received?’ Have students use the ‘repeated addition’ method to check their work.
Unit 36 Solving Problems
131
unit
Four Operations
37 Number and patterns
Student Book pp. 107–109
During this week look for students who can: • make mental and written computations using money • choose the appropriate method (written or mental) to complete calculations • use two operations to solve a problem • round off calculator displays to achieve a required result.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources advertising leaflets, whitegoods advertisements, CDs, Liquid Paper Maths Talk Model the following vocabulary in discussion throughout the week: BODMAS, methods, equation, pattern, repeated addition, extend, operations
Whole Class Focus — Introducing the Concept CD and Change Have a selection of CDs on hand; add price tags (if they don’t already have them) so that prices are between $20 and $30. Select a CD and write its price on the whiteboard, e.g. $22.95. Ask, ‘If we paid with $30, how can we work out what change we will get?’ Discuss methods: counting on, estimation, calculator, paper and pen. Ask, ‘Which method would you use? Would you change your method depending on the price?’ 13 is a Teenager Place the number 13 on the whiteboard. Ask, ‘What comes to your mind when you think of 13?’ Have students share their responses. Ask, ‘What is 13 made up of?’ (1 ten, 3 ones). In small groups, ask students to write 13 equations that use two operations each and total 13. Make sure students use all four operations in their 13 equations. Buy Me a Fridge Provide whitegoods advertising material; select an item that lists the full price, as well as weekly payments, e.g. a 243 L fridge for $669, with weekly interest-free payments of $5.03. Ask, ‘How can we work out how many weeks it will take to reach $669, if you pay $5.03 each week?’ Discuss the number of weeks in the year; have students use calculators to work out how many weeks and years it will take to pay off the fridge. Repeat, using other items that list full and weekly payments.
132
Nelson Maths Teacher’s Resource — Book 5
What’s in a Name? Write the name of a current pop star on the whiteboard, e.g. Elton John. Underneath it, write the equation: 5 × 4. Ask, ‘Can you see a connection between these two items?’ Discuss responses; highlight the number of letters in the first name and the family name. Ask students to write out their first name and family name, then use the number of letters in each to create a multiplication equation. Place several names and equations on the whiteboard and ask students to rank the names from the lowest equation to the greatest. And the Answer is 25 Write on the whiteboard: 25. Below it, write: _____ × _____ - _____ =.Write the numbers 2, 15 and 20 next to the signs. Ask, ‘Can you fill the gaps in the equation with these numbers so that the answer is 25?’ Have several students demonstrate their strategies; when the answer is reached, say, ‘Now put the numbers in a different order and reach a different answer.’
Small Group Focus — Applying the Concept Focus Teaching Group • Fun with Addition Write on the whiteboard: 27 + 4 = ? Ask students what the answer is, then pose this question: ‘If 27 + 4 = 31, what other addition equations equal 31?’ Have students compile and share their equations. Model the equation: 27 + 4 = 22 + ❐. Ask, ‘How do I work out the value of the blank square?’ Then have them create their own missing number addition equations, initially using 31 as the target. Students can then swap and solve each other’s equations. • 36 is an Interesting Number This activity focuses on addition and multiplication. Ask students to make six equations (which include both addition and multiplication). Model approaches such as 6 × 6 = 29 + 7. As an independent task, ask students to record ten such equations and then white out one number and replace it with a box. Students can then swap and complete each other’s equations. • The Missing Number Write on the whiteboard: 30 – 3 = (5 + ❐) × 3. Ask, ‘How do I approach this equation?’ Discuss the order of operations, and the concept of balancing answers on both sides of the equal sign.With 32 as the target, have students prepare equations using addition, subtraction and/or multiplication on either side of the equals sign, e.g. 16 + 16 = ❐ + 9 – 3. Brackets can also be used. Have students swap and compare equations so that they deal with different styles of presenting 32.
Independent Maths Individual, pair, small group
Change from $1 000 Provide each group with plenty of advertising material featuring electrical goods. Ask each group to select a specific product to focus on, e.g. CD players, freezers, etc. Have them work out how much change they would get from $1 000 for each electrical item, without using calculators. Then have them cut out the items and rank them from most expensive to least expensive. Key Numbers in Life Have students work in small groups. Discuss how some birthdays are ‘more important’ than others, e.g turning 21, 40, 50, 65 and 100 years old. Have each group select an ‘age’ and see if they can create the number of equations, using all four processes, equal to that birthday, e.g. 21 equations for 21: 10 + 11 = 21, 30 – 9 = 21, etc. Unit 37 Four Operations
133
Electrical Rental (Student Book p. 107) Have students work out the cost of renting each electrical item for 1, 3, 7 and 10 days. They then repeat the activity with an electrical item of their own choice. Multiplication Names (Student Book p. 108) Before students begin the activity, ask, ‘Who do you think will be the highest ranked athlete?’ Emphasise that each letter in a name is worth one digit. The numbers are used to create a multiplication equation, which is then multiplied by 10 and 100. Making Equations (Student Book p. 109) Have students make equations using the signs and numbers supplied; signs must be used in the given order. Remind them that if brackets appear in an equation they are calculated first, then division or multiplication as they occur reading from left to right; followed by addition or subtraction as they occur reading from left to right. Units 36–37 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 110).
Whole Class Share Time Have students share their task. Ask, ‘What was the best way to calculate the change from $1 000, without using a calculator?’ Discuss strategies used; have some groups check their answers with a calculator in front of the other groups. Invite students to share some of their equations for specific ages. Ask, ‘What was the hardest age to make equations for?’ Today I did not understand …
Ask students how they calculated the rental of the electrical goods for the 10-day period. Have students share their approaches; emphasise multiplying by 10. Ask, ‘What does the long-term rental cost of electrical goods show you?’ Have students share their experiences in ranking athletes. Ask, ‘Could the highest ranked athlete on the page have beaten Australian sprinter Matt Shirvington?’ Discuss the ranking when each equation was multiplied by 10 and 100. Ask, ‘Did the ranking change? Why not?’ Have students share some of their equations. Discuss the confusion that can occur when you think all you have to do is read the equation from left to right. Ask, ‘Why do you think mathematicians invented BODMAS?’
134
Nelson Maths Teacher’s Resource — Book 5
unit
38
Make These Shapes Student Book pp. 111–112
Space
BLM 66
During this week look for students who can: • • • •
identify and create 2D and 3D objects work with congruency view shapes from different perspectives identify lines and use them to construct drawings.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources 2D shapes, 3D objects, blu-tack, blank flash cards, empty coffee container, Salada packet, cone-shaped object, Centicubes, Unifix, Multilink cubes, digital camera, maths dictionaries, coloured whiteboard markers, attribute blocks, Word, PowerPoint, biscuit cartons, newspaper, BLM 66 ‘Venn Diagrams’ Maths Talk Model the following vocabulary in discussion throughout the week: bird’s-eye view, profile, angle view, congruency, congruent, vertical, horizontal, parallel, diagonal, curved, behind, hidden, Venn Diagram, profile
Whole Class Focus — Introducing the Concept Build Me a House Provide a collection of coloured whiteboard markers for this task. Ask, ‘If you are planning to design a picture of a house and garden, what lines will you need, and where will the lines go?’ Together, apply a colour scheme to vertical, horizontal, perpendicular, diagonal, parallel and curved lines, then have students construct a drawing of a house and garden from them. Plane Shapes from 3D Objects Ask, ‘How do you change a square into a cube?’ Discuss the direct relationship between the two, and how we recognise both a square and a cube by specific characteristics: a square has 4 sides the same length and 4 right angles; a cube has 6 faces, 12 edges, etc. Demonstrate this on the whiteboard by drawing a square, then extending it into a cube. Create a profile for the cube and square. A Triangle and a Pyramid Provide a triangle and a pyramid. Have students pass them around without speaking. Draw a two-circle Venn Diagram on the whiteboard; label the circles Triangle and Pyramid. Ask, ‘What are the characteristics of a pyramid?’ Record responses on flash cards and attach them to the Triangle circle. Repeat, using a pyramid, Unit 38 Make These Shapes
135
Triangle
Pyramid
attaching cards to the Pyramid circle. Ask, ‘Are there any characteristics that triangles and pyramids share?’ Have students share their responses, e.g. straight sides; move the relevant cards to the intersection of both circles. Discuss what the Venn Diagram shows, in terms of specific and shared characteristics. What is Seen from This Angle? Prepare a Rubic-style cube of 27 Multilink cubes; ask, ‘How many squares can you see in this construction?’ Discuss the number, then ask, ‘How many blocks are there actually in this construction?’ Discuss the difference between the two questions. Introduce ‘point of vision’: discuss bird’s-eye view, profile view and angle view. Give examples of each. Remove several blocks from the Multilink construction while students are recording their findings, and repeat the original set of questions. What is Congruency? Draw two circles on the whiteboard; write the question, ‘Are these circles congruent?’ Have students use maths dictionaries to find the definition of ‘congruent’: two shapes that are the same in all ways. Select students to draw congruent triangles, squares and rectangles on the whiteboard.
Small Group Focus — Applying the Concept Focus Teaching Group • What’s My View? Provide a Salada biscuit box; ask, ‘What shape is this?’ (A rectangular prism.) Have students sit in a circle around the box and draw the face or edge they see. Display the drawings, listing the perspectives the box was drawn from (profile, front on). Say, ‘What would the box look like from a bird’s-eye view?’ Discuss responses, then have students find an object in the room that they can independently draw from many view points (perspectives). • Coffee or a Cylinder Provide an empty coffee container or jar. Have students stand above the container and draw what it looks like from a bird’seye view. Ask, ‘Can you tell that it is a cylinder when you look at it from above?’ Make the connection between a circle and a cylinder, then have students draw the jar from its side profile. Ask, ‘How do you draw a cylinder so that it doesn’t appear to be too rectangular?’ Discuss responses, then have the group repeat the process with a cone-shaped object. • Profile Perspective Provide students with large sheets of paper and ask them to sketch their partner’s profile. Ask, ‘Can we recognise a person from a sketch of their profile?’ Take a 3D object, e.g. a hexagonal prism, and ask, ‘What does this object look like when we sketch it from a side or profile view?’ Have students select 3D objects and sketch them in profile. They can see if the group can correctly guess the name of the shape they sketched. After viewing the sketches of the prism, ask, ‘Is this the best angle to view a prism from?’ Have students suggest the best angle to draw other objects from.
Independent Maths Individual, pair, small group
A Picture of Lines (Student Book p. 111) Students are to use textas or highlighters to trace over the lines in the picture, following the colour key. 2D and 3D Shapes (Student Book p. 112) Have students complete the grid by drawing the 2D and 3D shapes, then listing their characteristics.
136
Nelson Maths Teacher’s Resource — Book 5
Have students make various 3D shapes from tape and onemetre lengths of rolled up newspaper. The shapes can be painted and labelled, e.g. cube: 6 faces, 10 vertices and 4 corners. Some students might like to note the number of angles, their type and the degree.
3D Shapes
Venn Diagram Shapes Have students work in pairs with a two-circle Venn diagram from BLM 66. Ask each pair to select a 2D shape and a 3D shape that have a connection, e.g. square and cube; rectangle and rectangular prism; triangle and pyramid. They label one circle for each shape and list its characteristics, then list the shared characteristics in the overlapping area. Count the Cubes Have students work in small groups, using Multilink cubes to make five cube-shaped constructions, each with a different number of cubes.They then take digital photographs of their constructions, and insert them into a PowerPoint presentation so other groups can view them and predict the number of cubes used in each construction. Can You Make These? Have students work in pairs. Using a computer and Word, one player creates a set of eight shapes from the Autoshapes menu bar. Player One then flood-fills their shapes in a specific colour. Player Two then makes shapes congruent with Player One’s shapes, without using any copy controls of the computer. They flood-fill using a complementary colour, then print out the page. Students without computer access can trace eight shapes onto a sheet of paper. They then swap with a partner and use a pen and ruler to make congruent shapes without tracing. Unit 38 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 113).
Whole Class Share Time Have students share their work: all pictures should be coloured the same way. Ask, ‘Which lines were hardest to identify? Why?’ Encourage discussion; ask, ‘What is the connection between perpendicular lines and vertical and horizontal lines?’
Today I discovered …
Ask, ‘What are the obvious visual characteristics of humans?’ From this discussion, have students reflect on their own answers. Ask students to name the characteristics of specific 2D and 3D shapes. Record responses for future reference. Have students share their Venn Diagrams; check to see that the items in the intersecting circle are common to both shapes. Have students read examples of attributes that are exclusive to only one of their chosen shapes. View the PowerPoint presentations; ask, ‘How do you calculate the number of cubes used when you can only see one side?’ Ask, ‘What do you have to look at if you want to replicate a shape exactly?’ Encourage discussion; view the created shapes on screen and on printout. Highlight the congruent shapes.
Unit 38 Make These Shapes
137
unit
Working with Numbers
39
Student Book pp. 114–115
Number and patterns
BLMs 59, 60, 73 & 74
During this week look for students who can: • • • •
use rules to complete number patterns and equations make statements of equality using whole number and decimals select the appropriate operations to complete equations complete addition, subtraction, multiplication and division equations.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources dice, calculators, coins, Inspiration 6, Word, BLM 59 ‘Hundred Grid’, BLM 60 ‘Operation Grid’, BLM 73 ‘Banknotes’, BLM 74 ‘Coins’ Maths Talk Model the following vocabulary in discussion throughout the week: even, uneven, strategies, count on, methods, balance, patterns, key numbers, continue, BODMAS
Whole Class Focus — Introducing the Concept Pick a Number Have students select a number between 1–10, then ask them to provide four equations that equal their chosen number: one for each operation. After sharing the equations, ask them to pick a number between 10 and 20 and make two equations for each operation. Three Operations Place these signs on the whiteboard: x, +, –. Ask students to select four numbers between 1–9. Have students randomly place their digits between the signs, copying the equation onto paper as they do so. Ask, ‘Which part of the equation do we begin with?’ Discuss the BODMAS acronym, then ask, ‘If we arrange the digits in different positions, how many equations can we make using these four digits?’ Have students record their 24 equations. Many Ways to Make $5 Pose this scenario: ‘In my pocket I have coins that equal $5. What might the coins be?’ Record responses on the whiteboard, and categorise them according to the number of coins used: 3 coins, 4 coins, 5 coins, etc. Story of an Excursion Write this number problem on the whiteboard: ‘There are 87 students on an excursion.Thirty-nine of the students are girls. How do we work out how many boys are on the excursion?’ Discuss the methods that could be used: calculator, mental maths, pen and paper. Ask, ‘Can we use addition and subtraction to work out the answer to the problem?’ Emphasise counting on and complementary addition.
138
Nelson Maths Teacher’s Resource — Book 5
Spot it and Carry On
Write these number patterns on the whiteboard:
★ 75, 78, 82, 85, 89, 92, 96, 99 ★ 100, 96, 93, 89, 86, 82, 79, 75 Ask, ‘What are the number patterns?’ After students identity the patterns (+ 3, + 4; – 4, – 3), circle the numbers with different colours on an A3 copy of BLM 59 ‘Hundred Grid’. Ask, ‘Can you see any connection between the two patterns? Are there any numbers that the two patterns share?’
Small Group Focus — Applying the Concept Focus Teaching Group • What Coins Make Up $20? Stick a $20 note from BLM 73 ‘Banknotes’ on the whiteboard. Ask, ‘Can you record the three different equations involving notes that equal $20?’ Have students record their responses, e.g. $10, $10; $10, $5, $5; $5, $5, $5, $5. Then ask, ‘What combinations of gold coins equal $20?’ Provide coins from BLM 74 ‘Coins’. Have students make $20 using ten different combinations of gold coins. Encourage students to use pen and paper as well as a calculator. • What Notes Make Up $50? Give each student a copy of BLM 73 ‘Banknotes’. Draw a large $50 note on the whiteboard and ask students to use banknotes to make three different equations that equal $50. Discuss their equations, then ask, ‘What other combinations of notes could you create if you were multiplying?’ Record responses of addition and multiplication equations, e.g. $10 + $20 + $20; 5 × $10; 2 × $20 + $10. Have students make further combinations of addition and multiplication equations. Then ask them to make $50 using only six notes. Discuss using the ‘guess and check’ strategy to find the six notes. Ask, ‘What notes can be used?’ Encourage students to use calculators. • What Notes Make Up $100? Attach a $100 note from BLM 73 ‘Banknotes’ to the whiteboard. Have students make three different note combinations that equal $100. Record responses, then have students create addition and multiplication equations that equal $100, e.g. $50 + $20 + $20 + $10; or 5 × $20. Record these equations on the whiteboard.Then ask, ‘Can you make up $100 with only six notes?’ Discuss strategies, and the ‘guess and check’ strategy involved.
Independent Maths Individual, pair, small group
20 Equations with 4 Signs An activity for small groups. Supply students with a large sheet of paper and ask them to write ‘12’ in the middle of the page.Then challenge them to make 20 equations that equal 12, using all four operations, e.g. 8 + 4 = 12, 18 – 6 = 12, 3 × 4 = 12, 96 ÷ 8 = 12. Students could record the above activity on the computer using Inspiration 6. Have groups swap and check each other’s work. Operation Grid Dice Roll Have students work in small groups. Supply students with copies of BLM 60 ‘Operation Grid’ and four dice. One player rolls the four dice. All players use the four numbers rolled to complete one row of the operations grid, putting numbers in the boxes to create new equations. Players have one minute to create their equations. Provide calculators, if needed, and have players check each other’s equations. To extend this activity, provide each player with a copy of BLM 60. The aim is for each player to make the highest/lowest total possible after throwing the Unit 39 Working with Numbers
139
four dice and recording the numbers in the boxes. The player with highest/lowest total for the round, wins a point. The player with the most points after thirteen rounds wins. What Makes Up $10? Ask each pair to write $10 in the middle of a large sheet of paper. Ask them to make two monetary amounts that equal $10, without using whole dollar amounts, e.g. $2.55 + $7.45. Discuss the amounts, then have each pair create 20 different totals that equal $10. Students could record this activity on the computer using Inspiration 6 or Word. A Day at the Footy (Student Book p. 114) Students read each word problem, identify the operation involved and the method they would use to calculate the answer, then provide the answer. Mission: Very Possible! (Student Book p. 115) Students study the number patterns and explain what and where the pattern is. In Question 2, students use the ‘secret code’ to complete the number patterns to 24.
Whole Class Share Time Share the groups’ responses to the challenge, then see if there are any ‘12’ equations that can be grouped together, e.g. 4 × 3 and 3 × 4. Ask, ‘What activity could you plan as the next step after this challenge?’ Share responses, e.g. ‘Looking at the factors of numbers such as 12, 16 and 24.’ Have students display the equations they created. Ask, ‘Why are the operation signs placed in that particular order: ×, +, –, =?’
Today I learnt …
Have pairs of students share their examples of two amounts that equal $10. Have pairs compare sheets of paper to find the amounts they both used, as well as the less common amounts. Ask, ‘What have you learnt from this money activity?’ Have students share their answers and methods of calculation for the word problems. Ask, ‘Which words in a word problem help you decide which operation to use?’ Check to see if there were differences in the methods used. Ask, ‘What approach did you use when you came across an unknown number pattern?’ Discuss methods for identifying gaps or bridges between numbers, and what to look for when extending a number pattern.
140
Nelson Maths Teacher’s Resource — Book 5
unit
40
Balance the Numbers Student Book pp. 116–117
Number and patterns
BLMs 61, 62 & 63
During this week look for students who can: • • • •
use rules to complete number patterns and equations make statements of equality using whole number and decimals select the appropriate operations to complete equations complete addition, subtraction, multiplication and division equations.
When planning this week’s work choose activities from ‘Whole Class Focus’, ‘Small Group Focus’ and ‘Whole Class Share Time’ that best suit the needs of your class.The identical symbols in each of these three sections, e.g. represent the common thread linking the activities.
Resources http://www.prongo.com/math/index.html, dice, BLM 61 ‘Balancing Equations’, BLM 62 ‘Timing Equations’, BLM 63 ‘A Balancing Act’ Maths Talk Model the following vocabulary in discussion throughout the week: even, uneven, strategies, methods, balance, patterns, key numbers, BODMAS
Whole Class Focus — Introducing the Concept Pens Ready, Go! Place two 2-digit addition equations on the whiteboard, e.g. 78 + 59, and select two students to solve them.Time the students with a stopwatch; record their times. Have those students create two more equations for another two students to solve.Time those students and repeat the process. Highlight the three fastest times; ask, ‘What makes them so fast at addition equations?’ Two Plus and a Subtract Write on the whiteboard: + + – . Ask students to suggest three numbers between 0–5, e.g. 4 2 3. Insert the numbers after each sign (after making sure the subtraction won’t cancel out the additions): + 4 + 2 – 3.Then ask students to provide the first ten numbers in that 3-stage sequence, e.g. 0, 4, 6, 3, 7, 9, 6, 10, 12, 9. Calculators at the Ready Have students enter 15.75 on their calculators; ask, ‘How much is this in dollars and cents?’ After a response, ask, ‘If this was the total pocket money for three students for a week, how would you divide it evenly?’ Have students explain their methods, then have the group find the answer: 15.75 ÷ 3 = 5.25 ($5.25). Now ask students to use their calculators to find three uneven amounts that total $15. Record responses, then have them repeat the task with another cash amount. Follow the Pattern Write on a flash card: 9 + 8 = 17. Hand the card around the group; ask, ‘Do you agree with this equation?’ Emphasise the ones pattern: 9, 8, 7. Ask students to produce on paper another equation that Unit 40 Balance the Numbers
141
follows this pattern, e.g. 19 + 18 = 37, 29 + 28 = 57, etc. After checking and recording possibilities, allow students 60 seconds to record as many addition equations as they can that follow the pattern 6 + 8 =14, e.g. 16 + 18 = 34. Answers can be worked out and discussed as a class. What to Do with Brackets Write on the whiteboard: 15 + (11 – 6) = ____ . Ask, ‘What do we do first to tackle this problem?’ Discuss responses, reminding students of the order of operations in BODMAS. Pose the question, ‘What do we do if a problem has two operations, e.g. addition and multiplication and brackets?’ Have students demonstrate brackets first, then multiplication. Write this on the whiteboard as if it’s on a pair of balance scales: 16 + 8 = (3 + 5) × ____ . Ask for responses. Have students explain what they did in order to find the missing number (3).
Small Group Focus — Applying the Concept Focus Teaching Group • Operations: What Comes First? Revisit BODMAS and discuss the rules about which operations must be done first.Together, create an equation that highlights the workings of BODMAS. After checking the workings of the equation, have students create their own equations. As a variation, have students create equations that combine the four operations. • Balance the Equations Draw a balance scale on the whiteboard and write on it: 4 × 6 = 30 – 3 × 2. Ask, ‘What part of this equation must we deal with before we can balance this activity?’ Together, solve 4 × 6 and write 24 above it. Remind students of BODMAS. Say, ‘Which part of 30 – 3 × 2 do we do next?’ Solve the next operation and write 6 above 3 × 2, then complete the task by solving 30 – 6. Emphasise the balance effect once the equation is solved. Have students create their own balancing equations that use all four processes, e.g. 12 + 14 = 22 + 12 ÷ 3 and record them on BLM 61 ‘Balancing Equations’. • Patterns to Follow Write on the whiteboard: 6 + 5 = 11. Ask, ‘What are the key numbers in this pattern?’ (6, 5, 1 or 11) Ask for examples where this pattern is repeated in larger numbers, e.g. 166 + 5 = 171. Look for other patterns and have student extend their examples.
Independent Maths Individual, pair, small group
Bat and Add An activity for small groups. Access the ‘Batter Up Baseball’ site from http://www.prongo.com/math/index.html and select addition. A single will give you single digit activities, double displays 2-digit numbers and home run provides two 3-digit numbers to add. Timed Equations Students not using the computer can work in pairs to complete BLM 62 ‘Timing Equations’. One student has a stopwatch; they time how long it takes their partner to complete the additions. They then swap roles.They could time each other again in the following week. Put in the Numbers Give each group three dice and a sheet of paper showing these signs, in order: ×, +, –. (This way, the signs follow the order of BODMAS.) One student rolls the dice.The group then have two minutes to make as many equations as they can using different combinations of the digits rolled without changing the order of the signs. Students can use calculators to check their equations; allocate points to the player with the most correct equations.
142
Nelson Maths Teacher’s Resource — Book 5
$100 Spent Give each pair two dice. Each student starts with $100. They take turns to roll both dice, add the digits rolled and subtract them from 100, e.g. roll 3 and 4; add them together; 100 – 7 = 93.They record the round, then repeat the steps, this time subtracting from the number they just created (93), e.g. roll 5 and 1; add them together; 93 – 6 = 87. Play continues for ten rounds, after which students check each other’s rounds; the winner is the player with the lowest number of ‘dollars’ remaining. The Key to the Problems (Student Book p. 116) Have students use the equations in the stars as the key to solving the rectangular addition and subtraction problems. They can then create their own stars and matching equations to share. Balance the Scales (Student Book p. 117) Have students work out the missing digits so that both sides of the scale balance; remind them to use BODMAS, especially the brackets. Students can then make up some balancing equations of their own and record them on BLM 63 ‘A Balancing Act’. Students could either complete each one, or leave a box blank so a partner can solve the problem. Units 39–40 To monitor and assess students’ understandings have them complete the ‘Check and Self-assessment’ page (Student Book p. 118).
Whole Class Share Time Have students share their experiences with ‘Batter Up Baseball’; ask, ‘How did you work quickly when playing a double?’ Today I understood …
Have students explain the rules and demonstrate the game. Ask, ‘Could you play this game with another combination of signs?’ Have students share how they worked through this activity; ask, ‘How far from $100 did you get in ten rounds?’ Highlight the stars, and ask students to identify the keys in the equations. Check students’ responses, then ask, ‘Can these patterns work when we are dealing with numbers in the hundreds and thousands?’ Select students to explain how they deal with equivalent equations. Ask the group, ‘What part must you always start with?’
Unit 40 Balance the Numbers
143
BLM 1
Name: ____________________________________ Date: _____________
Rounding Off Round off the numbers below.
To the nearest 1000
To the nearest 100
To the nearest 10
2 398 3 972 7 016 3 805 8 901 1 111
5 624 4 835
9 744 6 297 1 042 4 198 Number and patterns (See Unit 1 pp. 24–26.)
144
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 2
Name: ____________________________________ Date: _____________
Place Value Dice Roll You will need : four 10-sided dice, a partner
Take turns to: • Roll the dice. • Create the largest and smallest numbers you can from the rolled digits. • Record the numbers. Look for any number patterns.
Digits Rolled
Largest Number
Smallest Number
Player 1 Player 2 Player 1 Player 2 Player 1 Player 2 Player 1 Player 2 Player 1 Player 2 Player 1 Player 2 Record what you found out about number patterns.
_____________________________________________________ _____________________________________________________ Number and patterns (See Unit 1 pp. 24–26.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
145
BLM 3
Name: ____________________________________ Date: _____________
A-Z Number Plates 24 students are getting number plates for their bikes. The number plates will: • Have only these 4 digits:
____ , ____ , ____ , ____ .
• Be given out in alphabetical order. Alex will get the highest/lowest number, and Xavier will get the highest/lowest number. Complete the chart to show who will get which number plate.
Student
Number Plate
Student
Number Plate
1 Alex
____________
13 Manuk
____________
2 Bree
____________
14 Nial
____________
3 Chris
____________
15 Olivia
____________
4 Dion
____________
16 Pia
____________
5 Elise
____________
17 Quentin
____________
6 Farah
____________
18 Rosa
____________
7 Guy
____________
19 Sian
____________
8 Hugh
____________
20 Tom
____________
9 Iva
____________
21 Una
____________
10 Jill
____________
22 Violet
____________
11 Kiah
____________
23 Will
____________
12 Lee
____________
24 Xavier
____________
Teacher’s note: Fill in four digits, select highest or lowest, then copy for each group. Number and patterns (See Unit 1 pp. 24–26.)
146
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 4
Name: ____________________________________ Date: _____________
Skip-counting Challenge You will need: 2 partners, 4 dice
Two players start off, using 2 dice each. Players take turns to: • Roll the first dice. Record the number rolled; this is the skip -counting number. • Roll the second dice. Record the number; this is the starting number. • Start the game. The first player to skip count correctly 7 times wins. • The third player judges the results, then plays the winner. Dice 1 Skip count by
Round 1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
Dice 1 Skip count by
Round 2
Dice 2 Start Number
1
1
2
2
3
3
4
4
5
5
6
6
7
7
Dice 1 Skip count by
Round 3
Dice 2 Start Number
Dice 2 Start Number
1
1
2
2
3
3
4
4
5
5
6
6
7
7
Dice 1 Skip count by
Dice 2 Start Number
Dice 1 Skip count by
Dice 2 Start Number
Dice 1 Skip count by
Dice 2 Start Number
Number and patterns (See Unit 2 pp. 27–29.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
147
BLM 5
Name: ____________________________________ Date: _____________
Skip-counting Grids Start
Count by
Start
Count by
Start
Count by
Start
Count by
Teacher’s Note: Write the ‘count by’ number in each column, then have students skip count independently starting from 1 or a number that is appropriate to their ability level. Number and patterns (See Unit 2 pp. 27–29.)
148
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 6
Name: ____________________________________ Date: _____________
Rolling 5-digit Numbers You will need: a dice, a partner
Your aim is to make the biggest 5-digit number possible. Take turns to: • Roll the dice. Decide which column to record the digit in. • Repeat, until you have recorded a 5-digit number. • The player with the biggest number wins the round. • The player who wins the most rounds wins the set. Player 1
Round
Player 2
1 2 3 4 5 Set Winner: Player 1
Round
Player 2
1 2 3 4 5 Set Winner: Player 1
Round
Player 2
1 2 3 4 5 Set Winner: Player 1
Round
Player 2
1 2 3 4 5 Set Winner:
Number and patterns (See Unit 3 pp. 30–32.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
149
BLM 7
Name: ____________________________________ Date: _____________
Blank Survey Form ________________________________________ ____________________________________________________ Survey question:
Available responses: 1 2 3 4 5
___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________
Option 1
tally:
Option 2
Option 3
Option 4
Option 5
tally:
tally:
tally:
tally:
________________________________________________ ____________________________________________________
Result
Findings from the survey: • • •
___________________________________________________ ___________________________________________________ ___________________________________________________
Chance and data (See Unit 4 pp. 33–35.)
150
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 8
Name: ____________________________________ Date: _____________
Letters of the Alphabet
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Space (See Unit 6 pp. 39–41.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
151
BLM 9
Name: ____________________________________ Date: _____________
Line Descriptors
vertical
vertical
vertical
vertical
horizontal
horizontal
horizontal
horizontal
parallel
parallel
parallel
parallel
perpendicular
perpendicular
perpendicular
perpendicular
diagonal
diagonal
diagonal
diagonal
curved
curved
curved
curved
Space (See Unit 6 pp. 39–41.)
152
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 10
Name: ____________________________________ Date: _____________
Multiplication and Division Roll You will need : 3 dice, a partner
Take turns to: • Roll 3 dice, one at a time. Record the numbers in the columns. • Multiply the number on the first 2 dice by the number on the third dice. For example: 1 2 4 12 x 4 = 48 • Then write a division equation using the same numbers. For example: 48 ÷ 4 = 12 Dice 1
Dice 2
Dice 3 (x or ÷)
Multiplication Equation
Division Equation
Number and patterns (See Unit 8 pp. 45–47.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
153
BLM 11
Name: ____________________________________ Date: _____________
Analogue Clock
12 11
1
10
2
9
3
8
4 7
6
5
Measurement (See Unit 10 pp. 51–53.)
154
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 12
Name: ____________________________________ Date: _____________
Clocks 11
12
1
11 2
10 9
11
8
5
12
1
11
9 8
8
12
1
11
8
4
5
12
1
11 2
6
5
12
1 2
10 3
4 6
1
3
6
8
12
2
7
9
5
9
4
10
6
10 3
7
4
5
2
11
1
3
6
8
12
2
7
9
5
9
4
10
6
10 3
7
4
6
2
11
3 7
10
7
2
9
4 7
1
10 3
8
12
5
9
3 8
4 7
6
5
Measurement (See Unit 10 pp. 51–53.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
155
BLM 13
Name: ____________________________________ Date: _____________
Digital Clocks
Teacher’s Note: Enlarge this page to A3 and laminate it. Measurement (See Unit 10 pp. 51–53.)
156
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 14
Name: ____________________________________ Date: _____________
Blank Month Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Measurement (See Unit 11 pp. 54–56.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
157
BLM 15
Name: ____________________________________ Date: _____________
Time Cards • Work in a group. Cut out the cards and share them. • On each blank card, write (and draw) an activity to match one of the word cards. • Shuffle all the cards and play ‘Snap’ or ‘Concentration’.
Ten seconds 30 seconds One minute Five minutes 30 minutes One hour Ten hours One day Teacher’s Note: Enlarge this BLM to A3. Measurement (See Unit 11 pp. 54–56.)
158
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 16
Name: ____________________________________ Date: _____________
Blank Calendar January S
M
T
W
T
February F
S
S
M
T
April S
M
T
W
M
T
W
T
F
S
S
M
M
T
W
F
S
S
M
T
T
W
T
F
S
S
M
T
T
W
T
F
S
S
M
S
S
M
T
W
T
F
S
T
T
T
W
T
F
S
F
S
F
S
September F
S
S
M
November F
W
June
August
October S
T
May
July S
W
March
T
W
T
December F
S
S
M
T
W
T
Teacher’s Note: Enlarge and photocopy this BLM. Have students use it to make their own calendars. Measurement (See Unit 11 pp. 54–56.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
159
BLM 17
Name: ____________________________________ Date: _____________
Fraction Wall Colour and label the fractions shown in this fraction wall.
Number and patterns (See Unit 12 pp. 57–59.)
160
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 18
Name: ____________________________________ Date: _____________
Build Your Own Fraction Wall Follow these steps to create your own fraction wall using Word. 1
Open a Word document.
2
Go to the main menu. Click on TABLE; then click on INSERT TABLE.
3
On the TABLE SIZE menu, select NUMBER OF COLUMNS as 1, and NUMBER OF ROWS as 10. Press OK.
4
A wall will appear on the screen. It will be 1 column wide and 10 rows high.
5
Press Ctrl-A to highlight wall. Select font size 48.
6
Move cursor to second row of your wall and click TABLE on the main menu bar.
7
Click on SPLIT CELLS.
8
On the Split Cells menu, select NUMBER OF COLUMNS as 2, NUMBER OF ROWS 1. Press OK.
9
The second row of the fraction wall will now be split into 2 equal parts.
10
Click on the third row of your wall. Repeat Step 8, but select the number of columns as 3.
11
Repeat Step 10, with the number of columns increasing by 1 each time you move down a row.
12
You can print out your fraction wall and colour and label it using coloured pencils, OR …
13
You can shade your fraction wall using the computer. Go to FORMAT. Select BORDERS AND SHADING. Select SHADING and highlight the section of the wall you wish to shade. Choose a colour to fill your wall and press OK. Print out your completed fraction wall.
Number and patterns (See Unit 12 pp. 57–59.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
161
BLM 19
Name: ____________________________________ Date: _____________
Woolloomooloo in Gold 1 Woolloomooloo is a suburb in Sydney. The local council want to purchase a new set of gold letters of their suburb’s name. The total cost will be $130. Use this information to answer these questions. a How many letters will they need to buy?
____________
b
How many vowels are in the word?
____________
c
What fraction of the word are vowels?
____________
d
What fraction of the word are consonants?
____________
e
What is the cost of each letter?
____________
f
What is the cost of all the vowels?
____________
g What is the cost of all the consonants?
____________
2 The Victorian towns of Mooroopna and Torumbarry followed Woolloomooloo’s idea and purchased gold letters. They bought them from different suppliers and were charged different prices. • Use the questions above as a guide to make some fraction statements for Mooroopna and Torumbarry.
Mooroopna
Torumbarry
COST:
COST:
$180
$150
Number and patterns (See Unit 12 pp. 57–59.)
162
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 20
Name: ____________________________________ Date: _____________
Decimal Points and Numbers
0
1
2
3
4
5
6
7
8
9
10
100
.
.
.
Teacher’s Note: Enlarge and copy onto coloured paper. Number and patterns (See Unit 13 pp. 60–62.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
163
BLM 21
Name: ____________________________________ Date: _____________
Decimal Cards
1.00
1.01
1.1
1.10
1.11 10.00
10.01 10.1 10.10 10.11 11.0 11.01 11.1 11.10 11.11 Teacher’s Note: Enlarge and copy onto coloured paper. Number and patterns (See Unit 13 pp. 60–62.)
164
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 22
Name: ____________________________________ Date: _____________
Cents and Millilitres • Find the pairs of decimal fractions in each column. • Use different coloured pencils to show the pairs. (The first one has been done for you.)
Millilitres
Cents 0.05
twenty cents
0.05
800 mL
0.5
sixty cents
0.7
750 mL
0.3
seventy-five cents
0.9
50 mL
0.1
twenty-five cents
0.5
400 mL
0.8
five cents
0.1
250 mL
0.6
fifty cents
0.8
600 mL
0.9
thirty cents
0.75
700 mL
0.2
eighty cents
0.2
300 mL
0.75
ninety cents
0.4
200 mL
0.7
ten cents
0.25
500 mL
0.4
seventy cents
0.6
100 mL
forty cents
0.3
900 mL
0.25
Number and patterns (See Unit 13 pp. 60–62.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
165
BLM 23
Name: ____________________________________ Date: _____________
Measurement Data Sheet For each object that you find to measure: • Estimate its length. • Measure the object and record its actual length. • Find the difference between your estimate and the actual length.
Object
Estimated Length
Actual Length
Difference
Measurement (See Unit 14 pp. 63–65.)
166
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 24
Name: ____________________________________ Date: _____________
Head, Paper, Calculator You will need : 3 dice, a calculator
• Roll the 3 d ice. Record the d igits as one number. • Multiply the number by 2. You can use your head, pen and paper, or a calculator. • Record the answer in the correct column. • Repeat these steps, multiplying by 3 and by 5. Then roll the 3 d ice again. Number
Multiplied by 2 head
paper
calculator
Multiplied by 3 head
paper
calculator
Multiplied by 5 head
paper
calculator
• Roll the 3 dice, then repeat the above steps. This time, divide by 2, 3 and 5. Number
Divided by 2 head
paper
calculator
Divided by 3 head
paper
calculator
Divided by 5 head
paper
calculator
Number and patterns (See Unit 15 pp. 66–68.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
167
BLM 25
Name: ____________________________________ Date: _____________
Travelling Game You will need : a partner, 3 dice
Aim to travel 11 kilometres in as few rounds as possible. • Take turns to throw the 3 dice. • Record the digits thrown as decimal fractions.
0.3
+
0.5
+
0.2 = 1.0 km
• Total the fractions for each round to find the kilometres travelled. Player 1 Round
Dice 1 Dice 2 Dice 3
Player 2 Round Ongoing Total Total
Round
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
Player 1 Round
Dice 1 Dice 2 Dice 3
Dice 1 Dice 2 Dice 3
Round Ongoing Total Total
Player 2 Round Ongoing Total Total
Round
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
Dice 1 Dice 2 Dice 3
Round Ongoing Total Total
Number and patterns (See Unit 15 pp. 66–68.)
168
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 26
Name: ____________________________________ Date: _____________
Create a Golf Course You will need : 3 dice
• Roll the 3 dice, one at a time. • Record the numbers rolled in the columns: Dice 1 = hundreds of metres; Dice 2 = tens of metres; Dice 3 = metres. • Write the length of the hole. • Repeat for all 18 holes. • Add the total distance of your golf course. 1 1 • Now estimate 2 and 4 of the length of each hole.
Hole
Dice 1
Dice 2
Dice 3
Length
Half Distance
Quarter Distance
Estimate
Estimate
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total
Number and patterns (See Unit 16 pp. 69–71.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
169
BLM 27
Name: ____________________________________ Date: _____________
Three Triangles
equilateral triangle
right-angle triangle
scalene triangle
Space (See Unit 17 pp. 72–74.)
170
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 28
Name: ____________________________________ Date: _____________
Who Am I?
rectangle
equilateral triangle
octagon
pentagon
hexagon
rhombus
square
scalene triangle
heptagon
nonagon
decagon
right-angle triangle
Space (See Unit 17 pp. 72–74.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
171
BLM 29
Name: ____________________________________ Date: _____________
Tangram You will need: coloured paper, scissors
Space (See Unit 17 pp. 72–74.)
172
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 30
Name: ____________________________________ Date: _____________
Flags to Flip • Use an atlas or a flag website. • Select a continent, then choose 5 countries. • Copy the flag of each country into the first column. Write the name of the country. • Then slide, turn and flip the flag in the next columns. Flag and Country
Slide
Turn
Flip
Space (See Unit 18 pp. 75–77.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
173
BLM 31
Name: ____________________________________ Date: _____________
Dice Roll Decimals You will need: a dice, a calculator, a partner
Take turns to: • Roll the dice. Record the number rolled, then convert it into a decimal. Use a calculator to check your partner’s addition. KEY For example, 1 = 0.1; 6 = 0.6 1 = 0.1 2 3 4 5 6
• Add your decimal total after 6 rolls. • After the 4th game, add all the decimal totals. • Convert the total into dollars and cents. Player 1: ______________
Game 1
Game 2
Game 3
Game 4
= = = = =
Player 2: ______________
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Roll 1 2 3 4 5 6 Total
Number
Decimal
Decimal Total: _____ Total in Dollars and Cents: _____
0.2 0.3 0.4 0.5 0.6
Decimal Total: _____ Total in Dollars and Cents: _____
Number and patterns (See Unit 19 pp. 78–80.)
174
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 32
Name: ____________________________________ Date: _____________
Number Investigator • Write down the pattern in the 3 × table (see BLM 75). • Record the hundreds, tens and ones in separate columns. • Use a colour code to show the pattern. • Repeat these steps for each × table shown. 3 × T O 3 6 9 1 2
H
9 × T
4 × T O
O
H
5 × T O
10 × T
O
6 × T O
H
11 × T
7 × T
O
8 × O
H
T
O
12 × T
O
Number and patterns (See Unit 20 pp. 81–83.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
175
BLM 33
Name: ____________________________________ Date: _____________
Half, Please You will need : a partner, 3 dice, a calculator
Take turns to: • Roll the 3 dice, one at a time. Record the numbers rolled. • Work out if you can evenly halve the number rolled. For example, 1 2 4: Half of 124 is 62. Write the number in the ‘Half’ column. • Put a
if you can’t halve the number.
Half = 62
• Use a calculator to check each other’s calculations at the end of the round. • The winner is the player with the most correct calculations at the end of the game. Player 1: Round
Dice 1
Player 2: Dice 2
Dice 3
Half?
Round
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
Dice 1
Dice 2
Dice 3
Half?
Number and patterns (See Unit 22 pp. 87–89.)
176
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 34
Name: ____________________________________ Date: _____________
Oranges Eaten You will need: partners, a dice
Find out how many oranges were eaten by your team during the match. Take turns to: • Roll the dice 3 times. • Record the numbers rolled in the columns. These numbers represent the number of orange quarters eaten. For example: 6 4 • After each match, total the number of oranges eaten. Match
Quarter time (Dice 1)
Half time (Dice 2)
Three-quarter Total Oranges Eaten time (Dice 3)
1 2 3 4 5 6 7 8 9 10
Number and patterns (See Unit 23 pp. 90–92.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
177
BLM 35
Name: ____________________________________ Date: _____________
fold
fold
Build This Box
fold
fold
fold fold
fold fold
Teacher’s note: Photocopy onto card. Enlarge half the copies to A3; keep the remainder at A4. Measurement (See Unit 24 pp. 93–95.)
178
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 36
Name: ____________________________________ Date: _____________
Dice Roll Record Sheet You will need: a dice
1 • Roll the dice 30 times. • Put a ✓ in the column to show the number you rolled. • Fill in the last four columns to show if the number was odd, even, a 6, or less than 5. Roll Number
1
2
3
4
5
6
Odd
Even
Six
Less than 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
2 How many times did you roll: • An even number? • A 6? ____
___
• An odd number?
___
• A number less than 5? ____
Chance and data (See Unit 25 pp. 96–98.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
179
BLM 37
Name: ____________________________________ Date: _____________
Number Dominoes
Number and patterns (See Unit 26 pp. 99–101.)
180
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 38
Name: ____________________________________ Date: _____________
41 Up You will need : a dice
41
33 32 17 16 1
34 35 36 37 38 39 40 31 30 29 28 27 26 25 18 19 20 21 22 23 24 15 14 13 12 11 10 9 2
3
4
5
6
7
8
• Roll the dice twice. Record the numbers on the table below: ★
dice 1 is your starting number.
★
dice 2 is the number you count by.
• Colour your starting number on the chart above. • Use the same colour to put a on the next 10 numbers in the pattern. Your aim is to reach 41. • Record the pattern on the table below. • Keep playing. Use a different colour each time. • Swap with a partner. Check each other’s patterns. Starting number
Skip by
Next 10 numbers in pattern
Numbers marked with ?
Checked by
Number and patterns (See Unit 26 pp. 99–101.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
181
BLM 39
Name: ____________________________________ Date: _____________
Fabulous Four You will need: 4 dice
1 • Roll all 4 dice at once. • Make the highest and lowest numbers you can from the digits rolled. • Repeat another 9 times. Highest
Lowest
2 a What was the: • Highest number you made? _______ • Lowest number you made? ______ b What is the highest number possible to make with: • Four 6-sided dice? ______________
• Four 9-sided dice? _____________
Number and patterns (See Unit 26 pp. 99–101.)
182
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 40
Name: ____________________________________ Date: _____________
2 022 2 200
2 220
2 220 2 222
2 202
2 419 2 568
2 399
2 783 2 817
2 659
Hot Numbers
Number and patterns
(See Unit 27 pp. 102–104.)
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
183
BLM 41
Name: ____________________________________ Date: _____________
Are You Ready to Count On? You will need : a dice, 2 partners
• One person acts as the Judge. • The two players roll the dice. • They record the number rolled as their Starting Number. • The Judge rolls the dice. Players record the roll in their Count On column, then complete the row, counting on from their starting number. • The Judge then checks each player’s sequence. • Repeat the last two steps 9 times.
Starting Number: _____ Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Count on by _____
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Number and patterns (See Unit 27 pp. 102–104.)
184
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 42
Name: ____________________________________ Date: _____________
MAD Cards
Number and patterns (See Unit 27 pp. 102–104.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
185
BLM 43
Name: ____________________________________ Date: _____________
Investigating Millilitres You will need : a measuring cup
There are twelve 250 millilitre bottles around the classroom. Each bottle contains a different amount of water. For each bottle: • Estimate and record how much water is in it. • Pour the water into the measuring cup to find the actual capacity. • Record the actual capacity. • Carefully pour the water back into the bottle. • Record your findings on an Excel spread sheet or BLM 65.
Bottle
Estimated Capacity (mL)
Actual Capacity (mL)
A B C D E F G H I J K L Measurement (See Unit 28 pp. 105–107.)
186
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 44
Name: ____________________________________ Date: _____________
Weight of Eight You will need : bathroom and kitchen scales, classroom objects, a calculator
Your aim is to collect 8 classroom objects that when weighed, total exactly 10 kg. You need to: • Write the name of each object and its weight in Table 1. • Use a calculator to add up the weight of 8 objects so they total exactly 10 kg. You will need to weigh a number of objects before you have 8 that weigh exactly 10 kg. • Repeat the same steps for Table 2, where your aim is total 5 kg. Table 1 — total 10 kg Object
Weight
Total
Teachers’ note:
Table 2 — total 5 kg Object
Weight
Total
Extra spaces are available in each table so students can record more than 8 objects. Suggest to students that they draw a star beside the eight objects that total 10/5 kg. If students are having difficulty totalling exactly 10/5kg, have them total a weight as close as they can to the desired amount.
Measurement (See Unit 31 pp. 114–116.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
187
BLM 45
Name: ____________________________________ Date: _____________
Multiple Race You will need : 2 dice, a partner
Take turns to roll the 2 dice, one at a time, then: • Record Dice 1 in the first column.
2 3 (3 × 10 = 30) 2 × 30 = 60
• Multiply Dice 2 by 10, then record it. • Multiply the two numbers, then record the total. • Keep a running total as you play. • The first player to score 1 000 wins. Player 1 Dice 1
Dice 2
Total
Player 2 Running Total
Dice 1
Dice 2
Total
Running Total
Number and patterns (See Unit 32 pp. 117–119.)
188
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 46
Name: ____________________________________ Date: _____________
Round Off You will need: 3 dice, a calculator, a partner 6
Take turns to: • Roll 3 dice, one at a time.
2 3 = 62 ÷ 3 = 20.6 Rounded = 21
• Record the numbers rolled in the first 3 columns. Dice 1 = tens; Dice 2 = ones; Dice 3 is the divisor. • Complete the division equation using a calculator. • Round off the answer to the nearest whole number. • Swap with your partner after 10 rounds and check each other’s answers. Tens
Ones
Divided by
Calculation
Rounded off
Number and patterns (See Unit 32 pp. 117–119.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
189
BLM 47
Name: ____________________________________ Date: _____________
Average Maximum Temperatures Melbourne Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
25.8°C 25.8°C 23.8°C 20.2°C 16.6°C 14.0°C 13.4°C 14.9°C 17.1°C 19.6°C 21.8°C 24.1°C
Sydney Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
26.1°C 26.0°C 24.9°C 22.4°C 19.7°C 17.2°C 16.7°C 18.1°C 20.3°C 22.3°C 24.1°C 25.5°C
Adelaide Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
28.5°C 28.5°C 26.0°C 22.1°C 18.6°C 15.8°C 14.9°C 16.1°C 18.4°C 21.3°C 24.4°C 25.5°C
Perth Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
29.7°C 30.0°C 28.0°C 24.6°C 20.9°C 18.3°C 17.4°C 18.0°C 19.5°C 21.4°C 24.6°C 27.4°C
Brisbane Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
29.4°C 29.0°C 28.0°C 26.1°C 23.2°C 20.9°C 20.4°C 21.8°C 24.0°C 26.1°C 27.1°C 29.1°C
Hobart Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
21.5°C 21.6°C 20.1°C 17.3°C 14.4°C 11.9°C 11.6°C 13.0°C 15.0°C 16.9°C 18.6°C 20.2°C
Darwin Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
32.4°C 32.1°C 32.7°C 33.6°C 32.6°C 31.2°C 30.7°C 31.8°C 33.0°C 34.1°C 34.3°C 33.5°C
Canberra Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
28.5°C 28.1°C 24.7°C 20.1°C 15.8°C 12.3°C 11.5°C 14.9°C 16.2°C 19.6°C 23.5°C 26.3°C
Number and patterns (See Unit 33 pp. 120–122.)
190
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 48
Name: ____________________________________ Date: _____________
Temperatures: Up and Down • Select 2 cities from BLM 47. Write their names. • Write the months of the year, then record the temperatures for your chosen city. • Compare the temperature of each month with the month before it. (You will need to compare January with December.) • Select a difference symbol to show whether the temperature increased, decreased or stayed the same. City: –––––––––––––––––––––––––– Month
Temperature
(∞°C)
Difference
Difference Symbols
+ –
decreased
n/c
no change
increased
City: –––––––––––––––––––––––––– Month
Temperature
Difference
(∞°C)
Number and patterns (See Unit 33 pp. 120–122.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
191
BLM 49
Name: ____________________________________ Date: _____________
3D Objects Cube
Rectangular prism
Triangular prism
Cylinder
Pentagonal prism
Hexagonal prism
Octagonal prism
Sphere
Octagonal pyramid
Cone
Square pyramid
Hemisphere
Pentagonal pyramid
Triangular pyramid
Space (See Unit 34 pp. 123–125.)
192
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 50
Name: ____________________________________ Date: _____________
Square Pyramid Net
fold
fold
fold
fold Space (See Unit 34 pp. 123–125.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
193
BLM 51
Name: ____________________________________ Date: _____________
Triangular Pyramid Net
fold
fold
fold Space (See Unit 34 pp. 123–125.)
194
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 52
Name: ____________________________________ Date: _____________
Triangular Prism Net fold
fold
fold
fold
fold Space (See Unit 34 pp. 123–125.)
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
195
BLM 53
Name: ____________________________________ Date: _____________
Cube Net
fold
fold
fold
fold
fold
fold
fold Space (See Unit 34 pp. 123–125.)
196
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 54
Name: ____________________________________ Date: _____________
Rectangular Prism Net
fold
fold fold
fold
fold
fold
fold Space (See Unit 34 pp. 123–125.)
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
197
BLM 55
Name: ____________________________________ Date: _____________
fold
Octahedron Net
fold
fold fold
fold Space (See Unit 34 pp. 123–125.)
198
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 56
Name: ____________________________________ Date: _____________
fold
fold
fold
fold
fold
fold
fold
Pentagonal Prism Net
fold
fold Space (See Unit 34 pp. 123–125.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
199
BLM 57
Name: ____________________________________ Date: _____________
Chance Spinners
Chance and data (See Unit 35 pp. 126–128.)
200
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 58
Name: ____________________________________ Date: _____________
Chance Words
Certain Likely Impossible Possible Unlikely Even chance 50-50 chance Chance and data (See Unit 35 pp. 126–128.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
201
BLM 59
Name: ____________________________________ Date: _____________
Hundred Grid 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
Number and patterns (See Unit 39 pp. 138–140.)
202
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 60
Name: ____________________________________ Date: _____________
Operation Grid You will need: partners, 4 dice, a calculator
• One player rolls the 4 dice. • All players use the numbers rolled to create an equation. Each number must be used. • Use a calculator to check each other’s equations. • Continue, taking turns to roll the dice.
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
x
+
–
=
Number and patterns (See Unit 39 pp. 138–140.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
203
BLM 61
Name: ____________________________________ Date: _____________
Balancing Equations
Number and patterns (See Unit 40 pp. 141–143.)
204
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 62
Name: ____________________________________ Date: _____________
Timing Equations You will need: a stopwatch
72 + 59 ______
48 + 43 ______
38 + 10 ______
69 + 37 ______
92 + 57 ______
84 + 21 ______
55 + 68 ______
10 + 10 ______
79 + 37 ______
87 + 88 ______
47 + 73 ______
85 + 57 ______
10 + 38 ______
61 + 65 ______
73 + 47 ______
189 + 467 ______
218 + 353 ______
369 + 585 ______
762 + 298 ______
227 + 437 ______
395 + 367 ______
438 + 549 ______
875 + 266 ______
428 + 424 ______
768 + 399 ______
296 + 549 ______
487 + 262 ______
333 + 437 ______
898 + 362 ______
238 + 555 ______
Number and patterns (See Unit 40 pp. 141–143.) © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
205
BLM 63
Name: ____________________________________ Date: _____________
A Balancing Act
(
+
=
(
–
) ×
(
×
=
(
+
) ÷
(
+
) ÷
=
(
+
(
÷
+
=
(
×
(
–
=
(
+
) ÷
(
÷
=
(
×
+
(
+
=
(
+
–
(
×
=
(
÷
(
+
=
(
+ (
) ÷ ) ×
–
)
Number and patterns (See Unit 40 pp. 141–143.)
206
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 64
Name: ____________________________________ Date: _____________
5-digit Place-value Chart
TTh Th
H
T
O
Use with Unit 3 and other similar number activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
207
BLM 65
Name: ____________________________________ Date: _____________
My Graph Title: ___________________________________
Use with Units 4, 28, 31, 33 and other similar data activities.
208
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 66
Name: ____________________________________ Date: _____________
Venn Diagrams
Teacher’s note: Enlarge to A3. Use with Units 4, 38 and other similar measurement and data activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
209
BLM 67
Name: ____________________________________ Date: _____________
Centimetre Grid
Use with Units 9, 12, 21, 30, 33 and other similar space, number and measurement activities.
210
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 68
Name: ____________________________________ Date: _____________
Fraction Cards
1 __ 1 __ 3 __ 5 __ 1 __ 2 4 4 8 5 1 __ 1 __ 1 __ 2 __ 3 __ 8 16 10 3 8 1 __ 2 __ 3 __ 2 __ 6 __ 5 5 5 8 8 4 4 7 1 1 __ __ __ __ __ 8 5 4 8 3 Use with Units 12, 29 and other similar number activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
211
BLM 69
Name: ____________________________________ Date: _____________
Hundreds
Tens
Ones
.
Tenths
Hundredths
Hundreds, Tens, Ones, Tenths & Hundredths Chart
Use with Units 13, 33 and other similar number activities.
212
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 70
Name: ____________________________________ Date: _____________
Square Dot Paper
Use with Unit 17. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
213
BLM 71
Name: ____________________________________ Date: _____________
Triangle Shape Grid
Use with Unit 18.
214
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 72
Name: ____________________________________ Date: _____________
Tesselating Shapes
Use with Unit 18. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
215
BLM 73
Name: ____________________________________ Date: _____________
Banknotes
Use with Units 19, 32, 39 and other similar money activities.
216
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 74
Name: ____________________________________ Date: _____________
Coins
Use with Units 19, 22, 32, 39 and other similar money activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
217
BLM 75
Name: ____________________________________ Date: _____________
Tables Chart 1 11 x 1 =
1
1
x 2 =
2
1
x 3
=
3
12 x 1 =
2
2
x 2 =
4
2
x 3
=
6
13 x 1 =
3
3
x 2 =
6
3
x 3
=
9
14 x 1 =
4
4
x 2 =
8
4
x 3
= 12
15 x 1 =
5
5
x 2 = 10
5
x 3
= 15
16 x 1 =
6
6
x 2 = 12
6
x 3
= 18
17 x 1 =
7
7
x 2 = 14
7
x 3
= 21
18 x 1 =
8
8
x 2 = 16
8
x 3
= 24
19 x 1 =
9
9
x 2 = 18
9
x 3
= 27
10 x 1 = 10
10
x 2 = 20
10
x 3
= 30
11 x 1 = 11
11
x 2 = 22
11
x 3
= 33
12 x 1 = 12
12
x 2 = 24
12
x 3
= 36
11 x 4 =
4
1
x 5 =
5
1
x 6
=
6
12 x 4 =
8
2
x 5 = 10
2
x 6
= 12
13 x 4 = 12
3
x 5 = 15
3
x 6
= 18
14 x 4 = 16
4
x 5 = 20
4
x 6
= 24
15 x 4 = 20
5
x 5 = 25
5
x 6
= 30
16 x 4 = 24
6
x 5 = 30
6
x 6
= 36
17 x 4 = 28
7
x 5 = 35
7
x 6
= 42
18 x 4 = 32
8
x 5 = 40
8
x 6
= 48
19 x 4 = 36
9
x 5 = 45
9
x 6
= 54
10 x 4 = 40
10
x 5 = 50
10
x 6
= 60
11 x 4 = 44
11
x 5 = 55
11
x 6
= 66
12 x 4 = 48
12
x 5 = 60
12
x 6
= 72
Use with Units 20, 26 and other similar number activities.
218
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 76
Name: ____________________________________ Date: _____________
Tables Chart 2 11 x 7 =
7
1
x 8 =
8
1
x 9
=
9
12 x 7 = 14
2
x 8 = 16
2
x 9
= 18
13 x 7 = 21
3
x 8 = 24
3
x 9
= 27
14 x 7 = 28
4
x 8 = 32
4
x 9
= 36
15 x 7 = 35
5
x 8 = 40
5
x 9
= 45
16 x 7 = 42
6
x 8 = 48
6
x 9
= 54
17 x 7 = 49
7
x 8 = 56
7
x 9
= 63
18 x 7 = 56
8
x 8 = 64
8
x 9
= 72
19 x 7 = 63
9
x 8 = 72
9
x 9
= 81
10 x 7 = 70
10
x 8 = 80
10
x 9
= 90
11 x 7 = 77
11
x 8 = 88
11
x 9
= 99
12 x 7 = 84
12
x 8 = 96
12
x 9
= 108
11 x 10 = 10
1
x 11 =
11
1 x 12 = 12
12 x 10 = 20
2
x 11 =
22
2 x 12 = 24
13 x 10 = 30
3
x 11 =
33
3 x 12 = 36
14 x 10 = 40
4
x 11 =
44
4 x 12 = 48
15 x 10 = 50
5
x 11 =
55
5 x 12 = 60
16 x 10 = 60
6
x 11 =
66
6 x 12 = 72
17 x 10 = 70
7
x 11 =
77
7 x 12 = 84
18 x 10 = 80
8
x 11 =
88
8 x 12 = 96
19 x 10 = 90
9
x 11 =
99
9 x 12 = 108
10 x 10 = 100
10
x 11 = 110
10 x 12 = 120
11 x 10 = 110
11
x 11 = 121
11 x 12 = 132
12 x 10 = 120
12
x 11 = 132
12 x 12 = 144
Use with Units 20, 26 and other similar number activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
219
BLM 77
Name: ____________________________________ Date: _____________
Island Life
Use with Unit 21.
220
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 78
Name: ____________________________________ Date: _____________
Isometric Dot Paper
Use with Units 24, 34 and other similar space activities. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
221
BLM 79
Name: ____________________________________ Date: _____________
Ones Tens Thousands Tens of thousands
Hundreds
Ones Tens Thousands Tens of thousands
Hundreds
Thousands Tens of thousands
Hundreds
Tens
Ones
5-digit Number Expander
Use with Unit 27.
222
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 80
Name: ____________________________________ Date: _____________
Grid Coordinates A
B
C
D
E
F
G
H
I
1 2 3 4 5 6 7 8 9 10
Use with Unit 30. © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
223
BLM 81
Name: ____________________________________ Date: _____________
My Timetable Title:
Time
_______________________
Event
Use with Unit 35.
224
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 82
Student Profile Code:
NA not apparent
Week
B
beginning
C
consolidating
E
established
Unit
Name: ___________________________________________________________________ Year Level: __________
Term: __________
Year: __________
‘Plain Speak’ Statements
(Date)
1 Investigating Place Value
Read, say, write and place in order numbers up to 5 digits Recognise and represent different forms of the same number
2
Read, say, write and place in order whole numbers up to 5 digits Understand place value in whole numbers up to 5 digits Skip count by 2, 3, 4, 5 and 6 beyond 100 Skip count by 10s and 100s to 1000, starting at any given number Find and compare fractional parts of collections Use, order and compare decimals in real-life situations
Numbers That Count
3 What’s in a Number?
4 Data Collection
5 Patterns and Relationships
6 Lines in Our World
7 Addition and Subtraction
8 Multiplication and Division
Create, identify and order numbers up to 5 digits Skip count from set numbers by 2, 3, 4, 5, 6, 10, 100 and 1000
Conduct surveys to collect information Use Venn diagrams to show data Use graphs [bar (column), picture graph and line] to show information collected Interpret information collected and displayed Use rules involving addition, subtraction and multiplication to describe and continue a given number sequence Complete simple statements of equality involving addition, subtraction and multiplication
Recognise and describe the characteristics of lines in the environment Create pictorial representations of lines (straight, curved, diagonal, horizontal, vertical, parallel, perpendicular) Describe right, obtuse, acute (sharp) and straight angles
Explore and manipulate materials to assist their understanding of place value, subtraction and addition Solve addition and subtraction equations with different methods of calculation Solve addition and subtraction problems using everyday examples of 3- and 4-digit numbers Solve and record multiplication word problems and equations where whole numbers are multiplied by single numbers or multiples of ten Solve and record division word problems and equations using 3-digit numbers and a single divisor
9 Measuring and Estimating Angles
Identify, name and create angles [obtuse (blunt), acute (sharp), right and straight] Order angles from smallest to largest
10 Analogue and Digital Times
Read and record digital time in hours and minutes Read and record analogue time to 5-minute intervals
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
225
BLM 83
Student Profile Code:
NA not apparent
Week (Date)
B
beginning
C
consolidating
E
established
Unit
Name: ___________________________________________________________________ Year Level: __________
Term: __________
Year: __________
‘Plain Speak’ Statements
11 Timetables and Schedules
12 Fractions
13 Decimals
14 Length
Explore periods of time and elapsed time Explore and use everyday calendars and schedules to plan events
Identify, name and represent fractional parts of models, charts and collections Compare and order simple common fractions Identify unit fractional parts of discrete collections Use fractions as an operator
Read, write, compare and order decimals to two decimal places Use decimals to compare familiar objects Interpret decimal numbers to the first decimal place Recognise that a position of a decimal point affects the size and value of a number
Measure everyday items using formal and informal units Estimate and measure using centimetres and metres
15 Travelling with Numbers
16 Numbers in Golf
17 2D Shapes
18 Flip, Slide and Turn
19 Value for Money
20 Words and Numbers
226
Use their knowledge of addition, subtraction, division and multiplication to solve problems Use methods of calculation to determine the best way to reach an accurate outcome
Double and halve numbers to work out equations Round off numbers to assist with estimations Select the appropriate operation and computation method to solve problems
Recognise, name, describe and construct simple 2D shapes Use rulers and computer software to draw lines, shapes and angles Construct recognisable objects using combinations of shapes Draw and explain lines of symmetry in regular 2D shapes
Identify and use the terms slide, turn and flip when manipulating shapes Identify shapes that will and will not tessellate Create a series of tiles that involve sliding, turning and flipping
Round off money values using a calculator Identify different combinations of money to make equal amounts Select the appropriate methods to solve money problems and equations Convert common fractions to decimals
Identify, name, extend and create number patterns Complete and create word problems involving operations
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 84
Student Profile Code:
NA not apparent
Week (Date)
B
beginning
C
consolidating
E
established
Unit
21 Area
22 More Multiplication and Division
23 Everyday Numbers
24 Volume
25 Chance
26 Numbers Close Up
27 Numbers Beware!
28 Capacity
29 Fractions as Operators
30 Location
Name: ___________________________________________________________________ Year Level: __________
Term: __________
Year: __________
‘Plain Speak’ Statements
Measure, order and record the area of regular and irregular shapes using both informal and formal units
Make the connection between division and multiplication tasks Use a variety of computation methods to solve problems Use a calculator to solve decimal problems in everyday situations
Create, name and rank decimal numbers in order Solve everyday problems by selecting the appropriate computation methods Use their knowledge of numbers to complete complex addition and multiplication tasks Investigate volume and its relationship to capacity Use various informal and formal units to calculate the volume of everyday objects Identify successful and unsuccessful units for measuring volume Make and draw Centicube models Identify and order and apply possible outcomes with defined terms of chance Identify and record all possible outcomes in simple chance experiments Identify situations and activities that are fair or unfair Use the vocabulary of chance Use their knowledge of table facts and place value to solve problems Use mental and written strategies to simplify number tasks Use the calculator to perform number tasks
Use their knowledge of place value to round off and order numbers Use mental and written methods to simplify number tasks Skip count by 2, 3, 4, 5, 6 from any given number
Make predictions about capacity Make connections between function and the use of litres or millilitres Use containers of various units to conduct capacity experiments Identify the relationship between capacity and volume
Work with fractions to create and solve word problems Use fractions as an operator when dealing with amounts, length and groups of objects Identify and order fractions according to size
Use grid references to locate specific venues Use cardinal compass points to plot pathways Plan and draw locations from a bird’s-eye view Use and understand turns in terms of degrees
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
227
BLM 85
Student Profile Code:
NA not apparent
Week (Date)
B
beginning
C
consolidating
E
established
Unit
31 Mass
32 Multiplication and Decimals
33 More About Decimals
34 3D Objects
35 Revision
36 Solving Problems
37 Four Operations
38 Make These Shapes
39 Working with Numbers
228
Name: ___________________________________________________________________ Year Level: __________
Term: __________
Year: __________
‘Plain Speak’ Statements Estimate the mass of items in grams and kilograms Use and apply the appropriate mass units to measure objects Multiply single-digit numbers by factors of 10 Round off answers on a calculator Use fractions as operators Apply decimals to everyday situations Read, write and say decimals Compare, order and round off decimals Calculate the average and range using decimals Choose appropriate methods to calculate problems Display knowledge of decimals Recognise, name, describe and construct simple 3D shapes Use rulers or computer software to draw lines, shapes and angles Construct recognisable objects using combinations of shapes Identify the important features of 3D objects Round off money to the nearest five cents, ten cents and dollar Estimate short periods of time Plan timetables Experiment with fair and unfair chance activities Make mental and written computations using money Choose the appropriate method (written or mental) to complete calculations Use two operations to solve a problem Round off calculator displays to achieve a required result
Make mental and written computations using money Choose the appropriate method (written or mental) to complete calculations Use two operations to solve a problem Round off calculator displays to achieve a required result Identify and create 2D and 3D objects Work with congruency View shapes from different perspectives Identify lines and use them to construct drawings Use rules to complete number patterns and equations Make statements of equality using whole number and decimals Select the appropriate operations to complete equations
Complete addition, subtraction, multiplication and division equations
40
Use rules to complete number patterns and equations
Complete addition,
Balance the Numbers
Make statements of equality using whole number and decimals Select the appropriate operations to complete equations
subtraction, multiplication and division equations
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 86 Unit: _______
Weekly Maths Planner A Week: _______
Term: _______
Date: _______
Year Level: _______
Resources:
Monday
Tuesday
Wednesday
Thursday
Friday
Whole Class Focus
Small Group Focus
Focus Teaching Group
Independent Maths (individual, pair, small group)
Whole Class Share Time
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
229
BLM 87 Unit: _______
Weekly Maths Planner
Week: _______
Term: _______
B Date: _______
Year Level: ________
Resources:
Whole Class Focus (Shared) Learning Experience (activities)
Teaching Focus M T W Th F Small Group Focus Focus Teaching Group Teaching Approach: M (modelled) Approach/Teaching Focus
S (shared) G (guided)
Learning Experience (activities)
Independent Maths (individual, pair, small group) Independent Activities
M S G
M
Focus: Students: M S G
T
Focus: Students: M S G
W
Focus: Students: M S G
Th
Focus: Students: M S G
F
Focus: Students: Whole Class Share Time
Other
230
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 88 Unit: _______
Weekly Maths Planner
Week: _______
Term: _______
C Date: _______
Year Level: _______
Resources:
Whole Class Focus (Shared) Teaching Focus
Learning Experience (activities)
M T W Th F Small Group Focus (Focus Teaching Group) Teaching Approach – Modelled Shared Guided
Teaching Focus: Learning Experience: Students:
M
Teaching Approach – Modelled Shared Guided
Teaching Focus: Learning Experience: Students:
T
Teaching Approach – Modelled Shared Guided
Teaching Focus: Learning Experience: Students:
W
Teaching Approach – Modelled Shared Guided
Th
Teaching Focus: Learning Experience: Students: Teaching Approach – Modelled Shared Guided
F
Teaching Focus: Learning Experience: Students:
Independent Maths (individual, pair, small group)
Whole Class Share Time
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
231
232
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
M S G M S G M S G M S G M S G
Teaching Approach: Focus:
Teaching Approach: Focus:
Teaching Approach: Focus:
Teaching Approach: Focus:
Week: ___________
Learning Experience (activities)
Learning Experience (activities)
Resources:
Unit: _____________
Teaching Approach: Focus:
Other (reflection/future planning)
Whole Class Share Time
Students
Small Group Focus
Teaching Focus
D
Focus Teaching Group
Weekly Maths Planner
Whole Class Focus (Shared)
BLM 89 Date: ___________
Year Level: ___________
Independent Maths (individual, pair, small group)
Term: ___________
BLM 90
Term Maths Planner Year Level: __________
Week
Unit/Page no.
Term: __________
Year: __________
Major Learning Outcomes
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
233
Year: _____________
BLM 91 Term 1
Year Level: _____________ Unit
Term 3
Week 1
Week 1
Week 2
Week 2
Week 3
Week 3
Week 4
Week 4
Week 5
Week 5
Week 6
Week 6
Week 7
Week 7
Week 8
Week 8
Week 9
Week 9
Week 10
Week 10
Term 2
234
Yearly Maths Planner A
Unit
Term 4
Week 1
Week 1
Week 2
Week 2
Week 3
Week 3
Week 4
Week 4
Week 5
Week 5
Week 6
Week 6
Week 7
Week 7
Week 8
Week 8
Week 9
Week 9
Week 10
Week 10
Unit
Unit
© Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
BLM 92 Unit/Page no.
Year: _____________
Yearly Maths Planner
B Year Level: _____________
Major Learning Outcomes
Term 1 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10
Term 2 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10
Term 3 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10
Term 4 Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 © Thomson Learning, 2004. This page from Nelson Maths Teacher's Resource — Book 5 may be photocopied for educational use within the purchasing institution.
235
Answers to Student Book Pages Page 5
Page 1 (continued)
1 9 900, 99 hundreds, Nine thousand nine hundred 6 200, 62 hundreds, Six thousand two hundred 1 000, 100 tens, One thousand 2 020, 202 tens, Two thousand and twenty 7 600, 76 hundreds, Seven thousand six hundred 1 200, 12 hundreds, One thousand two hundred 897, 897 ones, Eight hundred and ninety-seven 128, 128 ones, One hundred and twenty-eight 1 219, 1 219 ones, One thousand two hundred and nineteen 2 420, 242 tens, Two thousand four hundred and twenty, 560, 56 tens, Five hundred and sixty 230, 23 tens, Two hundred and thirty 3 190, 319 tens, Three thousand one hundred and ninety 1 280, 128 tens, One thousand two hundred and eighty
Star number
+5
395 600 715 830 975 1020 1095 1190 1205 1410 1595 1640 1790 1820 1855 1955
400 605 720 835 980 1025 1100 1195 1210 1415 1600 1645 1795 1825 1860 1960
Page 6 Family
Last 4 numbers
Cash Won
Lucky 7?
Chew Noonan Haas Goh Pearce Feast Jark Unger Dunn Gill HU Lim Hartz Barcou Jeffris
9 997 6825 6178 5643 3302 2845 2749 2293 2134 1997 1940 0989 0872 0701 0170
$9 997 $6825 $6178 $5643 $3302 $2845 $2749 $2293 $2134 $1997 $1940 $989 $872 $701 $170
7 days free — 7 — — — 7 — — 7 — 7 7 7
Page 7 1 a 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167 b 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137 c 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130 d 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123 e 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119 f 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130 126, 136, 146, 156, 166, 176, 186, 196, 206, 216, 226, 236 970, 980, 990, 1 000, 1 010, 1 020, 1 030, 1 040, 1 050, 1 060, 1 070, 1 080 g 33, 133, 233, 333, 433, 533, 633, 733, 833, 933, 1 033, 1 133 200, 300, 400, 500, 600, 700, 800, 900, 1 000, 1 100, 1 200 478, 578, 678, 778, 878, 978, 1 078, 1 178, 1 278, 1 378, 1 478
Page 8
236
Star number
+5
–5
85 160 295 315
90 165 300 320
80 155 290 310
Nelson Maths Teacher’s Resource — Book 5
–5 390 595 710 825 970 1015 1090 1185 1200 1405 1590 1635 1785 1815 1850 1950
Page 9 Digits coloured should read: 007
Page 10 1a 3 4 5 10 b 2 3 4 5 10 c 2 3 4 5 10
32, 35, 38, 41, 44, 47, 50, 53, 56, 59 33, 37, 41, 45, 49, 53, 57, 61, 65, 69 34, 39, 44, 49, 54, 59, 64, 69, 74, 79 39, 49, 59, 69, 79, 89, 99, 109, 119, 129 54, 56, 58, 60, 62, 64, 66, 68, 70, 72 55, 58, 61, 64, 67, 70, 73, 76, 79, 82 56, 60, 64, 68, 72, 76, 80, 84, 88, 92 57, 62, 67, 72, 77, 82, 87, 92, 97, 102 62, 72, 82, 92, 102, 112, 122, 132, 142, 152 83, 85, 87, 89, 91, 93, 95, 97, 99, 101 84, 87, 90, 93, 96, 99, 102, 105, 108, 111 85, 89, 93, 97, 101, 105, 109, 113, 117, 121 86, 91, 96, 101, 106, 111, 116, 121, 126, 131 91, 101, 111, 121, 131, 141, 151, 161, 171, 181
Page 11 4 a = 5000 + 900 + 10 + 8 b 6 ones + 2 hundreds + 2 tens + 8 thousands
Page 12 1 a 18 b 6 c 8 d 4 e 2 f 5
Page 13 1 a 12 b 23 c 11 d 16 e 29 f 21 g 14 2 a chocolate, lime, strawberry b banana, iced coffee, honeycomb c no they equal it d banana, iced coffee, honeycomb e yes, because it was the third most popular f answers will vary
Page 14 1 a 10 b Nial c Jeff d Harry and Sian 2 a no b included more hair colours
answers will vary
Page 15 1a b c d e f 2a
1, 5, 8, 12, 15, 19, 22, 26, 29, 33, 36 11, 13, 18, 20, 25, 27, 32, 34, 39, 41, 46 100, 90, 89, 79, 78, 68, 67, 57, 56, 46, 45 30, 36, 33, 39, 36, 42, 39, 45, 42, 48, 45 56, 61, 57, 62, 58, 63, 59, 64, 60, 65, 61 120, 130, 125, 135, 130, 140, 135, 145, 140, 150, 145 +8 –4 b –5 +2 c –2 –3 d –100 +50 e +6 –1 f –5 +10
Page 16 1 4 2 3 3 15 4 3 5 40 6 3 7 & 8 answers will vary
b answers will vary c lime, strawberry d 12c, 36c, 24c, 48c 2a DC DC DC DC DC MC MC MC MC MC
Page 17 2 a +5 +2 b –4 +1 c +2 +3 +4 +5 3 a 15, 20, 17, 22, 19, 24, 21 b 50, 55, 65, 70, 80, 85, 95, 100 c 39, 43, 46, 49, 53, 56, 59, 63 4 a 9 b 2 c & d answers will vary
DC
Page 20
DC
DC
DC
DC
WC WC WC WC WC
order can vary a each piece 14 c, dark choc $1.40, milk choc 70c, white choc 70c
1 a vertical b diagonal c parallel d perpendicular e horizontal f curved
Page 36 Page 21
b 2,1, 1
1a
1 39 2 81 3 83 4 123 5 353 6 389 7 401 8 505 9 266 10 132 11 319 12 1211 13 5681 14 725 15 1611 16 5422 17 991 18 2725 19 3988 20 911
6 8 4
2 a Fiona b Bridget c Kate 3 a $2, $8 b $2, $14 c $4, $12
Page 22 Page 38
1 Hamilton 22123, Brighton 19281, Kingston 17132, Richmond 22756 2 Hamilton 7140 & 2303 (+ 9443, – 4837), Brighton 7030 & 3186 (+ 10216, – 3844), Kingston 7050 & 2604 (+ 9654, – 4446), Richmond 7027 & 2753 (+ 9780, – 4274)
Page 23
1 1st Jack 3.52 m 3.5m; 2nd Dean 3.43 m 3.4 m; 3rd Kate 3.37 m 3.4 m; 4th Bridget 3.28 m 3.3 m; 5th Kiah 3.21 m 3.2 m; 6th Skye 3.19 m 3.2 m; 7th Emily 3.05 m 3.1 m; 8th Jeff 3.03 m 3.0 m; 9th Declan 2.97 m 3.0 m; 10th Harry 2.93 m 2.9 m 2 a 3.0 m b Jeff c answers will vary
1 a 15 b 25 c 18 d 16 e 16 r 2 f 13 r 3 g 142 h 161 i 234 j 262 k 151 l 109 m 81 r 1 n 184 r 3 o 227 r 3
Page 39 1 1 9
Page 24 Reads: MULTIPLIED MUSKETEERS
Page 40 1 Jack 12.5 cm 3rd Bree 12 cm 4th Nial 11 cm 6th Liam 13.5 cm 1st Ky 9.5 cm 7th Kate 13 cm 2nd Kelly 7.5 cm 10th Yuri 9 cm 8th Sean 11.5 cm 5th Pia 8 cm 9th
Page 25 2 a 850 b 942 c 612 d 4344 e 3341 f 38 4 a 21 b 24 c 45 d 32 e 7 r 1 f 114 g 30 r 2 h 33 5 7 groups of 8
Page 43
Page 26 1 a red (right) b yellow (acute) c purple (straight) d green (obtuse) e green (right) f yellow (acute) g green (obtuse) h red (right) i yellow (acute) j green (obtuse) k purple (straight) l green (obtuse)
1 1 097 km 2 362 km 3 797 km 4 1 015 km 5 a Gilgandra b 797 km
Page 44 Distance
Page 27
12
11
1
1 b acute
9
11
12
1
11
g obtuse
3 4
8 7
6
12
1
11
h obtuse
3 4 7
6
12
5
11
i straight
3 4
12
5
1 2
9
5
6
6
10
2
7
3 4
8
1
8
3 4
8 7
6
5
Page 28 1
2
4
3
Brisbane to Cairns Brisbane to Darwin Adelaide to Melbourne Perth to Darwin Melbourne to Sydney Brisbane to Sydney
Page 30
Distance
1 & 2 woke up 6:45, dress for school 7:00, cereal for breakfast 7:30, school starts 9:00, recess time 10:45, lunchtime 12:45, school finishes 3:30, Mum picks me up 3:35, favourite TV show 5:05, dinner with family 6:30, bath 7:25
Brisbane to Cairns Brisbane to Darwin Adelaide to Melbourne Perth to Darwin Melbourne to Sydney Brisbane to Sydney
Page 31 1 a 9:30 b 11:00 c 2:35 d 4:10 2 a twenty past two b five past six c five to four d half past seven 11
12
1
11 2
10
3a
9 4
8 7
6
12
1
9:45 b
5
11 2
10 3
9 4
8 7
6
12
1
9:55 c
5
11 2
10 3
9 4
8 7
6
12
10:05
d
5
3 4
8 7
6
10:15
Page 34 1 a 20th b 8th c 24th to 26th d 29th 2 a 8 b 5 c no, Feb. has only 28/29 days 3 2nd & 30th 4 Saturday
O
O
C
C
L
Return trip
2 days
3 days
4 days
3404 6816 1872 8328 1748 1964
1702 3408 936 4164 874 982
1134.7 2272 624 2776 582.7 654.7
851 1704 468 2082 437 491
Page 45 Please note: answers will vary ‘My est.’ section. CR 1 (morn.) My est. $75, Actual tot. $75.10, Diff. $0.10 CR 2 (morn.) My est. $83, Actual tot. $82.95, Diff. $0.05 CR 3 (morn.) My est. $76, Actual tot. $75.45, Diff. $0.55 CR 1 (after.) My est. $75, Actual tot. $75.45, Diff. $0.45 CR 2 (after.) My est. $75, Actual tot. $73.25, Diff. $1.75 CR 3 (after.) My est. $120, Actual tot. $120.45, Diff. $0.45
Page 46 2 240 3 50 4 15 5 172 6 205 7 111 8 63 9 8 10 38 11 304 12 7 13 186 14 164 15 97 16 16 17 104 18 132
Page 35 O
3404 km 6816 km 1872 km 8328 km 1748 km 1964 km
5
1 a 7:15 b 7:10 c 5:55 d 8:15 2 a Totals: Guy 90 mins, Kyle 2 hrs, Lin 1 hour 55 mins, Mandy 2 hrs b Mandy, Family Ties & Home Improvement
S
851 km 1704 km 468 km 2082 km 437 km 491 km
2
9
Page 33
1a
1702 km 3408 km 936 km 4164 km 874 km 982 km
1
10 3
Return trip
2
7
9
Half way
1
9
5
10
2
8
e obtuse
3
6
12
10
4
8 7
9
5
11 2
9
5
6
10
2
9
d acute
3 4 7
1
10
9 8
12
11 2
5
6
10
f obtuse
c obtuse
3
7
1
10
4
8
12
11 2
10
4
3
L
L
L
order can vary
Page 47 1 a $2.50 b $6.50 c $5.25 d $6 e $3 f $3 g $2.40 h $2 i $1.58
Answers to Student Book Pages
237
Page 47 (continued)
Page 58
2 a Birdie (1), Exocet (2), Stingers (3) b Eagle (1), Arrow (2), Top Putt (3) 3 Ace
2 increasing by 2 each time; 32, 44, 58, 74, 92, 112, 134, 158, 184, 212
Page 59 Page 48
Pool A 55 squares Pool B 64 squares
1 $0.75 2 630 km, 315 km 3 37, $37.09
Page 60 Page 49 (reading left to right) octagon, regular pentagon, hexagon, square, parrallelogram, triangle, right-angle triangle, rectangle, trapezium
smallest to largest area: Tin Tin Is. 16 sq km, Big Bay Is. 28 sq km, Easy Day Is. 40 sq km, Kayak Is. 42 sq km
Page 61
Page 51
2 square centimetres because square meters are used to measure large areas
1 turn, slide 2 slide, turn 3 slide, flip 4 turn, flip 5 flip, slide 6 turn, slide 7 slide, turn
Page 62
Page 52 Original Shape
Slide
Flip horizontally
1 4
Turn right
1 4
Turn again
Shonky Travel $860 ($172) *Biplane Travel $580 ($116) Mega Travel $1070 ($214) Beyond Travel $880 ($176) Rapid Travel $695 ($139) Camel Travel $955 ($191) Trevor’s Travel $840 ($168) Slowcoach Travel $795 ($159) Dodgy Travel $985 ($197) Freak Out Travel $735 ($147)
Page 63 1 from Melb. to … Sydney 87 kph, Canberra 72 kph, Adelaide 66 kph, Perth 73 kph, Brisbane 64 kph, Darwin 68 kph 2 fastest to slowest: Sydney, Perth, Canberra, Darwin, Adelaide, Brisbane
Page 64 1st (lane 3) 27.98 2nd (lane 5) 28.49 3rd (lane 8) 28.83 4th (lane 6) 28.85 5th (lane 4) 28.99 6th (lane 3) 29.13 7th (lane 7) 29.16 8th (lane 1) 29.63
Page 65 1 a Satay Thai 455 Bombay Belly 374 Yummy Yum Cha 421 Noodle Bar 506 Man Cuisine 523 Kev’s Kebabs 506 b Mean Cuisine, Noodle bar, Kev’s Kebabs 2 a 301 b answers will vary
Page 66 1 most to least: $1.91, $1.19, $1.11, $1.10 Total: $5.31 2 40 g 3 a 754 b 213 c 152 r 1 d 375 4 answers may vary & 640 indiv. shoes
Page 69 1 a Unifix blocks b they leave no gaps
Page 53
Page 70
3 see definitions on Student Book pp. 119–120 4 right-angle triangle: turned, flipped, slid hexagon: turned, slid, flipped
3 a 3 in 4
Page 72
Page 54
2 1 in 2 4 a 1 in 6
(answers are rounded to the nearest cents) 1 Lime 70 c Cola 75 c Bonus Apple & Berry 65 c Fizzy Lemon 80 c Raspberry 60c Fruity $1.25 Leomonade 90 c Big Sars 75 c Zinger 80 c 2 Best deal 1: Raspberry 60 c a can, Best deal 2: Bonus Apple & Berry 65 c a can, Best deal 3: Lime 70 c a can
Page 73
Page 55
Page 74
1 Tia $8.20 Tara $8.30 Tomas $10.30 Ty $8.50 Timmy $8.10 Tyrone $6.90 2
Total
Rank (Most to least
$10.30 1$8.50 1$8.30 1$8.20 1$8.10 1$6.90
1 2 3 4 5 6
Name Thomas Ty Tara Tia Timmy Tyrone
Page 56 a 3600 b 720 c 4500 d 415 e $3.00 f 72679
238
1 red 119.2 2 green 885 3 red 1582.25 4 orange 96 5 red 9820 6 red 319.2 7 orange 256 8 green 15442 9 orange 318 10 orange 1461 11 orange 8554 12 green 353 13 red 15040 14 green 20131 15 green 4997 16 red 857.14 17 green 123837 18 green 1235 19 red 112.7 20 orange 324
Nelson Maths Teacher’s Resource — Book 5
Amount needed to have $20 $9.70 $11.50 $11.70 $11.80 $11.90 $13.10
(answers may vary to those below) 2 (25) 10 + 15 = 25 3 (32) 12 + 20 = 33 4 (33) 20 + 13 = 33 5 (43) 30 + 13 = 43 6 (27) 20 + 7 = 27 7 (52) 40 + 12 = 52 8 (33) 20 + 13 = 33 9 (27) 17 + 10 = 27 10 (23) 10 + 13 = 23 11 (45) 30 + 15 = 45 12 (37) 30 + 7 = 37 13 (67) 40 + 27 = 67 14 (52) 40 + 12 = 52 15 (102) 30 + 72 = 102
Page 75 1a b c 2a b 3a 4a
seven thousand four hundred and eighty-two one thousand and eighty-seven nine thousand nine hundred and one largest to smallest: 1111, 1110, 1100, 1011, 1010, 1001 largest to smallest: 9911, 9910, 9191, 9119, 9101, 9019 8212 b 4096 c 3511 d 10001 700 b 7 c 7000 d 700, 7 e 70 f 70
5 b 9872 = 9000 + 800 + 70 + 2 c 2561 = 2000 + 500 + 60 + 1 d 2181 = 2000 + 100 + 80 + 1 e 1004 = 1000 + 0 + 0 + 4 f 9018 = 9000 + 0 + 10 + 8
Page 76 (working out as per example) 1 b $85 c $108 d $115 e $108 f $132 g $192 h $60 i $195 j $261 k $192 l $270
Page 91 1 a & b Harry 1.25 m (4th) Zac 1.31 m (3rd) Effie 1.17 m (9th) Susan 1.23 m(5th) Fiona 1.13 m (10th) Celeste 1.09 m (12th) Tia 1.41 m (1st) Dare 1.12 m (11th) Andrew 1.35 m (2nd) Jack 1.23 m (5th) Kiah 1.2 m (7th) Bridget 1.18 m (8th) 2 Tia, Celeste 3 2.41 m, 2.29 m
Page 92 Page 77
1
Bag
1 a 1189 (1190) b 1728 (1730) c 1821 (1820) d 1291 (1290) e 1198 (1200) f 1903 (1900) smallest to largest: 1190, 1200, 1290, 1730, 1820, 1900 2 b 5000 + 800 + 20 + 7 c 2000 + 800 + 70 + 6 d 1000 + 700 + 90 + 3 e 6000 + 700 + 50 + 2 f 1000 + 400 + 90 + 2 g 1000 + 90 + 7 h 9000 + 800 + 70 + 6 3 3s: 71, 74, 77, 80, 83, 86, 89, 92, 95 5s: 71, 76, 81, 86, 91, 96, 101, 106, 111 9s 71, 80, 89, 98, 107, 116, 125, 134, 143
Fraction Eaten
Number Eaten
Fraction Remaining
3 4 1 2 1 4 1 9 1 3 5 6 4 9 2 3
27
1 4 1 2 3 4 8 9 2 3 1 6 5 9 1 3
A B C D E
Page 78
F
1 14 mL 2 30 mL 3 22.5 mL 4 45 mL 5 60 mL 6 20 mL
G
Page 80 1 greatest: bottle 3, lowest bottle 7, same amount: bottle 8 & 9 2 95 mL 3 245 mL 4 bottle 6 5 lowest to highest volume: 7, 5, 8 & 9, 2, 4, 10, 1, 6, 3
H
18 9 4 12 30 16 24
2 a A, B, E b A & C, E & H
Page 93
Page 82 1 a 4, 4 ( 1 ) b 5, 5 ( 1 ) c 5, 5 ( 1 ) d 4, 4 ( 1 ) e 9, 9 ( 1 ) f 11, 11 ( 1 ) 22 2 12 3 30 6 15 3 16 4 18 2
1a
Page 83
✗
Sydney
Adelaide
Perth
Brisbane
Hobart
Darwin
Canberra
25.8
26.1
28.5
30.0
29.4
21.6
34.3
28.5
Lowest Temperature °C
13.4
16.7
14.9
17.4
20.4
11.6
30.7
11.5
12.4
9.4
13.6
12.6
9.0
10.0
3.6
17
Melbourne
Sydney
Adelaide
Perth
Brisbane
Hobart
Darwin
Canberra
19.8
21.9
21.7
23.3
25.4
16.8
32.7
20.1
Range °C
2a
✗
Average Temperature °C
✗
b highest to lowest temp.: Darwin, Brisbane, Perth, Sydney, Adelaide, Canberra, Melbourne, Hobart
✗ 1 4
Melbourne Highest Temperature °C
1 3
✗ ✗
1 2
3 4
✗
✗
Page 84 1 16 2 smallest to largest: 1 , 1 , 1 , 1 10 5 4 2
3 56
Page 95 1 b 3.9 c 5.2 d 5.3 e 4.0 f 5.5 g 2.3 h 1.2 i 9.9 j 6.3 k 5.1 l 1.8
Page 96 1 smallest to tallest: 1.22 m (1st), 1.23 m (2nd), 1.32 m (3rd), 1.33 m (4th) 1.43 m (5th) 2 a 29 b 12 c 18 d 25 0.25
3
4 21
0.33
0.5
0.75
0.9
0 1
Page 97 1
Page 85 1 WORKING WITH GRIDS IS FABULOUS FUN
Page 86 1 a east b north c south d east e west
Page 87
1 4
2 west
Solid
Name
a b c d e
cylinder cube rectangular prism cone triangular prism
Faces
Edges
Vertices
3 6 6 2 5
2 12 12 1 9
0 8 8 1 6
N
Page 98 W
E
3 a letter S
Page 89 1 a g b g c kg d kg e kg f kg g kg h g i g j kg k g
Page 90 3 least to most mass: newspaper, tin of spaghetti, Prep child, large TV 4 the weight of an object without packaging
(reading left to right) cube, square pyramid, rectangular prism, sphere, cone, cylinder (examples will vary)
Page 99 2 A pyramid is a 3D shape with a polygon for a base; all other faces are triangles and rise to a point (apex). A prism is a 3D shape with its two ends the same size and shape.
Answers to Student Book Pages
239
Page 100
Page 109
1 blue 4 , red 3 , yellow 2 , green 1
2 9 + 4 × 3 = 21 3 5 + 8 ÷ 4 = 7 4 5 + 2 × 6 = 17 5 8 + 9 ÷ 3 = 11 6 3 + 9 × 3 = 30 7 2 + 9 ÷ 3 = 5 8 4 + 7 – 5 = 6, 4 + 7 – 6 = 5 9 7 + 15 ÷ 5 = 10 10 4 + 9 – 8 = 5, 4 + 9 – 5 = 8
10 10 10 10 4 blue 8 , red 6 , yellow 4 , green 2 20 20 20 20
Page 101
Page 110
Item
Cost
To nearest 5c To nearest 10c To nearest $1
Bananas $2.26 $2.25 Cereal $4.58 $4.60 Mineral water $1.09 $1.10 Cake $1.99 $2.00 Peanut Butter $4.69 $4.70 Yoghurt $3.05 $3.05 Flavoured milk $2.26 $2.25 Juice $2.35 $2.35 Celery $0.89 $0.90 Beans $1.59 $1.60 BBQ Sausages $2.12 $2.10 Cheese $4.99 $5.00 Meat $9.99 $10.00 Fruit bars $2.93 $2.95 My Estimate Answers will vary Actual total $44.78 $44.85
$2.30 $4.60 $1.10 $2.00 $4.70 $3.10 $2.30 $2.40 $0.90 $1.60 $2.10 $5.00 $10.00 $2.90
$2.00 $5.00 $1.00 $2.00 $5.00 $3.00 $2.00 $2.00 $1.00 $2.00 $2.00 $5.00 $10.00 $3.00
$45.00
$45.00
2 a nearest 5c (7c diff.), nearest 10c (22c diff.), nearest $1 (22c diff.) b answers will vary
Page 103 3
To nearest 5
To nearest 10
To nearest 100
125 680 210 5760 725
120 680 210 5760 730
100 700 200 5800 700
a 123 b 678 c 209 d 5762 e 726
1 a 4 b 3 c 7 d answers will vary 2 mentally, calculator, pen and paper 3 $3.95 to $4.00, therefore $10.00 – $4.00 = $6.00, add the diff. between $3.95 and $4.00 and the answer is $6.05 4 a $120 b $119.70
Page 112 trapezium: a quadrilateral with 4 sides; 2 of the sides are parallel pyramid: a 3D shape with a polygon for a base; all other faces are triangles and rise to a point (apex) rectangle: a quadrilateral with 2 pairs of equal parallel sides and 4 right angles hexagon: a 2D shape with 6 sides; if regular all sides are the same length and all angles are the same rectangular prism: a 3D shape with a rectangular base; it has 6 faces, 12 edges and 8 vertices scalene triangle: a triangle with no sides the same length and no angles the same size triangular prism: a 3D shape with 2 triangular faces that are parallel and the same shape and size and 3 rectangular faces; it has 5 faces, 9 edges and 6 vertices octagon: a 2D shape with 8 sides; if regular all sides are the same length and all angles are the same
Page 113 2 All 4 sides of a square are equal in length. In a rectangle only the 2 opposite sides are equal in length 3 perpendicular vertical
diagonal
horizontal
Page 104
Page 114
1 5.6 slices per share 2 300 mL per share 3 $100.10
Page 105 1 a $21.00 b $7.60 c $24.90 d $23.05 e $22.40 f $72.55 g $60.00 h $32.85 i $59.35 j $71.65 k $31.35
(reading left to right) 1 ×, calculator, $20 562.50 2 ÷, calculator, 30 3 +, pen and paper or calculator, 12 531 4 –, pen and paper or calculator, 685 5 +, pen and paper or calculator, 1064 6 ÷, mentally or calculator, 11
Page 106 1 a $76.50 b $69.30 c $69.00 d $71.10 e $64.80 f $66.50 g $54.40 h $44.10 i $64.75 2 most to least pay: Sally, Abdul, Scott, Ky, Tom, Kate, Darcy, Lin, Jessica
Page 115 19, 25, 31, 37, 43, 49, 54 (+6) 12, 17, 23, 30, 38, 47, 57 (+1 +2 +3 +4 +5 etc.) 25, 31, 38, 46, 54, 64 (+2 +3 +4 +5 etc.) 44, 64, 88, 116, 148, 184 (+4 +8 +12 +16 +20 etc.) 29, 30, 35, 36, 41, 42 (+5 +1 etc.) 12, 9, 3, 0 (–6 –3) 0, 5, 4, 9, 8, 13, 12, 17, 16, 21, 20, 25, 24 0, 3, 8, 11, 16, 19, 24 c 0, 7, 6, 13, 12, 19, 18, 25, 24 0, 3, 7, 10, 14, 17, 20, 24
(reading left to right) 1 a CD Burner $9.55, $28.65, $66.85, $95.50 b Scanner $8.75, $26.25, $61.25, 87.50 c Video Camera $7.60, $22.80, $53.20, $76.00 d Desktop Computer $6.55, $19.65, $48.85, $65.50
1a b c d e f 2a b d
Page 108
Page 116
Page 107
Name
Multiplication Equation
× 10
× 100
Ranking
Ian Thorpe Cathy Freeman Adam Gilchrist Petria Thomas Harry Kewell Emma George Evie Dominikovic James Hird Patrick Rafter George Gregan
3 × 16 = 18 5 × 17 = 35 4 × 19 = 36 6 × 16 = 36 5 × 16 = 30 4 × 16 = 24 4 × 11 = 44 5 × 14 = 20 7 × 16 = 42 6 × 16 = 36
180 350 360 360 300 240 440 200 420 360
1800 3500 3600 3600 3000 2400 4400 2000 4200 3600
=8 =6 =3 =3 =7 =8 =1 =9 =2 =3
240
Nelson Maths Teacher’s Resource — Book 5
1 a 113 b 63 c 103 d 1283 e 623 f 353 g 163 h 337 i 207 j 247 k 987 l 157 m 97
Page 117 a 16 + 7 = 5 × 5 – 2 b 1 of 16 = 22 – 14 2
c 100 + 5 = (3 × 20) + (3 × 15) d 25 – 7 = ( 1 of 12) × 3 2
e 1 of 36 = (4 + 2) × 2 f 13 + 16 = 53 – (8 × 3) g 3 × 10 + 1 = 25 + 6 3 h 1 of 36 + 1 = (29 + 7) ÷ 4 4
i 10 + 8 = (30 + 6) ÷ 2 j answers will vary
Page 118 1 a 57 b 184 c 433 d 402 e 892 f 724 2 a 6 × 5 + 11 – 5 = 36 b (15 + 5) ÷ 4 = 5 c 17 – 4 + 9 = 22
Nelson Maths (Books 1–7) provides creative, stimulating and open-ended tasks allowing children to work at a learning level appropriate to their needs. This series supports the whole class — small group — whole class teaching approach.
Teacher’s Resource
Nelson
Maths
Each Teacher’s Resource Book contains:
Nelson
more than 520 activities over 40 weekly units of work ‘Plain Speak’ Statements (teaching focus), Resources and Maths Talk 81 unit and resource blackline masters 11 assessment and planning blackline masters ideas for setting up an effective mathematics classroom, parent participation, five-minute maths activities, and assessment and monitoring.
Maths T ONY D OYLE
Planning Assessme and nt Tool + TRB
© Nelson Austr alia Pty Ltd, 2004. Jay Dale and Jenny Feely Minimum syst em requirem ents Microsof t® Windows ® 98 or later; MacOS 8.5–9.2. and OSX Adobe® Acro bat® Reader (supplied on CD-ROM) is required to view documents.
N
son Mel aths
Installation instructions PC: Insert CDROM into CD drive for auto matic play, or navigate to CD-ROM with Windows® Explorer and double-click on Title. Mac: Insert CD-ROM into CD drive. Doub le-click on the Title icon, then double-click on Title.
If you experienc e difficultie s using this email Nelson product, Thomson Lear ning Australi helpdesk@th a on omsonlearnin g.com.au
Book
M RO ins
Book
e id
CD -
The complete Teacher’s Resource Book is on CD-ROM and features time-saving and easy-to-use interactive planning and assessment software. The CD-ROM also features an Enabler function which allows teachers to plan across grade levels, and a Correlation Chart linking units in Nelson Maths to individual Education Department syllabuses.
T ONY D OYLE has taught in a number of schools over the past 20 years. He is the author of various maths texts and teacher’s guides. Tony has a passion for integrating learning technologies into the curriculum and has always had a keen interest in the ways in which children learn mathematics. Tony is currently Deputy Head
F ifth
of Sc Ye ho ar ol
and ICT Coordinator for an independent school.
