Grade 1
NEW YORK • TORONTO • LONDON • AUCKLAND • SYDNEY MEXICO CITY • NEW DELHI • HONG KONG • BUENOS AIRES Algebra Rea...
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Grade 1
NEW YORK • TORONTO • LONDON • AUCKLAND • SYDNEY MEXICO CITY • NEW DELHI • HONG KONG • BUENOS AIRES Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Scholastic Inc. grants teachers permission to photocopy the activity sheets from this book for classroom use. No other part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission of the publisher. For information regarding permission, write to Scholastic Inc., 557 Broadway, New York, NY 10012. Editor: Maria L. Chang Cover design by Jason Robinson Interior design by Melinda Belter Illustrations by Teresa Anderko ISBN-13: 978-0-439-83924-2 ISBN-10: 0-439-83924-6 Copyright © 2008 by Carole Greenes, Carol Findell, and Mary Cavanagh All rights reserved. Printed in China. 1 2 3 4 5 6 7 8 9 10
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Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
PROBLEM SETS Fishy Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Guess the Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Count the Spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Find the Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Face the Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 How Much Is This Bag? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
PROBLEM-SOLVING TRANSPARENCY MASTER . . . . . . . . . . . . . 77
SOLVE IT TRANSPARENCY MASTERS . . . . . . . . . . . . . . . . . . . . 78
ANSWER KEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 COLOR TRANSPARENCIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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Table of Contents
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Introduction
Welcome to Algebra Readiness Made Easy! This book is designed to help you introduce young children to problem-solving strategies and algebraic-reasoning techniques, to give them practice with major number concepts and skills, and to motivate them to write and talk about big ideas in mathematics. It also sets the stage for the formal study of algebra in the upper grades.
Algebra Standards The National Council of Teachers of Mathematics identifies algebra as one of the five major content areas of the mathematics curriculum to be studied by children in all grades (NCTM, 2000). The council emphasizes that early and regular experience with the key ideas of algebra helps students make the transition into the more formal study of algebra in late middle school or high school. This view is consistent with the general theory of learning—that understanding is enhanced when connections are made between what is new and what was previously studied. The key algebraic concepts developed in this book are: • representing quantitative relationships • representing unknowns with letters • reasoning about proportional relationships • identifying and continuing patterns • interpreting mathematical relationships • writing and solving equations • solving for the values of one or two unknowns • replacing unknowns with their values
Building Key Math Skills NCTM also identifies problem solving as a key process skill and the teaching of strategies and methods of reasoning to solve problems as a major part of the mathematics curriculum for children of all ages. The problem-solving model first described in 1957 by renowned mathematician George Polya has been adopted by teachers and instructional developers nationwide and provides the framework for the problem-solving focus of this book. All the problems contained here require children to interpret data displays—such as text, charts,
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Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
INTRODUCTION
diagrams, graphs, pictures, and tables—and answer questions about them. As they work on the problems, children learn and practice the following problem-solving strategies: • making lists or cases of possible solutions and testing those solutions • identifying, describing, and generalizing patterns • working backward • reasoning logically • reasoning proportionally The development of problem-solving strategies and algebraic concepts is linked to the development of number concepts and skills. As children solve the problems in this book, they’ll practice counting, computing, applying concepts of place value and number theory, and reasoning about the magnitudes of numbers. Throughout this book, we emphasize the language of mathematics. This language includes terminology (e.g., odd number, variable) as well as symbols (e.g., >, <). Children will see the language in the problems and illustrations and use the language in their discussions and written descriptions of their solution processes.
How to Use This Book Inside this book you’ll find six problem sets—each composed of nine problems featuring the same type of data display (e.g., diagrams, scales, and arrays of numbers)—that focus on one or more problem-solving strategies and algebraic concepts. Each set opens with an overview of the type of How much does each fish cost? problems/tasks in the set, the algebra and problemsolving focus, the number concepts or skills needed to solve the problems, the math language that is emphasized in the problems, and guiding questions to be used with the first two problems of the set to help I’ll start with children grasp the key concepts and strategies. Flash. His price tag has the least The first two problems in each set are designed to be number. discussed and solved in a whole-class setting. The first, “Solve the Problem,” introduces children to the type of Ima Thinker display and problem they will encounter in the rest of 1. How much does Flash cost? __________ 2. How much does Bronco cost? __________ the set. We suggest that you have children work on this 3. How much does Arty cost? __________ first problem individually or in pairs before you engage 4. How much less does Flash cost than Arty? __________ in any formal instruction. Encourage children to wrestle Name _____________________________________________ Date __________________ FISHY PRICES
SOLVE
THE PROBLEM
I cost $1 less
I cost $2 more
than Bronco.
than Flash.
Bronco
Arty $1
$2
$3
I cost the least.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Match each price tag with its fish.
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Flash
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with the problem and come up with some strategies they might use to solve it. Then gather children together and use the guiding questions provided to help them discover key mathematical relationships and understand the special vocabulary used in the problem. This whole-class discussion will enhance student understanding and success with the problemsolving strategies and algebraic concepts in each problem set. The second problem, “Make the Case,” comes as an overhead transparency and uses a multiple-choice format. Three different characters offer possible solutions to the problem. Children have to determine which character—Shorty Trunks, Carl Cargo, or Levi Sam—has the correct answer. How much do PB and J cost together? Before they can identify the correct solution, children have to solve the problem themselves and analyze each of the responses. Invite them to speculate about why the other two characters got the wrong answers. (Note: Although we offer a rationale for each wrong answer, No, PB and J cost $7. Clearly, PB and J other explanations are possible.) As children justify their are $3. I see that PB and J together choices in the “Make the Case” problems, they gain cost $5. greater experience using math language. While working on these first two problems it is important to encourage children to talk about their observations and hypotheses. This talk provides a window into what children do and do not understand. Working Shorty Trunks Carl Cargo Levi Sam on “Solve the Problem” and “Make the Case” should take Who is wearing smarty pants? approximately one math period. The rest of the problems in each set are sequenced by difficulty. All problems feature a series of questions that involve analyses of the data display. In the first three or four problems of each set, problem-solving “guru” Ima Thinker provides hints about how to begin solving the problems. No hints are provided for the rest of the problems. If children have difficulty solving these latter problems, you might want to write “Ima” hints for each of them or ask children to develop hints before beginning to solve the problems. An answer key is provided at the back of the book. The problem sets are independent of one another and may be used in any order and incorporated into the regular mathematics curriculum at whatever point makes sense. We recommend that you work with each problem set in its entirety before moving on to the next one. Once you and your students work through the first two problems, you can assign problems 1 through 7 for children to do on their own or in pairs. You may wish to have them complete the problems during class or for homework. Name _____________________________________________ Date __________________ FISHY PRICES
MAKE THE CASE
We cost $3 more
I cost $5 less
than Dolly.
than Ringo.
Dolly
PB and J
$2
$7
$5
I cost the most.
Match each price tag with its fish.
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Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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INTRODUCTION
Using the Transparencies In addition to the reproducible problem sets, you’ll find ten overhead transparencies at the back of this book. (Black-line masters of all transparencies also appear in the book.) The first six transparencies are reproductions of the “Make the Case” problems, to help you in leading a whole-class discussion of each problem. The remaining four transparencies are designed to How much does each fish cost? be used together. Three of these transparencies feature six problems, one from each of the problem sets. Cut these three transparencies in half and overlay each problem on the Problem-Solving Transparency. Then invite children to apply our three-step problem-solving process: SOLVE IT : FISHY PRICES
PROBLEM-SOLVING TRANSPARENCY
SOLVE IT
Barb
Shaggy
Glow
Use the clues to figure out the price of each fish. CLUES: A) Shaggy costs $4 less than Barb. B) Barb costs $7 more than Glow. C) Glow costs the least.
1.
2) Plan and Do: How will you solve the problem? What strategies will you use? What will you do first? What’s the next step? What comes after that? 3) Answer and Check: What is the answer? How can you be sure that your answer is correct?
$2
$9
What is the problem?
SOLVE IT : GUESS THE NUMBER Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1) Look: What is the problem? What information do you have? What information do you need?
Look
$5
What is Z? 30 20 10 for Do a number. Z2.stands 0 Plan and What will you do first? How will you 31solve the problem?
Use the clues. CLUES: 1)
Z
2)
Z is a number you say when you count by 10s.
3)
Z
3.
is between 19 and 35.
is greater than 25.
Answer and Check
21 11 1 32 22 12 2 33 23 13 3 34 24 14 4 35 25 15 5 36 26 16 6 37 27 17 7 38 28 18 8 39 29 19 9
How can you be sure your answer is correct?
76
These problem-solving transparencies encourage writing about mathematics and may be used at any time. They are particularly effective when used as culminating activities for the set of problems.
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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References Findell, Carol, Mary Cavanagh, Linda Dacey, Carole Greenes, Linda Sheffield, & Marian Small. (2004). Navigating through problem solving and reasoning in grade 1. Reston, VA: National Council of Teachers of Mathematics. Greenes, Carole, Mary Cavanagh, Linda Dacey, Carol Findell, & Marian Small. (2001). Navigating through algebra in grades pre-kindergarten–grade 2. Reston, VA: National Council of Teachers of Mathematics. Greenes, Carole, & Carol Findell. (Eds.) (2005). Developing students’ algebraic reasoning abilities. (Vol. 3 in the NCSM Monograph Series.) Boston, MA: Houghton Mifflin. Greenes, Carole, & Carol Findell. (2005). Groundworks: Algebraic thinking. Chicago: Wright Group/McGraw Hill. Moses, Barbara (Ed.). (1999). Algebraic thinking, grades K–12: Readings from NCTM’s school-based journals and other publications. Reston, VA: National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Polya, George. (1957). How to solve it. Princeton, NJ: Princeton University Press. Usiskin, Zalman. (1997). Doing algebra in grades K–4. Teaching Children Mathematics. 3 (6), 346–356.
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Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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Fishy Prices
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Overview Children use clues to interpret mathematical relationships and work backward through the clues to answer the questions.
Algebra Represent quantitative relationships • Write and solve equations
Problem-Solving Strategies Work backward • Use logical reasoning
Related Math Skills Compare dollar amounts • Add basic facts • Subtract basic facts
Math Language Cost, cost more, cost less • $ (dollar sign) • Greatest • How much? • Least, less than • Most, more than • Price tag
Introducing the Problem Set Make photocopies of “Solve the Problem: Fishy Prices” (page 11) and distribute to children. Have children work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • What did Ima do first to figure out how much each fish costs? (She matched the tag with the least price to the fish that cost the least.) • Which fish costs the least? (Flash) • How much does Flash cost? ($1) • Which fish’s price tag can you figure out next? (Bronco) Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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FISHY PRICES
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Name _____________________________________________ Date __________________ FISHY PRICES
SOLVE THE PROBLEM
• Why can’t you figure out Arty’s cost before finding Bronco’s cost? (The first fact states that Arty is $1 less than Bronco, so we have to figure out Bronco’s cost before we can find out Arty’s cost.)
How much does each fish cost? I cost $1 less
I cost $2 more
than Bronco.
than Flash. Bronco
Arty $2
$1
$3
I cost the least. Flash
Match each price tag with its fish.
Work together as a class to answer the questions in “Solve the Problem: Fishy Prices.”
I’ll start with Flash. His price tag
Display the “Make the Case: Fishy Prices” transparency on the overhead. Before children can decide which character is “wearing smarty pants,” they need to figure out the answer to the problem. Encourage children to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Math Chat With the Transparency
has the least number.
Ima Thinker 1. How much does Flash cost? __________ 2. How much does Bronco cost? __________ 3. How much does Arty cost? __________ 4. How much less does Flash cost than Arty? __________ 11
• Who has the right answer? (Carl Cargo) • What do you think Carl Cargo did first to solve the problem? (He matched the greatest cost with the fish that costs the most. Ringo costs $7.)
Name _____________________________________________ Date __________________ FISHY PRICES
MAKE THE CASE
• What did Carl do next? (He found Dolly’s cost next. Dolly costs $5 less than Ringo; 7 – 5 = 2, or $2.)
How much do PB and J cost together? We cost $3 more
I cost $5 less
than Dolly.
than Ringo. Dolly
PB and J
$2
$7 $5
I cost the most.
Match each price tag with its fish.
• How did Carl find PB and J’s cost? (PB and J cost $3 more than Dolly; 2 + 3 = 5, or $5.)
Clearly, PB and J are $3.
No, PB and J cost $7. I see that PB and J together cost $5.
• How do you think Levi Sam got his answer? (He might have thought that the words more than in the first clue meant that PB and J’s cost must be the greatest number.) Shorty Trunks 12
10
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
• How do you think Shorty Trunks got his answer? (He probably thought the number in the first clue was PB and J’s cost.)
Ringo
Name _____________________________________________ Date __________________ FISHY PRICES
SOLVE THE PROBLEM
How much does each fish cost? I cost $1 less
I cost $2 more
than Bronco.
than Flash. Bronco
Arty $1
$2 $3
I cost the least. Flash
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Match each price tag with its fish.
I’ll start with Flash. His price tag has the least number.
Ima Thinker 1. How much does Flash cost? __________ 2. How much does Bronco cost? __________ 3. How much does Arty cost? __________ 4. How much less does Flash cost than Arty? __________ 11
Name _____________________________________________ Date __________________ FISHY PRICES
MAKE THE CASE
How much do PB and J cost together? We cost $3 more
I cost $5 less
than Dolly.
than Ringo. Dolly
PB and J
$2
$7 $5
I cost the most.
Match each price tag with its fish.
Clearly, PB and J are $3.
12
No, PB and J cost $7. I see that PB and J together cost $5.
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Shorty Trunks
Ringo
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
1
How much does each fish cost? I cost $3 less
I cost $2 less
than Tutu.
than Ray. Tutu
Ja Ja $4
$6 $1
I cost the most.
Match each price tag with its fish.
Ray
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll start with Ray. His price tag has the greatest number.
Ima Thinker 1. How much does Ray cost? __________ 2. How much does Tutu cost? __________ 3. How much does Ja Ja cost? __________ 4. How much less does Ja Ja cost than Ray? __________ 13
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
2
How much does each fish cost? I cost $4 more than Mambo.
I cost $2 more than Salsa. Mambo
Tango $3
I cost the least.
$9 $5
Salsa
Match each price tag with its fish.
I’ll start with Salsa. Her price tag has the least number.
1. How much does Salsa cost? __________ 2. How much does Mambo cost? __________ 3. How much does Tango cost? __________ 4. How much more does Tango cost than Salsa? __________ 14
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Ima Thinker
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
3
How much does each fish cost? I cost $6 less I cost $4 more
than Ruby.
than Pokey.
Pokey
Tic and Tac $8
$2
I cost the most. $6
Match each price tag with its fish.
Ruby
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll start with Ruby. Her price tag has the greatest number.
Ima Thinker 1. How much does Ruby cost? __________ 2. How much does Pokey cost? __________ 3. How much do Tic and Tac cost? __________ 4. How much more does Ruby cost than Tic and Tac? __________ 15
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
4
How much does each fish cost? I cost $4 more I cost $1 less
than Strings.
than Banjo. Banjo
Reed
$5
$2 $6
I cost the least. Strings
Match each price tag with its fish.
Ima Thinker 1. How much does Strings cost? __________ 2. How much does Banjo cost? __________ 3. How much does Reed cost? __________ 4. How much more does Reed cost than Strings? __________ 16
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll start with Strings. His price tag has the least number.
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
5
How much does each fish cost? I cost $4 less than Bozo.
I cost $7 more than Puffy.
Zip
$2
Bozo $5 $9
I cost the least.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Match each price tag with its fish.
Puffy
1. How much does Puffy cost? __________ 2. How much does Bozo cost? __________ 3. How much does Zip cost? __________ 4. How much more does Zip cost than Puffy? __________
17
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
6
How much does each animal cost? I cost $5 more
I cost $7 less
than Octo.
than Froggy. Octo
Pogo $8
I cost the most.
$10 $3
Match each price tag with its animal.
Froggy
2. How much does Octo cost? __________ 3. How much does Pogo cost? __________ 4. How much less does Pogo cost than Froggy? __________
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Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. How much does Froggy cost? __________
Name _____________________________________________ Date __________________ FISHY PRICES
PROBLEM
7
How much does each item cost?
This plant costs $3
This chest costs $4
This ship costs
less than the chest.
more than the ship.
the least.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Match each price tag with its item.
$6
$10 $7
1. How much does the ship cost? __________ 2. How much does the chest cost? __________ 3. How much does the plant cost? __________ 4. How much less does the ship cost than the plant? __________
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Guess the Number Overview
Presented with a list of numbers, children use clues to cross off numbers that don’t fit the clues and identify the special number.
Algebra Letters used to stand for unknowns
Problem-Solving Strategies Eliminate candidates from a list • Use logical reasoning
Related Math Skills Compare numbers • Skip counting • Add basic facts
Math Language Between • Count by 5s and 10s • Greater than • Less than • Not
Introducing the Problem Set Make photocopies of “Solve the Problem: Guess the Number” (page 22) and distribute to children. Have children work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Why did Ima cross 10, 11, and 12 off the list? (Clue 1 says that A is less than 10. Ima crossed off numbers that are not less than 10.) • If you use Clue 2 next, what numbers will you cross off the list? (0 to 7) • What numbers are left after Clue 1 and Clue 2? (8 and 9) Work together as a class to answer the questions in “Solve the Problem: Guess the Number.” 20
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
GUESS THE NUMBER
Name _____________________________________________ Date __________________ GUESS THE NUMBER
SOLVE THE PROBLEM
Math Chat With the Transparency
What is A?
A stands
for a number on this list.
Use the clues. CLUES: 1)
Display the “Make the Case: Guess the Number” transparency on the overhead. Before children can decide which character is “wearing smarty pants,” they need to figure out the answer to the problem. Encourage children to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:
2) 3)
A A A
is less than 10.
0
7
1
8
2
9
3
10
4
11
5
12
is greater than 7. is not 4
+ 4.
6
I’ll start with Clue 1. I’ll cross some numbers off my list. Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
• Who has the right answer? (Shorty Trunks)
Ima Thinker 1. Which numbers does Ima cross off the list?_____________
• How did you figure it out? (Using Clue 1, cross off 0, 1, 2, and 3. Using Clue 2, cross off 6 to 12. That leaves 4 and 5. Clue 3 gets rid of 5. So B is 4.)
_________________________ Cross off those numbers. 2. Look at Clue 2. Which numbers will you cross off the list? _______________________________________________ 3. Look at Clue 3. Which number will you cross off the list now?
• How do you think Carl Cargo got the answer 6? (He might have thought that Clue 2 said that B was 6.)
_______________________________________________ 22
• How do you think Levi Sam got the answer of 5? (He might not have seen the word not in Clue 3.)
4. What is A ? __________
Name _____________________________________________ Date __________________ GUESS THE NUMBER
MAKE THE CASE
What is B?
B stands
7
0 for a number on this list.
Use the clues. CLUES: 1) 2) 3)
B B B
8
1
9
2 is greater than 3.
3
is less than 6.
4
is not a number that you say when you count by 5s.
10 11
5
12
6
No, no. B is 5.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I see that B is 4. That’s easy.
B is 6.
Shorty Trunks
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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21
Name _____________________________________________ Date __________________ GUESS THE NUMBER
SOLVE THE PROBLEM
What is A?
A stands
for a number on this list.
Use the clues. CLUES: 1) 2) 3)
A A A
is less than 10. is greater than 7. is not 4
+ 4.
0
7
1
8
2
9
3
10
4
11
5
12
6
I’ll start with Clue 1. I’ll cross some numbers off my list.
1. Which numbers does Ima cross off the list?_____________ _________________________ Cross off those numbers. 2. Look at Clue 2. Which numbers will you cross off the list? _______________________________________________ 3. Look at Clue 3. Which number will you cross off the list now? _______________________________________________ 22
4. What is A ? __________
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Ima Thinker
Name _____________________________________________ Date __________________ GUESS THE NUMBER
MAKE THE CASE
What is B?
B stands
7
0 for a number on this list.
Use the clues. CLUES: 1) 2) 3)
B B B
8
1
9
2 is greater than 3.
3
is less than 6.
4
is not a number that you say when you count by 5s.
10 11
5
12
6
No, no. B is 5.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I see that B is 4. That’s easy. B is 6.
Shorty Trunks
Carl Cargo
Levi Sam
Who is wearing smarty pants?
23
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
1
What is C? C stands
for a number on this list.
Use the clues. CLUES: 1) 2) 3)
C is between 4 and 9. C is not 4 + 3. C is greater than 6.
0
7
1
8
2
9
3
10
4
11
5
12
6
I’ll start with Clue 1. I’ll cross some numbers off my list.
1. Which numbers does Ima cross off the list? ______________ ____________________ Cross off those numbers. 2. Look at Clue 3. Which numbers will you cross off the list? ________________________________________________ 3. Look at Clue 2. Which number will you cross off the list now? ________________________________________________ 24
4. What is C ? __________
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Ima Thinker
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
2
What is D? D stands
for a number on this list.
0
7
1
8
2
9
3
10
4
11
5
12
Use the clues. CLUES: 1) 2) 3)
D is not 2 + 2. D is less than 5. D is greater than 2.
6
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll start with Clue 2. I’ll cross some numbers off my list.
Ima Thinker 1. Which numbers does Ima cross off the list? _____________ ______________________ Cross off those numbers. 2. Look at Clue 3. Which numbers will you cross off the list? _______________________________________________ 3. Look at Clue 1. Which number will you cross off the list now? _______________________________________________ 4. What is D ? __________
25
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
3
What is E? E stands
for a number on this list.
Use the clues. CLUES: 1)
E is a number you say when you count by 5s.
2) 3)
E is greater than 8. E is less than 15.
0
10
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
Ima Thinker 1. What numbers does Ima cross off the list? _____________ ___________________________ Cross off those numbers. 2. Look at Clue 3. Which numbers will you cross off the list? _______________________________________________ 3. Look at Clue 1. Which number will you cross off the list now? _______________________________________________ 26
4. What is E ? __________
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll start with Clue 2. I’ll cross some numbers off my list.
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
4
What is F? F stands
for a number on this list.
Use the clues. CLUES: 1) 2)
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
3)
F is greater than 11. F is not 6 + 6. F is between 8 and 14.
0
10
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
I’ll start with Clue 3. I’ll cross some numbers off my list.
Ima Thinker 1. What numbers does Ima cross off the list? _____________ __________________________ Cross off those numbers. 2. Look at Clue 1. Which numbers will you cross off the list? ______________________________________________ 3. Look at Clue 2. Which number will you cross off the list now? ______________________________________________ 4. What is F ? __________
27
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
5
What is G? G stands
for a number on this list.
Use the clues. CLUES: 1) 2) 3)
G is greater than 15. G is less than 9 + 9. G is not 8 + 8.
0
10
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
_______________________________________________ 2. Look at Clue 2. Which numbers will you cross off the list now? _______________________________________________ 3. What is G ? __________ 4. What is G + G ? __________
28
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. Look at Clue 1. Which numbers will you cross off the list?
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
6
What is H? H stands
for a number on this list.
Use the clues. CLUES: 1) 2)
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
3)
H is greater than 17. H is less than 20. H is not 13 + 5.
0
10
20
1
11
21
2
12
22
3
13
23
4
14
24
5
15
25
6
16
26
7
17
27
8
18
28
9
19
29
1. Look at Clue 2. Which numbers will you cross off the list? _______________________________________________ 2. Look at Clue 1. Which numbers will you cross off the list now? _______________________________________________ 3. What is H ? __________ 4. What is H – 4? __________
29
Name _____________________________________________ Date __________________ GUESS THE NUMBER
PROBLEM
7
What is J? J stands
for a number on this list.
Use the clues. CLUES:
0
10
20
1
11
21
2
12
22
3
13
23
1)
J is greater than 24.
2)
J is less than 27.
4
14
24
3)
J is not a number you say
5
15
25
6
16
26
7
17
27
8
18
28
9
19
29
when you count by 5s.
______________________________________________ 2. Look at Clue 2. Which numbers will you cross off the list now? ______________________________________________ 3. What is J ? __________ 4. What is J + 6? __________
30
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. Look at Clue 1. Which numbers will you cross off the list?
ALGE B
Count the Spots
1
SS NE
READ I RA
Overview Given an animal with a specific number of spots, children draw the same number of spots on each similar animal and identify the total number of spots.
Algebra Reason about proportional relationships
Problem-Solving Strategies Drawing pictures to solve problems
Related Math Skills Add basic facts • Count by 2s, 3s, 4s, and 5s
Math Language How many • In all
Introducing the Problem Set Make photocopies of “Solve the Problem: Count the Spots” (page 33) and distribute to children. Have children work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Look at the picture of the dog on top of the page. How many spots does he have? (2) • What do the numbers in the top rectangle describe? (1 dog. 2 spots.) • What do you need to do? (Draw two spots on each dog, then tell the number of spots in all.) • What do you see in the picture in question 1? (Two dogs and no spots) • What will you do first? (Draw two spots on each dog.) Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
31
1
SS NE
ALGE B
COUNT THE SPOTS
READ I RA
Name _____________________________________________ Date __________________ COUNT THE SPOTS
SOLVE THE PROBLEM
Work together as a class to answer the questions in “Solve the Problem: Count the Spots.”
Math Chat With the Transparency Display the “Make the Case: Count the Spots” transparency on the overhead. Before children can decide which character is “wearing smarty pants,” they need to figure out the answer to the problem. Encourage children to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:
Tell how many spots in all.
Draw the spots.
Make sure you draw two spots on each dog.
1. _____ dogs
_____ spots in all
_____ dogs
_____ spots in all
_____ dogs
_____ spots in all
2.
Ima Thinker
3.
33
Name _____________________________________________ Date __________________ COUNT THE SPOTS
MAKE THE CASE
• Who has the right answer? (Levi Sam) • How did you figure it out? (Since one shark has 5 spots, then 3 sharks will have 5 + 5 + 5, or 15 spots in all. You can also count the spots by 5s—5, 10, 15.) • How do you think Shorty Trunks got the answer of 8? (Maybe he added 3 + 5 and got 8.) • How do you think Carl Cargo got the answer of 10? (He might have counted only two 5s instead of three 5s.)
How many spots in all?
1 shark _____
5 spots _____
_____ sharks
_____ spots in all
No. There are 15
I know. There are 8 spots in all.
spots in all. I think there are
Shorty Trunks
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
10 spots in all.
34
32
2 spots _____
1 dog _____
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
• How many spots are on the two dogs in all? (4) • How can you figure out the number of spots in all on three dogs? (Count each spot, or count by 2s—2, 4, 6—or add 2 + 2 + 2 = 6.) • How can you figure out the number of spots in all on four dogs? (Count each spot, or count by 2s—2, 4, 6, 8—or add 2 + 2 + 2 + 2 = 8.)
Name _____________________________________________ Date __________________ COUNT THE SPOTS
SOLVE THE PROBLEM
Tell how many spots in all.
1 dog _____
2 spots _____
Draw the spots.
Make sure you draw two spots on each dog.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. _____ dogs
_____ spots in all
_____ dogs
_____ spots in all
_____ dogs
_____ spots in all
2.
Ima Thinker
3.
33
Name _____________________________________________ Date __________________ COUNT THE SPOTS
MAKE THE CASE
How many spots in all?
1 shark _____
5 spots _____
_____ sharks
_____ spots in all
No. There are 15 spots in all.
I know. There are 8 spots in all.
Shorty Trunks 34
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I think there are 10 spots in all.
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
1
Tell how many spots in all.
1 leopard _____
2 spots _____
Draw the spots.
Make sure you draw two spots on each leopard.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. _____ leopards
_____ spots in all
_____ leopards
_____ spots in all
_____ leopards
_____ spots in all
2.
Ima Thinker
3. 35
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
2
Tell how many spots in all. 1 horse _____
4 spots _____
Draw the spots.
Make sure you draw four spots on each horse.
1. _____ horses
_____ spots in all
_____ horses
_____ spots in all
_____ horses
_____ spots in all
3.
36
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Ima Thinker
2.
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
3
Tell how many spots in all.
1 turtle _____
5 spots _____
Draw the spots.
Make sure you draw five spots on each turtle.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. _____ turtles
_____ spots in all
_____ turtles
_____ spots in all
_____ turtles
_____ spots in all
2.
Ima Thinker
3.
37
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
4
Tell how many spots in all. 1 cow _____
3 spots _____
Draw the spots.
Make sure you draw three spots on each cow.
1. _____ spots in all
_____ cows
_____ spots in all
_____ cows
_____ spots in all
2.
3. 38
Ima Thinker
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
_____ cows
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
5
Tell how many spots in all. 1 fish _____
4 spots _____
Draw the spots.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. _____ fish
_____ spots in all
_____ fish
_____ spots in all
_____ fish
_____ spots in all
2.
3.
39
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
6
Tell how many spots in all. 1 cheetah _____
10 spots _____
Draw the spots.
1. _____ spots in all
_____ cheetahs
_____ spots in all
_____ cheetahs
_____ spots in all
2.
3. 40
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
_____ cheetahs
Name _____________________________________________ Date __________________ COUNT THE SPOTS
PROBLEM
7
Tell how many spots in all. 1 bug _____
6 spots _____
Draw the spots.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. _____ bugs
_____ spots in all
_____ bugs
_____ spots in all
_____ bugs
_____ spots in all
2.
3.
41
ALGE B
1
SS NE
READ I RA
Find the Pattern Overview
Presented with patterns of black and white circles, children continue the pattern and identify the relationship between the picture number and the number of circles of each color.
Algebra Identify and continue growing patterns • Identify the relationship between the picture number and the number of black and white circles in that picture
Problem-Solving Strategies Make drawings • Generalize patterns
Related Math Skills Count circles in a set • Compare numbers • Count by 2s • Add, or count up to 24
Math Language How many • Pattern • Picture number
Introducing the Problem Set Make photocopies of “Solve the Problem: Find the Pattern” (page 44) and distribute to children. Have children work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • How many black circles are in Picture 1? (1) in Picture 2? (2) in Picture 3? (3) • What pattern does Ima see? (The number of white circles is always one. The number of black circles is the same as the picture number.)
42
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
FIND THE PATTERN
Name _____________________________________________ Date __________________ FIND THE PATTERN
SOLVE THE PROBLEM
If the pattern continues, how many and will there be in Picture 5?
• If the pattern continued, how many white circles would be in picture 5? (1) How many black circles would there be? (5) • How many white circles would be in picture 8? (1) How many black circles would there be? (8)
Picture 1
Work together as a class to answer the questions in “Solve the Problem: Find the Pattern.”
Display the “Make the Case: Find the Pattern” transparency on the overhead. Before children can decide which character is “wearing smarty pants,” they need to figure out the answer to the problem. Encourage children to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:
Picture 4
Picture 5
Picture 6
1. Draw the circles in Picture 5.
I see a pattern. Picture 1 has 1 and 1
.
2. Picture 5 will have _____
.
Picture 2 has 1 Picture 3 has 1
. .
Picture 5 will have _____
.
3. Picture 6 will have _____
.
Picture 6 will have _____
.
4. Picture 8 will have _____
.
Picture 8 will have _____
.
5. Picture 10 will have _____
.
Picture 10 will have _____
.
and 2 and 3
Ima Thinker
44
Name _____________________________________________ Date __________________
• Who has the right answer? (Shorty Trunks)
FIND THE PATTERN
MAKE THE CASE
• How did you figure it out? (All pictures have 2 white circles. The number of black circles is one less than the picture number.) • How do you think Carl Cargo got the answer of 2 white and 6 black circles? (He might have thought that the number of black circles was the same as the picture number.)
If the pattern continues, how many and will there be in Picture 6?
Picture 1
Picture 2
Picture 3
Picture 4
2
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
.
Picture 6
and 7
.
There will be 2
Shorty Trunks
Picture 5
There will be
I am sure there will be 2 of the and 5 of the
• How do you think that Levi Sam got the answer of 2 white and 7 black circles? (To figure out the number of black circles, he might have given the total number of circles instead of just the black ones.)
Picture 3
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Math Chat With the Transparency
Picture 2
and 6
.
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
45
43
Name _____________________________________________ Date __________________ FIND THE PATTERN
SOLVE THE PROBLEM
If the pattern continues, how many and will there be in Picture 5?
Picture 1
Picture 2
Picture 3
Picture 4
Picture 5 will have _____
.
3. Picture 6 will have _____
.
Picture 6 will have _____
.
4. Picture 8 will have _____
.
Picture 8 will have _____
.
5. Picture 10 will have _____
.
Picture 10 will have _____
.
Ima Thinker
. . . Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
44
.
Picture 6
I see a pattern. Picture 1 has 1 and 1 Picture 2 has 1 and 2 Picture 3 has 1 and 3
1. Draw the circles in Picture 5. 2. Picture 5 will have _____
Picture 5
Name _____________________________________________ Date __________________ FIND THE PATTERN
MAKE THE CASE
If the pattern continues, how many and will there be in Picture 6?
Picture 1
Picture 2
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I am sure there will be 2 of the and 5 of the .
Shorty Trunks
Picture 3
Picture 4
Picture 5
Picture 6
There will be 2 and 7 . There will be 2 and 6 .
Carl Cargo
Levi Sam
Who is wearing smarty pants?
45
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
1
If the pattern continues, how many and will there be in Picture 5?
Picture 1
Picture 2
Picture 3
1. Draw the circles in Picture 5. .
Picture 5 will have _____
.
3. Picture 6 will have _____
.
Picture 6 will have _____
.
4. Picture 7 will have _____
.
Picture 7 will have _____
.
5. Picture 8 will have _____
.
Picture 8 will have _____
.
Picture 5
I see a pattern. Picture 1 has 1 and 1 Picture 2 has 2 and 2 Picture 3 has 3 and 3
Ima Thinker
. . .
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
46
2. Picture 5 will have _____
Picture 4
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
2
If the pattern continues, how many and will there be in Picture 5?
Picture 1
Picture 2
Picture 3
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. Draw the circles in Picture 5. 2. Picture 5 will have _____
.
Picture 5 will have _____
.
3. Picture 6 will have _____
.
Picture 6 will have _____
.
4. Picture 7 will have _____
.
Picture 7 will have _____
.
Picture 4
Picture 5
I see a pattern. Picture 1 has 2 and 1 Picture 2 has 2 and 2 Picture 3 has 2 and 3
5. Picture 10 will have _____
.
Picture 10 will have _____
.
. . .
Ima Thinker 47
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
3
If the pattern continues, how many and will there be in Picture 5?
Picture 1
Picture 2
Picture 3
.
Picture 5 will have _____
.
2. Picture 6 will have _____
.
Picture 6 will have _____
.
3. Picture 7 will have _____
.
Picture 7 will have _____
.
4. Picture 9 will have _____
.
Picture 9 will have _____
.
Picture 5
I see a pattern. Picture 1 has 1 and 2 Picture 2 has 1 and 3 Picture 3 has 1 and 4
Ima Thinker 48
5. Picture 10 will have _____
.
Picture 10 will have _____
.
. . .
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1. Picture 5 will have _____
Picture 4
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
4
If the pattern continues, how many and will there be in Picture 5?
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Picture 1
Picture 2
Picture 3
1. Picture 5 will have _____
.
Picture 5 will have _____
.
2. Picture 6 will have _____
.
Picture 6 will have _____
.
3. Picture 7 will have _____
.
Picture 7 will have _____
.
4. Picture 8 will have _____
.
Picture 8 will have _____
.
Picture 4
Picture 5
I see a pattern. Picture 1 has 1 and 0 Picture 2 has 2 and 1 Picture 3 has 3 and 2
. . .
Ima Thinker 5. Picture 10 will have _____
.
Picture 10 will have _____
. 49
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
5
If the pattern continues . . .
Picture 1
Picture 3
1. Picture 5 will have _____
.
Picture 5 will have _____
.
2. Picture 6 will have _____
.
Picture 6 will have _____
.
3. Picture 8 will have _____
.
Picture 8 will have _____
.
4. Picture 10 will have _____
.
Picture 10 will have _____
.
5. Picture 15 will have _____
.
Picture 15 will have _____
.
Picture 4
Picture 5
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
50
Picture 2
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
6
If the pattern continues . . .
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Picture 1
Picture 2
Picture 3
1. Picture 5 will have _____
.
Picture 5 will have _____
.
2. Picture 6 will have _____
.
Picture 6 will have _____
.
3. Picture 8 will have _____
.
Picture 8 will have _____
.
4. Picture 10 will have _____
.
Picture 10 will have _____
.
5. Picture 12 will have _____
.
Picture 12 will have _____
.
Picture 4
Picture 5
51
Name _____________________________________________ Date __________________ FIND THE PATTERN
PROBLEM
7
If the pattern continues . . .
Picture 1
Picture 3
1. Picture 5 will have _____
.
Picture 5 will have _____
.
2. Picture 6 will have _____
.
Picture 6 will have _____
.
3. Picture 7 will have _____
.
Picture 7 will have _____
.
4. Picture 10 will have _____
.
Picture 10 will have _____
.
5. Picture 20 will have _____
.
Picture 20 will have _____
.
Picture 4
Picture 5
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
52
Picture 2
ALGE B
Face the Numbers
1
SS NE
READ I RA
Overview Clues are given in the form of two equations with two unknowns (animal faces). Children figure out the values of the faces.
Algebra Solve for the values of two unknowns • Replace unknowns with their values
Problem-Solving Strategies Reason deductively • Test values
Related Math Skills Add, sums of 20 or less • Subtract, 20 or less
Math Language Equation • Same numbers • Stands for a number
Introducing the Problem Set Make photocopies of “Solve the Problem: Face the Numbers” (page 55) and distribute to children. Have children work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Look at Equation A. What do you see? (An addition sentence — when you add 2 to the monkey face, you get a sum of 7.) • Look at Equation B. What do you see? (Two different faces — a monkey face and a dog face. The two faces add up to 8.) • Why did Ima start with Equation A? (There is only one kind of face. The monkey face stands for the number 5. 5 + 2 = 7) Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
53
1
SS NE
ALGE B
FACE THE NUMBERS
READ I RA
Name _____________________________________________ Date __________________ FACE THE NUMBERS
SOLVE THE PROBLEM
• If the monkey face stands for 5, how can you figure out what number the dog face stands for? (In Equation B, replace the monkey face with 5. The dog face will then equal 3. 3 + 5 = 8)
What are the numbers?
Faces that are the same stand for the same numbers. Use the clues.
CLUES:
• Look at question 5. How can you figure out the sum? (Replace each face with its number and then add: 3 + 3 = 6.)
Math Chat With the Transparency Display the “Make the Case: Face the Numbers” transparency on the overhead. Before children can decide which character is “wearing smarty pants,” they need to figure out the answer to the problem. Encourage children to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:
+
A
2 = 7
+
B
= 8
I’ll use Clue A first. I can find the number for the monkey face. Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Work together as a class to answer the questions in “Solve the Problem: Face the Numbers.”
stand for numbers.
and
1.
= _____
2.
= _____
3.
+
4. 6
+
Ima Thinker
4 = _____
= _____
+
5.
= _____ 55
Name _____________________________________________ Date __________________ FACE THE NUMBERS
MAKE THE CASE
What are the numbers?
• Who has the right answer? (Carl Cargo) and
• How did you figure it out? (Equation A shows that a duck face + 3 = 9, so a duck face is 6. In equation B, replace the duck face with 6. Then, the cat face + 6 = 10, and the cat face is 4.)
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues. CLUES:
A
+
3 = 9
B
+
= 10
I’ve got it! The That’s easy. The duck face is 6 and the cat face is 5.
duck face is 3 and the cat face is 7. The duck face is 6 and the cat face is 4. I am sure!
• How do you think Levi Sam got the answer that the duck face stands for 3 and the cat face stands for 7? (He may have made a mistake solving Shorty Trunks Carl Cargo Levi Sam for the value of the duck face in Equation A, thinkWho is wearing smarty pants? ing that it was 3. Or, he might have just used the number 3 in Equation A for the duck face. He then replaced the duck face with 3 in Equation B and found the cat face to be 7.) 56
54
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
• How do you think Shorty Trunks got the answer that the duck face stands for 6 and the cat face stands for 5? (He got the number for the duck, but he might have mistakenly thought that each face in Equation B stands for the same number. So, he took half of 10 and got 5.)
Name _____________________________________________ Date __________________ FACE THE NUMBERS
SOLVE THE PROBLEM
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues.
CLUES:
+
A
2 = 7
B
+
= 8
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll use Clue A first. I can find the number for the monkey face.
1.
= _____
2.
= _____
3.
+
4. 6
5.
+
Ima Thinker
4 = _____
= _____
+
= _____ 55
Name _____________________________________________ Date __________________ FACE THE NUMBERS
MAKE THE CASE
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues. CLUES:
A
That’s easy. The duck face is 6 and the cat face is 5.
56
3 = 9
B
+
= 10
I’ve got it! The duck face is 3 and the cat face is 7. The duck face is 6 and the cat face is 4. I am sure!
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Shorty Trunks
+
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
1
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues.
+
CLUES: A
1 = 10
B
+
= 12
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll use Clue A first. I can find the number for the lion face.
1.
= _____
Ima Thinker 2.
= _____
3.
+
2 = _____
4.
+
4 = _____
5.
+
= _____ 57
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
2
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues. CLUES:
+
A
4 = 6
B
+
= 7
I’ll use Clue A first. I can find the number for the pig face.
= _____
Ima Thinker
58
2.
= _____
3.
+
4.
+
= _____
5.
+
= _____
4 = _____
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1.
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
3
What are the numbers? <
and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues. CLUES:
+
A
= 7
B
+
5 = 9
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
I’ll use Clue B first. I can find the number for the eagle face.
1.
= _____
Ima Thinker 2.
= _____
3.
+
4.
+
= _____
5.
+
= _____
7 = _____
59
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
4
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues.
+
CLUES: A
= 10
B
4
+
= 12
I’ll use Clue B first. I can find the number for the tiger face.
= _____
Ima Thinker
60
2.
= _____
3.
+
4.
+
= _____
5.
+
+
1
+
1 = _____
= _____
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1.
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
5
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
CLUES:
+
A
= 7
B
1.
= _____
2.
= _____
3.
+
= _____
4.
+
+
= _____
5.
+
+
= _____
8
+
= 14
61
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
6
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues. CLUES:
9
+
= 19
1.
= _____
2.
= _____
3.
+
= _____
4.
+
= _____
5.
–
= _____
B
+
= 18
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
62
A
Name _____________________________________________ Date __________________ FACE THE NUMBERS
PROBLEM
7
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
CLUES:
+
A
= 10
B
1.
= _____
2.
= _____
3.
–
= _____
4.
+
+
= _____
5.
+
–
= _____
+
= 12
63
ALGE B
1
SS NE
READ I RA
How Much Is This Bag? Overview
Clues are given in the form of two food bags, each showing the total cost of different foods. Children solve for the cost of each food.
Algebra Solve for the values of one or two unknowns • Replace unknowns with their values
Problem-Solving Strategies Reason deductively • Test values
Related Math Skills Add single-digit numbers, or multiples of 10 • Use skip counting to solve problems • Find half of a number • Double a number
Math Language ¢ (cents symbol) • Cost • Costs the same
Introducing the Problem Set Make photocopies of “Solve the Problem: How Much Is This Bag?” (page 66) and distribute to children. Have children work in pairs, encouraging them to discuss strategies they might use to solve the problem. You may want to walk around and listen in on some of their discussions. After a few minutes, display the problem on the board (or on the overhead if you made a transparency) and use the following questions to guide a whole-class discussion on how to solve the problem: • Look at the two bags. What is in the bag with two things? (2 apples) • How much is the bag of apples? (10¢) • How can you figure out the cost of one apple? (Two apples are 10¢, so one apple is half of 10¢ or 5¢. Or, like Ima, think of two numbers that are the same and that add to 10: ____ + ____ = 10) 64
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
HOW MUCH IS THIS BAG?
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
SOLVE THE PROBLEM
How much does each bag cost?
• What is the cost of one cherry? (2¢) 10¢
2¢
• How can you figure out the cost of one apple and one cherry? (Add their prices: 5¢ + 2¢ = 7¢)
2 apples
• How can you figure out the cost of 2 apples and 2 cherries? (The bag with 2 apples is 10¢. Two cherries are 2¢ + 2¢ = 4¢. The total cost is 10¢ + 4¢ = 14¢.)
1 cherry
The apples each cost the same.
1.
The apples cost the same. So, ____ ¢ + ____ ¢ = 10¢.
1 apple
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Work together as a class to answer the questions in “Solve the Problem: How Much Is This Bag?”
2. 1 apple and 1 cherry
3.
Math Chat With the Transparency
3 apples
Ima Thinker
Display the “Make the Case: How Much Is This Bag?” transparency on the overhead. Before children can decide which character is “wearing smarty pants,” they need to figure out the answer to the problem. Encourage children to work in pairs to solve the problem. Then bring the class together for another whole-class discussion. Ask:
4. 2 apples and 2 cherries 66
Name _____________________________________________ Date __________________
THE CASE
• How did you figure it out? (Two oranges are 12¢, so one orange is half of 12¢, or 6¢. Then 6¢ + 4¢ + 5¢ = 15¢, the total cost of the three pieces of fruit.)
How much does the big bag cost? 12¢
?
2 oranges
1 orange 1 strawberry and 1 plum
4¢ 5¢
1 strawberry
1 plum
The oranges each cost the same.
• How do you think Shorty Trunks got the answer of 21¢? (He might have added the costs of the three bags: 12¢ + 4¢ + 5¢ = 21¢.)
That’s easy. The big bag of fruit is 21¢. Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
• How do you think that Levi Sam got the answer of 14¢? (He might have found the total cost of 2 plums and one strawberry by mistake; 5¢ + 5¢ + 4¢ = 14¢.)
HOW MUCH IS THIS BAG?
MAKE
• Who has the right answer? (Carl Cargo)
I’m sure that the big bag of fruit is 14¢. The big bag of fruit is really 15¢.
Shorty Trunks
Carl Cargo
Levi Sam
Who is wearing smarty pants?
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
67
65
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
SOLVE THE PROBLEM
How much does each bag cost? 10¢
2¢ 2 apples
1 cherry
The apples each cost the same.
1. 1 apple
The apples cost the same. So, ____ ¢ + ____ ¢ = 10¢.
1 apple and 1 cherry
3. 3 apples
Ima Thinker 4. 2 apples and 2 cherries 66
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
2.
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
MAKE THE CASE
How much does the big bag cost? 12¢
?
2 oranges
1 orange 1 strawberry and 1 plum
4¢ 5¢
1 strawberry
1 plum
The oranges each cost the same.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
That’s easy. The big bag of fruit is 21¢.
Shorty Trunks
I’m sure that the big bag of fruit is 14¢. The big bag of fruit is really 15¢.
Carl Cargo
Levi Sam
Who is wearing smarty pants?
67
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
1
How much does each bag cost? 6¢
7¢
2 carrots
1 tomato
The carrots each cost the same.
1. 1 carrot
The carrots cost the same. So, ____ ¢ + ____ ¢ = 6¢
1 carrot and 1 tomato
3. 1 carrot and 2 tomatoes
Ima Thinker 4. 2 carrots and 1 tomato 68
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
2.
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
2
How much does each bag cost? 4¢
16¢ 1 bunch of grapes
2 peaches
The peaches each cost the same.
1.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1 peach
2.
3.
The peaches cost the same. So, ____ ¢ + ____ ¢ = 16¢
1 peach and 1 grape bunch
1 peach and 2 grape bunches
Ima Thinker 4.
2 peaches and 2 grape bunches 69
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
3
How much does each bag cost? 15¢
9¢
1 pear
3 pineapples
The pineapples each cost the same.
1. 1 pineapple
The pineapples cost the same. So, ____ ¢ + ____ ¢ + ____ ¢ = 15¢
1 pear and 1 pineapple
3.
2 pineapples
Ima Thinker
4. 1 pear and 2 pineapples 70
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
2.
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
4
How much does each bag cost? 8¢
18¢
3¢ 1 blueberry
1 tangerine
2 kiwis
The kiwis each cost the same.
1.
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1 kiwi
The kiwis cost the same. So, ___ ¢ + ___ ¢ = 18¢.
2. 1 kiwi and 1 blueberry
3. 1 blueberry and 1 tangerine
Ima Thinker 4. 1 kiwi and 2 blueberries 71
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
5
How much does each bag cost? 12¢
10¢
4¢
3 cucumbers
1 mushroom
1 pepper
The cucumbers each cost the same.
1.
2. 1 cucumber
3.
4. 1 cucumber 1 pepper and 1 mushroom
72
1 cucumber 1 pepper and 2 mushrooms
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1 mushroom and 2 cucumbers
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
6
How much does each bag cost? 30¢
20¢ 1 pumpkin
19¢ 3 radishes
1 beet
The radishes each cost the same.
2.
1.
1 radish and 1 pumpkin
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1 radish
3.
1 beet and 2 radishes
4.
1 radish 1 beet and 1 pumpkin
73
Name _____________________________________________ Date __________________ HOW MUCH IS THIS BAG?
PROBLEM
7
How much does each bag cost? 15¢
20¢
20¢ 1 head of lettuce
1 squash
4 pea pods
The pea pods each cost the same.
1.
2.
3.
74
1 pea pod 1 squash and 1 lettuce
4.
1 pea pod 2 squashes and 1 lettuce
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
2 pea pods and 1 squash
1 pea pod
PROBLEM-SOLVING TRANSPARENCY
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
SOLVE IT
1.
Look
2.
Plan and Do
3.
Answer and Check
What is the problem?
What will you do first? How will you solve the problem?
How can you be sure your answer is correct?
SOLVE IT : FISHY PRICES
How much does each fish cost?
Barb
Shaggy
Glow
Use the clues to figure out the price of each fish. CLUES: A) Shaggy costs $4 less than Barb. B) Barb costs $7 more than Glow. C) Glow costs the least.
$5
$2
SOLVE IT : GUESS THE NUMBER
What is Z? Z
stands for a number.
Use the clues. CLUES: is between 19 and 35.
2)
Z Z
is a number you say when you count by 10s.
3)
Z
is greater than 25.
1)
30 20 10 0 31 21 11 1 32 22 12 2 33 23 13 3 34 24 14 4 35 25 15 5 36 26 16 6 37 27 17 7 38 28 8 1 8 39 29 19 9
76 Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
$9
SOLVE IT : COUNT THE SPOTS
How many spots in all? 1 pig _____ 10 spots _____
6 pigs _____ _____ spots in all
SOLVE IT : FIND THE PATTERN
If the pattern continues, how many and will be in Picture 8?
Picture 1
Picture 2
Picture 3
Picture 4
Picture 5
77 Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
SOLVE IT : FACE THE NUMBERS
What are the numbers?
and
stand for numbers.
Same faces are same numbers. Use the clues.
CLUES: A
10
+
= 16
+
B
= 13
SOLVE IT : HOW MUCH IS THIS BAG?
How much does this bag cost?
1 banana 1 pear and 1 apple
The bananas each cost the same.
40¢
10¢
12¢ 4 bananas
1 pear
1 apple
78 Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
ANSWER KEY Fishy Prices (pages 11–19) Solve the Problem 1. $1 2. $3 3. $2 4. $1 Make the Case Who’s wearing smarty pants? Carl Cargo Problem 1 1. $6 2. $4 3. $1 4. $5
add $7 to Glow’s cost. For Shaggy’s cost, we need to subtract $4 from Barb’s cost. 2. Plan and Do: Work backward. Fact C: Glow costs $2. Fact B: Barb is $2 + $7, or $9. Fact A: Shaggy’s cost is $9 – $4, or $5. 3. Answer and Check: Shaggy cost $5. Barb cost $9. Glow cost $2. Check the clues: $9 = $7 + $2, so Facts B and C check. $9 – $4 = $5, so Facts, A and B check. Guess the Number (pages 22–30) Solve the Problem 1. 10, 11, 12 2. 0, 1, 2, 3, 4, 5, 6, 7 3. 8 4. 9
Problem 2 1. $3 2. $5 3. $9 4. $6
Make the Case Who’s wearing smarty pants? Shorty Trunks Problem 1 1. 0, 1, 2, 3, 4, and 9, 10, 11, 12 2. 5 and 6 3. 7 4. 8
Problem 3 1. $8 2. $2 3. $6 4. $2 Problem 4 1. $2 2. $6 3. $5 4. $3
Problem 2 1. 5, 6, 7, 8, 9, 10, 11, 12 2. 0, 1, 2 3. 4 4. 3
Problem 5 1. $2 2. $9 3. $5 4. $3
Problem 3 1. 0, 1, 2, 3, 4, 5, 6, 7, 8 2. 15, 16, 17, 18, 19 3. 9, 11, 12, 13, 14 4. 10
Problem 6 1. $10 2. $3 3. $8 4. $2
Problem 4 1. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 14, 15, 16, 17, 18, 19 2. 9, 10, 11 3. 12 4. 13
Problem 7 1. $6 2. $10 3. $7 4. $1 Solve It: Fishy Prices 1. Look: Facts are given about the prices of fish. From Fact C we know that Glow costs the least. The least number is $2, so Glow costs $2. To figure out Barb’s cost,
Problem 5 1. 0, 1, 2, 3, 4, 5, …, 14, 15 2. 18, 19 3. 17 4. 34 Problem 6 1. 20, 21, …, 28, 29 2. 0, 1, 2, 3, …, 16, 17 3. 19 4. 15
Problem 7 1. 0, 1, 2, …, 23, 24 2. 27, 28, 29 3. 26 4. 32 Solve It: Guess the Number 1. Look: There is a list of numbers 0 – 39. There are 3 clues about the number Z. The problem is to use the clues to figure out the number that is shown by Z. 2. Plan and Do: Choose the clue to use first. Clue 1 eliminates the greatest number of numbers. Clue 1 eliminates all numbers except for 20 through 34. Clue 3 eliminates all numbers except 26 through 34. Then Clue 2 eliminates all numbers except for 30. 3. Answer and Check: 30. Check 30 with each clue. Clue 1: The number 30 is between 19 and 25. Clue 2: You say 30 when you count by 10s. Clue 3: 30 is greater than 25.
Problem 5 1. 3 fish, 12 spots 2. 5 fish, 20 spots 3. 6 fish, 24 spots Problem 6 1. 2 cheetahs, 20 spots 2. 3 cheetahs, 30 spots 3. 4 cheetahs, 40 spots Problem 7 1. 4 bugs, 24 spots 2. 5 bugs, 30 spots 3. 6 bugs, 36 spots Solve It: Count the Spots 1. Look: There is one pig with 10 spots. There are 6 pigs with no spots. 2. Plan and Do: The problem is to figure out the number of spots in all on 6 pigs. Draw 10 spots on each pig. Count the number of dots in all. 3. Answer and Check: 60 spots; Count the number of spots by 10s to check.
Count the Spots (pages 33–41) Solve the Problem 1. 2 dogs, 4 spots 2. 3 dogs, 6 spots 3. 4 dogs, 8 spots
Find the Pattern (pages 44–52) Solve the Problem 1. 5 ●, 1 ❍ 2. 6 ●, 1 ❍ 3. 8 ●, 1 ❍ 4. 10 ●, 1 ❍
Make the Case Who’s wearing smarty pants? Levi Sam
Make the Case Who’s wearing smarty pants? Shorty Trunks
Problem 1 1. 2 leopards, 4 spots 2. 5 leopards, 10 spots 3. 6 leopards, 12 spots
Problem 1 1. Draw 5 black and 5 white circles. 2. 5 ●, 5 ❍ 3. 6 ●, 6 ❍ 4. 7 ●, 7 ❍ 5. 8 ●, 8 ❍
Problem 2 1. 2 horses, 8 spots 2. 3 horses, 12 spots 3. 4 horses, 16 spots Problem 3 1. 2 turtles, 10 spots 2. 4 turtles, 20 spots 3. 6 turtles, 30 spots Problem 4 1. 3 cows, 9 spots 2. 4 cows, 12 spots 3. 6 cows, 18 spots
Problem 2 1. Draw 5 black and 2 white circles. 2. 5 ●, 2 ❍ 3. 6 ●, 2 ❍ 4. 7 ●, 2 ❍ 5. 10 ●, 2 ❍ Problem 3 1. 1 ●, 6 ❍ 2. 1 ●, 7 ❍ 3. 1 ●, 8 ❍ 4. 1 ●, 10 ❍ 5. 1 ●, 11 ❍
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
79
Face the Numbers (pages 55–63) Solve the Problem 1. 5 2. 3 3. 9 4. 9 5. 6
Problem 4 1. 5 ●, 4 ❍ 2. 6 ●, 5 ❍ 3. 7 ●, 6 ❍ 4. 8 ●, 7 ❍ 5. 10 ●, 9 ❍ Problem 5 1. 7 ●, 5 ❍ 2. 8 ●, 6 ❍ 3. 10 ●, 8 ❍ 4. 12 ●, 10 ❍ 5. 17 ●, 15 ❍
Make the Case Who’s wearing smarty pants? Carl Cargo Problem 1 1. 9 2. 3 3. 11 4. 7 5. 6
Problem 6 1. 1 ●, 10 ❍ 2. 1 ●, 12 ❍ 3. 1 ●, 16 ❍ 4. 1 ●, 20 ❍ 5. 1 ●, 24 ❍
Problem 2 1. 2 2. 5 3. 9 4. 4 5. 10
Problem 7 1. 6 ●, 4 ❍ 2. 7 ●, 5 ❍ 3. 8 ●, 6 ❍ 4. 11 ●, 9 ❍ 5. 21 ●, 19 ❍ Solve It: Find the Pattern 1. Look: There is a pattern of black and white circles. There are 2 white circles in each picture. There are different numbers of black circles. 2. Plan and Do: Look for a pattern. Figure out how the numbers of white and black circles are related to the picture number. There are 2 white circles in all pictures. The number of black circles is one more than the picture number. Make drawings of pictures 5 and 6. 3. Answer and Check: There are 2 white circles and 9 black circles in Picture 8. The number of white circles is the same in each picture; there are 2 in each picture. The number of black circles starts with 2 in Picture 1 and each picture has one more black circle than the picture before it.
80
Problem 3 1. 4 2. 3 3. 10 4. 8 5. 6 Problem 4 1. 8 2. 2 3. 10 4. 16 5. 6 Problem 5 1. 6 2. 1 3. 12 4. 8 5. 13 Problem 6 1. 10 2. 8 3. 20 4. 16 5. 2 Problem 7 1. 5 2. 7 3. 2 4. 15 5. 9
Solve It: Face the Numbers 1. Look: Two equations are shown with faces standing for numbers. Equation A shows that 10 + a rhino =16. Equation B shows that the sum of the rooster face number and the rhino face number is 13. The equations have to be solved to figure out the numbers the two faces stand for. 2. Plan and Do: Use Equation A to find the value of the rhino, which is 16 – 10, or 6. Replace the rhino in Equation B with 6. Then the rooster is 13 – 6, or 7. 3. Answer and Check: 7 and 6; Replace the faces with their values in Equations A and B. The sums should check. How Much Is This Bag? (pages 66–74) Solve the Problem 1. 5¢ 2. 7¢ 3. 15¢ 4. 14¢ Make the Case Who’s wearing smarty pants? Carl Cargo Problem 1 1. 3¢ 2. 10¢ 3. 17¢ 4. 13¢ Problem 2 1. 8¢ 2. 12¢ 3. 16¢ 4. 24¢
Problem 5 1. 4¢ 2. 18¢ 3. 18¢ 4. 28¢ Problem 6 1. 10¢ 2. 30¢ 3. 39¢ 4. 49¢ Problem 7 1. 5¢ 2. 30¢ 3. 40¢ 4. 60¢ Solve It: How Much Is This Bag? 1. Look: Three bags. In the bag for 40¢, there are 4 bananas. The second bag has one pear for 12¢. The third bag has one apple for 10¢, The problem is to figure out the cost of the bag with one banana, one pear, and one apple. 2. Plan and Do: In the first bag, the 4 bananas are 40¢, so one banana is 10¢. To find the cost of the bag with one banana, one pear, and one apple, add the costs of the three fruits: 10¢ + 12¢ + 10¢ = 32¢. 3. Answer and Check: 32¢. To check, replace each banana with 10¢, and check the total cost of the 4 bananas with the number of cents shown on the bag’s tag. Then check the addition of the costs of the three fruits. In the addition, add the two prices that are each 10¢ (10¢ + 10¢ = 20¢); then add 12¢ to that total (20¢ + 12¢ = 32¢).
Problem 3 1. 5¢ 2. 14¢ 3. 10¢ 4. 19¢ Problem 4 1. 9¢ 2. 12¢ 3. 11¢ 4. 15¢
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
KE
THE C
1
FISHY PRICES
E AS
MA
TEACHING TRANSPARENCY
How much do PB and J cost together? We cost $3 more than Dolly.
I cost $5 less than Ringo. Dolly
PB and J $2
$7 $5
I cost the most.
Match each price tag with its fish.
Clearly, PB and J are $3.
Shorty Trunks
Ringo
No, PB and J cost $7. I see that PB and J together cost $5.
Carl Cargo
Levi Sam
Who is wearing smarty pants? Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
81
KE
THE C
1
GUESS THE NUMBER
E AS
MA
TEACHING TRANSPARENCY
What is B?
B stands for a number on this list.
0
7
Use the clues.
1
8
2
9
is greater than 3.
3
10
is less than 6.
4
11
5
12
CLUES:
1) 2) 3)
B B B
is not a number that you say when you count by 5s.
6
No, no. I see that
B is 5.
B is 4. That’s easy. B is 6.
Shorty Trunks
Carl Cargo
Levi Sam
Who is wearing smarty pants? Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
82
KE
THE C
1
COUNT THE SPOTS
E AS
MA
TEACHING TRANSPARENCY
How many spots in all?
1 shark _____
5 spots _____ _____ sharks
_____ spots in all
No. There are 15 spots in all.
I know. There are 8 spots in all. I think there are 10 spots in all.
Shorty Trunks
Carl Cargo
Levi Sam
Who is wearing smarty pants? Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
83
KE
THE C
1
FIND THE PATTERN
E AS
MA
TEACHING TRANSPARENCY
If the pattern continues, how many and will there be in Picture 6?
Picture 1
Picture 2
I am sure there will be 2 of the and 5 of the .
Shorty Trunks
Picture 3
Picture 4
Picture 5
Picture 6
There will be 2 and 7 . There will be 2 and 6 .
Carl Cargo
Levi Sam
Who is wearing smarty pants? Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
84
KE
THE C
1
FACE THE NUMBERS
E AS
MA
TEACHING TRANSPARENCY
What are the numbers? and
stand for numbers.
Faces that are the same stand for the same numbers. Use the clues. CLUES: A
That’s easy. The duck face is 6 and the cat face is 5.
Shorty Trunks
+
3 = 9
B
+
= 10
I’ve got it! The duck face is 3 and the cat face is 7. The duck face is 6 and the cat face is 4. I am sure!
Carl Cargo
Levi Sam
Who is wearing smarty pants? Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
85
KE
THE C
HOW MUCH IS THIS BAG?
E AS
MA
TEACHING TRANSPARENCY
1
How much does the big bag cost? 12¢
? 2 oranges
1 orange 1 strawberry and 1 plum
4¢ 5¢ 1 strawberry
1 plum
The oranges each cost the same.
That’s easy. The big bag of fruit is 21¢.
Shorty Trunks
I’m sure that the big bag of fruit is 14¢. The big bag of fruit is really 15¢.
Carl Cargo
Levi Sam
Who is wearing smarty pants? Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
86
S
TEACHING TRANSPARENCY
E I
PROBLEM - SOLVING TRANSPARENCY
T
OLV
1
1.
Look
2.
Plan and Do
3.
Answer and Check
What is the problem?
What will you do first? How will you solve the problem?
How can you be sure your answer is correct?
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
87
TEACHING TRANSPARENCY
SOLVE IT : FISHY PRICES
How much does each fish cost?
Barb
Shaggy
Glow
Use the clues to figure out the price of each fish. CLUES: A) Shaggy costs $4 less than Barb. B) Barb costs $7 more than Glow. C) Glow costs the least.
$5
$2 $9
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
SOLVE IT : GUESS THE NUMBER
What is Z? Z stands for a number. Use the clues. CLUES:
Z is between 19 and 35. 2) Z is a number you say 1)
when you count by 10s. 3)
Z
is greater than 25.
30 20 10 0 31 21 11 1 32 22 12 2 33 23 13 3 34 24 14 4 35 25 15 5 36 26 16 6 37 27 17 7 38 28 18 8 39 29 19 9
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
88
TEACHING TRANSPARENCY
SOLVE IT : COUNT THE SPOTS
How many spots in all? 1 pig _____ 10 spots _____
6 pigs _____ _____ spots in all
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
SOLVE IT : FIND THE PATTERN
If the pattern continues, how many and will be in Picture 8?
Picture 1
Picture 2
Picture 3
Picture 4
Picture 5
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
89
TEACHING TRANSPARENCY
SOLVE IT : FACE THE NUMBERS
What are the numbers? and
stand for numbers.
Same faces are same numbers. Use the clues. CLUES: A
10 +
= 16
+
B
= 13
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
SOLVE IT : HOW MUCH IS THIS BAG?
How much does this bag cost?
1 banana 1 pear and 1 apple
The bananas each cost the same.
40¢
10¢
12¢ 4 bananas
1 pear
Algebra Readiness Made Easy: Gr. 1 © 2008 by Greenes, Findell & Cavanagh, Scholastic Teaching Resources
1 apple
90
