MightY Math for 7-9 year olds Maturing Mathematician BOOK 1
Sailing Into
Mathematics Kim Freeman
MightY Math for 7-9...
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MightY Math for 7-9 year olds Maturing Mathematician BOOK 1
Sailing Into
Mathematics Kim Freeman
MightY Math for 7-9 year olds Maturing Mathematician BOOK 1
Sailing Into
Mathematics Kim Freeman
Mighty Math, Maturing Mathematician Book 1, Sailing Into Mathematics Author, Kim Freeman eBook Version First Published in 2007 by: Mahobe Resources (NZ) Ltd P.O. Box 109-760 Newmarket, Auckland 1149 New Zealand. www.mahobe.com © Mahobe Resources (NZ) Ltd. ISBN10: 1877216879 ISBN13: 9781877216879
2
HOW CAN YOU HELP YOUR CHILD IN MATHEMATICS? Mastering mathematics is essential for future opportunities in school and careers. Your children need to reach a certain level of competency in mathematics to be able to progress in many advanced high-school courses, and then to have a wider variety of career choices. Doing mathematics homework reinforces all the skills being learnt in class. The more time children spend practising their skills, the sooner they will develop confidence in their abilities. However don’t just give this book to your children and expect them to learn by themselves. Any activity is fun when done with others or when there is reinforcement and encouragement. Praise and attention to what they are doing will help towards getting them to sit down to learn next time. This green Mighty Maths series, Maturing Mathematician, reinforces and continues on with the work covered in the previous Mighty Maths series (Beginning Mathematician, Developing Mathematician and Advancing Mathematician). The work is progressively more challenging and new concepts are introduced in each book at various points. To help reinforce mathematical skills as well as to maintain motivation, the same type of question is asked in different ways and contexts. This specific book covers Sudoku, strategies for multiplication, number patterns, and counting up to 1000, adding and subtracting strategies, fractions and money. For best results: C
Make sure your children understand the different concepts. Mathematics is not just a meaningless mental exercise of memorizing rules and doing rote drills. Making mathematics part of their daily lives will make it more meaningful. For example, ask them to space new plants a certain distance apart in the garden, double a recipe or pay bills in stores.
C
Help them to master the basic facts and learn the vocabulary of mathematics. By now, your children should be competent in the multiplication tables, and simple arithmetic. Having these basic skills and being able to understand the vocabulary means that they can move up to a higher level of learning. If they have not mastered these, use flash cards and drills to help them learn.
C
Encourage your children to write neatly. Many errors in solving mathematics problems can be traced back to sloppy number writing.
C
Provide help immediately when needed. Mathematics is a subject in which everything builds upon what has been previously learned. For example, a failure to understand fractions and decimals will lead to problems with percentages.
We hope that you and your children have fun with Mighty Maths. At Mahobe, we certainly had fun putting it all together for you. 3
What is found in this book? In this book you look at: Methods of Multiplication, Addition and Subtraction.
5H4 = 20
20 30
half of 4 = 2 add the zero
39
+
10
18
2 H
3 = 6 50
8 H
30+ 9 + 10 + 8 40 + 17
40
7 = 56
= 57 Money
Fractions
20
50
20 10
10 = $1 one
Maturing Mathematician
4
10 Mahobe Resources (NZ) Ltd
NUMBERS and PATTERNS Complete the pattern and the rule.
2, 4, 6, ........, ........, ........, ........, ........, ........, ........, ....... Rule = ..........................................................................
5, 10, 15, ......., ......., ......., ......., ......., ......., ......., ....... Rule = ..........................................................................
100, 99, 98, ......., ......., ......., ......., ......., ......., ....... Rule = ..........................................................................
100, 90, 80, ......., ......., ......., ......., ......., ......., ....... Rule = ..........................................................................
1, 2, 4, 8, ......., ......., ......., ......., .........., ..........., ............ Rule = .......................................................................... The sum of any two adjacent numbers is the number directly above. Fill in all the missing numbers
30 50 20 40
20 20 10 15 5 Mahobe Resources (NZ) Ltd
5
Maturing Mathematician
SUDOKU The challenge of Sudoko is to fill the grid with numbers. The big grid has the dimensions 9 x 9. This is separated into 9 smaller boards of 3 x 3. Here are the rules: 1. You can only use the numbers 1 to 9. 2. Within each 3 x 3 grid you must place ALL the numbers from 1 - 9. 3. You cannot use the same number twice in any row or column. This means ALL the numbers from 1 - 9 must appear on each row and each column. Now complete the Sudoku challenge.
1 5 4 7 8 3 6 3 2 5 9 6 6 4 5 8 2 1 7 Mahobe MaturingResources Mathematician (NZ) Ltd
6 1 9 8 7 8 6 4 1 9 5 2 9 7 1 4 2 3 6
8 2 9 5 3 4 7 5 2 7 3 6 4 1 2 3 7 6 5 4 Mahobe Maturing Resources Mathematician (NZ) Ltd
SUDOKU Complete the Sudoku challenges.
1 5 2 4 7 1 3 6 7 5 2 1 7 4 5 6 2 8 3 6 7 2 4 9 6 4
6 2 8 4 7 8 3 9 4 9 5 2 9 4 7 3 6 6 9 8 3 4 1 2 6 7 4 5 3 9 1 7 3 4 6 7 2 5 5 7 8 9 1 9 1 9 8 7 2 3 1 9 2 4 1 6 8 7 2
Mahobe Resources (NZ) Ltd
7
1 8 9 2 4 5 6 7 3
2 8 9 3 5 4 6 6 3 9 5 2 7 4 8 5 6 1 Maturing Mathematician
LEARNING THE 2s To multiply by 2: Double the number.
4 4 = .................... 8 4H2 =...............+...............
5H2 =...............+............... = .................... 12H2 =...............+............... = .................... 15H2 =...............+............... = .................... 18H2 =...............+............... = .................... 23H2= ............... + ............... =....................
34H2= ............... + ............... =....................
47H2= ............... + ............... =....................
55H2= ............... + ............... =....................
Maturing Mathematician
8
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LEARNING THE 4s To multiply by 4 : Add the number 4 times. or Double the number, then double again.
4H12
12 doubled is 24 24 doubled is 48 4H12 = 48
4H3 = ........................
4H22 = ........................
4H7 = ........................
4H25 = ........................
4H9 = ........................
4H32 = ........................
4H13 = ........................
4H34 = ........................
4H15 = ........................
4H47 = ........................
4H18 = ........................
4H55 = ........................
Mahobe Resources (NZ) Ltd
9
Maturing Mathematician
LEARNING THE 5s 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 To multiply by 5: 1.
2.
If the number is even, take half the number and put a zero after it.
5H4 = 20
5H16 = 80
half of 4 = 2 add the zero
half of 16 = 8 add the zero
If the number is odd, subtract 1 from the number, halve it Then put a five after it.
5H7 = 35
5H13 = 65
7 - 1 = 6 half of 6 = 3
13 - 1 = 12 half of 12 = 6
Maturing Mathematician
add the 5
add the 5
10
Mahobe Resources (NZ) Ltd
Even Numbers
Odd Numbers
5H6 = ........................ 5H9 = ........................ 5H8 = ........................ 5H11 = ........................ 5H14 = ........................ 5H15 = ........................ 5H18 = ........................ 5H17 = ........................ 5H20 = ........................ 5H19 = ........................ 5H22 = ........................ 5H21 = ........................ 5H26 = ........................ 5H23 = ........................ 5H28 = ........................ 5H25 = ........................ 5H30 = ........................ 5H31 = ........................ Mahobe Resources (NZ) Ltd
11
Maturing Mathematician
FINDING MULTIPLES When you multiply a number by another the result is a multiple. e.g. Multiplying 3 H 5 = 15 therefore 15 is a multiple of 3. The first few multiples of the 3 are 3, 6, 9, 12, 15, 18, ... Find each of the multiples.
Circle each multiple of 2.
22 65 13 4780 34 71 96 59
Circle each multiple of 5.
35 20 60 47 70 82 96 14 Circle each multiple of 10.
80 92 65 50 28 70 30 43 Maturing Mathematician
12
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FINGER MULTIPLICATION We all carry a calculator around with us that is simple to use and easy to learn. We can all use our fingers to learn the multiplication tables for the hardest number combinations - 6, 7, 8, 9, and 10. Step ONE: Remember these finger values.
6
7
8
9
10
Step TWO: Now try multiplying 8 H 7 =
8 H
7
Step THREE: Count the extended fingers - these are 10s
20 30
40 50
10 Mahobe Resources (NZ) Ltd
13
Maturing Mathematician
Step FOUR: Multiply the folded fingers.
2 H 3 = 6 Step FIVE: Finally, add the two numbers together.
50 + 6 = 56
8 H
You have now found the answer.
7
H
9
40 20 30 50 60 10 3H1=3
7 Maturing Mathematician
7 = 56
14
H 9 = 63 Mahobe Resources (NZ) Ltd
Use your finger calculator to multiply the following.
7H7 = ...............
6H8 = ...............
9H9 = ...............
8H7 = ...............
6H10 = ............... Mahobe Resources (NZ) Ltd
15
Maturing Mathematician
Use your finger calculator to multiply the following.
7H8 = ...............
7H10 = ...............
9H8 = ...............
9H6 = ...............
8H8 = ...............
8H6 = ...............
9H7 = ...............
6H9 = ...............
9H10 = ...............
6H6 = ...............
8H10 = ...............
7H9 = ...............
8H9 = ...............
6H7 = ...............
9H9 = ...............
7H6 = ...............
Maturing Mathematician
16
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MORE MULTIPLICATION Multiplication by 9: Method 1 This method is called fingers multiplication by 9. The previous finger multiplication works for combinations of 6, 7, 8, 9 and 10. This method only works for the 9 times tables. Step ONE: Put your two hands on the table in front of you. Your fingers can each represent the numbers 1 to 10.
1
2
789
34 5 6
10
Step TWO: Try multiplying 9 H 3. Curl under the finger representing 3.
1
4 56
1 2 2 3
7
Step THREE: The first digit in the answer is the number of fingers before the curled under finger. The second digit in the answer is the number of fingers after the curled under finger.
9 H Mahobe Resources (NZ) Ltd
3 = 27 17
Maturing Mathematician
Fingers Multiplication by 9 Use the fingers method to calculate these 9 x multiplications.
9H3=...............
9H8=............... 9H5=............... 9H7=............... 9H2=...............
9H9=...............
9H10=...............
9H6=...............
Maturing Mathematician
18
Mahobe Resources (NZ) Ltd
Multiplication by 9: Method 2 This is called the one less = nine method. Step ONE: Subtract 1 from the number you are multiplying 9 by. This is the first digit. Step TWO: The two digits that make up the answer add to give 9. Calculate the second digit.
9 H
4 = 36 4-1=3
3+6=9
Remember that these methods only work up until 9x10. Find a calculator and write out the 9 times table up to 30. Can you see a pattern emerging?
9H3=...............
9H7=...............
9H8=...............
9H2=...............
9H5=...............
9H9=...............
9H10=...............
9H6=...............
Mahobe Resources (NZ) Ltd
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Maturing Mathematician
NUMBERS 0 TO 100 Count and write the correct number in each box.
1 1 1 10 1 1 1 10 10 1 1 1 10 10
1
10
1
1 10
10
10 10 1 1 1 1 1
Maturing Mathematician
=
1
10 1 1 1 1 1 1 10
1 1 1
=
10 10 10 1 1 1 1 1
=
10
=
10 10
= 20
=
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NUMBER RELATIONSHIPS Complete the tables.
-2
31 41 51 61
28
-5
+2
56
9
15
22 32 42 52
-7
82
+5
+7
15 25 35 45
37 44
Put the circled numbers above in order - smallest to biggest ................................................................................... Complete these additions
50 + 43
37 + 52
+
+ 56
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50
26
21
+
77
45 86
Maturing Mathematician
ARITHMETIC Use the diagrams to complete the sums.
16 + .......... = ............... 21 - .......... = 16 17 + .......... = ............... 25 - .......... = 17
......... + 5 = ............... .......... - .......... = 41 ......... + 16 = ............... .......... - .......... = ............... Maturing Mathematician
22
Mahobe Resources (NZ) Ltd
15 + .......... = ............... 27 - .......... = ...............
......... + 8 = ............... .......... - .......... = 24
1.
1.
5, 10, 15, ....., 25
1.
100 - 78
3.
8, 6, 4, ....., 0
2.
100 - 4
4.
1, 2, 4, 8, ....., 32
4.
100 - 90
5.
10, 20, 30, .....
5.
100 - 58
6.
3, 6, 9, ....., 15
7.
100 - 91
Mahobe Resources (NZ) Ltd
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2.
3.
4.
5. 6.
7.
Maturing Mathematician
ARITHMETIC Fill in the missing numbers.
34 + ............= 39
............ + 5= 50
6 + ............= 93
46 + ............= 48
............ + 7= 29
8 + ............= 61
73 + ............= 77
............ + 3= 68
............ + 27= 34
98 - ............= 90
............ - 3= 30
77 - ............= 72
............ - 2= 56
28 - ............= 21
............ - 6= 44 1.
1. 10 + 6
1. 20 - 1
3. 6 + 3
2. 32 - 4
4. 25 + 11 + 2
4. 40 - 6
5. 32 + 52
5. 87 - 5
6. 6 + 16
7. 12 - 4
Maturing Mathematician
24
2.
3.
4.
5. 6.
7.
Mahobe Resources (NZ) Ltd
= 50
+
+
= ...............
= 30 = 20
+
-
= ...............
-
+
= ...............
Circle 2 numbers that add up to 20
19 15 4 18 11 3 5
4 17 1 6 3 10
3 6 9 12 14 15
Circle 3 numbers that add up to 50
20 18 11 25 32 45 5 If and
9 22 2 15 12 13 20 5 32 44 11 2 8 10
+ = 50 + + = 36
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then
25
+
= .......... Maturing Mathematician
NUMBERS to 1000 The blocks shown are arranged in 3 different ways - in single units, in groups of ten and groups of one hundred.
1 group of 100 units (hundreds) 2 groups of 10 units (tens) 6 single units (ones)
1 2 6 One hundred and twenty six
2 0 4 4 single units
2 group of 100 units
zero groups of 10 units
Two hundred and four Maturing Mathematician
26
Mahobe Resources (NZ) Ltd
Write down the number that each picture represents.
.....................
.....................
.....................
.....................
..................... .....................
.....................
..................... Mahobe Resources (NZ) Ltd
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Maturing Mathematician
Write down the number that each picture represents
.....................
.....................
.....................
.....................
..................... .....................
..................... Maturing Mathematician
..................... 28
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PLACE VALUE Write the number of objects in each place-value table.
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29
H
T
U
H
T
U
H
T
U
H
T
U
Maturing Mathematician
PLACE VALUE Write the correct number.
10
100
10 10
135
100 100 10 100 10
1
1 1 1 1
1 1 1 1
1 1 1 1
.......................................................
100 10 10 100 100 10 10 100 100 10 10 1 1
100 10 10 10 10 100 10 10 10 10 10
.......................................................
.......................................................
100 11 11 100 100
100 100 10 10 1 1 1 1 1 100 100 10 1 1 1 1
.......................................................
.......................................................
100 100 100 100
100 100 100 100 10 10 100 100 10 10 1 1 1 1 100 100 10 10 1 1
100 100
....................................................... Maturing Mathematician
10 10 1 1 10 1 10
....................................................... 30
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PLACE VALUE Write the number and the number word.
H
T
O
H
T
O
342 three hundred and forty two
H
T
H
Mahobe Resources (NZ) Ltd
T
O
O
31
H
T
O
H
T
O
Maturing Mathematician
NUMBERS to 1000 Write each sum and then write the number word.
H
T
H
O
T
O
500+80+4=584 five hundred and eighty four
H
H
T
T
Maturing Mathematician
H
O
O
H
32
T
T
O
O
Mahobe Resources (NZ) Ltd
NUMBERS to 1000 Draw the correct number of beads and write the number formed.
H
T
H
O
T
O
4 hundreds, 3 tens, 5 ones
6 hundreds, 2 tens, 9 ones
629
H
T
H
O
T
H
O
7 hundreds, 2 tens 9 ones
Mahobe Resources (NZ) Ltd
O
5 hundreds, 8 tens, 0 ones
....................................................
H
T
T
O
1 hundred 5 tens, 20 ones
33
Maturing Mathematician
NUMBERS to 1000 Draw the correct number of beads and write the number formed.
H
T
H
O
927 ones
H
T
T
H
O
T
O
30 tens 16 ones
H
O
1 ten, 80 ones
Maturing Mathematician
O
72 tens, 4 ones
22 tens, 16 ones ....................................................
H
T
T
O
3 tens, 15 ones
34
Mahobe Resources (NZ) Ltd
NUMBERS to 1000 Which numbers have been labelled?
a 150
160
b 170
e f
c d 180
190 200 210
g
h
220 230 240
i 250
one hundred and sixty four a = 164 ........................................................................................... b = ........................................................................................... c = ........................................................................................... d = ........................................................................................... e = ........................................................................................... f = ........................................................................................... g = ........................................................................................... h = ........................................................................................... i = ........................................................................................... Mahobe Resources (NZ) Ltd
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Maturing Mathematician
PARTITIONING NUMBERS Write in the missing digits.
452 348 601 794
= 4 0 0 + = + = + = +
0 + + + +
Now, write in the missing numbers.
351 = + 50 + 1 867 = + + 7 422 = 400 + + 105 = + + Finally, write the answers.
400 + 50 700 + 60 900 200 Maturing Mathematician
+ + + +
8 2 3 10
= = = = 36
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ADDITION Arithmetic is always easier when the sum is broken into smaller bits.
26 + 18 = 20+6 + 10+8
Which is easier to calculate? or
= 30 + = 44
14
Write in the missing numbers and find the answers.
39
+
18
30+ 9 + 10 + 8 +
47
+
25
40+
+
+
=
+
=
65
+
26
26
+
54
60+
+
+
20+
+
+
+ Mahobe Resources (NZ) Ltd
=
+ 37
= Maturing Mathematician
36
+
19
25
+
17
30+
+
+
20+
+
+
+
=
33
+
48
30+
+
+
+
+ 49
+
29
40+
+
+
=
19
+
44
10+
+
+
+
+
+
29
20+
+
+
+ Maturing Mathematician
=
49
+
38
40+
+
+
=
25
=
+
=
54
+
48
50+
+
+
+ 38
=
= Mahobe Resources (NZ) Ltd
28
+
29
20+
+
+
+
16 10+ =
+
27
+
+
+
=
55
+
25
57
+
19
50+
+
+
50+
+
+
+
=
+
=
Write the answers.
23 + 17 =
71 + 29 =
46 + 14 =
55 + 35 =
35 + 15 =
42 + 28 =
Mahobe Resources (NZ) Ltd
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Maturing Mathematician
MENTAL STRATEGIES Make each pair of number cards add up to 10.
6 4E
2E C
1E
7E
E
E
6
3
5E 8E
Find pairs that add up to 10 to help you answer these.
10
10
20 2 + 9 + 8 + 1 = ............... 1 + 3 + 2 + 8 + 9 + 6 + 4 = ............... 5 + 7 + 3 + 9 + 8 + 2 + 1 = ............... 5 + 2 + 5 + 5 = ............... Treat each 9 as a 10 then take away the extra 1s at the end.
7 + 10 - 1 = 16 7 + 9 = .................................................................. 14 + 9 = .................................................................. 28 + 9 = .................................................................. 35 + 9 = .................................................................. Maturing Mathematician
40
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ARITHMETIC STRATEGIES 1. Making Tens
9 + 7
9 + 7
Take 1 from the 7 to leave 6. Add it to the 9 to make 10.
= 10 + 6 = 16
2. Doubles
14 + 16
14 + 16
Take 1 from the 16 to leave 15. Add it to the 14 to make 15.
= 15 + 15 = 30
3. Partitioning
13 + 19
13 + 19
Separate all the tens and units. Add all together.
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= 10 + 10 + 3 + 9 = 32 41
Maturing Mathematician
Calculate the following.
5 6 8 11
+ + + +
4= 5= 7= 10=
6 + 14= 9 + 11= 15 + 5= 17 + 13=
16 + 24= 28 + 32= 46 + 24= 35 + 15= Maturing Mathematician
11 + 12= 9 + 8= 6 + 7= 10 + 12=
7 5 12 13
10 + 15= 17 + 20= 18 + 22= 22 + 28=
26 + 34= 23 + 27= 32 + 48= 15 + 55=
48 + 52= 27 + 33= 32 + 28= 79 + 21= 42
+ + + +
9= 7= 8= 7=
29 + 38= 14 + 27= 81 + 19= 57 + 43= Mahobe Resources (NZ) Ltd
ADD TO 100 Fill in the blanks.
95 =100 +............... +............... =100
+............... =100
+............... =100 +............... =100 +............... =100
+............... =100 +............... =100 Mahobe Resources (NZ) Ltd
43
Maturing Mathematician
SUBTRACTION Arithmetic is easier when the sum is broken down into smaller bits.
73
-
7 = 66
73 - 3 - 4 70 - 4 = 66 Write in the missing numbers and find the answers.
65
-
9 =
65 - 5 60 52
-
= 8 =
52 - 2 50 Maturing Mathematician
= 44
Mahobe Resources (NZ) Ltd
52
-
52 -
91
-
91 -
-
82 -
= 63
6 =
-
Mahobe Resources (NZ) Ltd
= 9
57
9 =
57 -
80 -
=
-
=
5 -
-
45
= 8
=
50 -
=
=
-
60 -
90 -
-
63 =
=
-
88 -
80 -
91 -
88
-
82
8
70 -
= 6 =
90 -
-
75 -
50 -
91
75
9 =
= Maturing Mathematician
Write the answers.
96 - 8 =
74 - 6 =
52 - 9 =
61 - 7 =
75 - 6 =
44 - 9 =
Use a strategy to find the answers.
55
-
27
=
43
28
55 - 20 - 7
43 -
28
-
30 - 2 = 28 88
- 39
73
=
88 - 30 58 -
50 Maturing Mathematician
-
73 -
-
=
35
=
-
-
-
= 46
=
-
23 -
5 - 2
35 -
-
=
Mahobe Resources (NZ) Ltd
Fraction Man is here to introduce...
This square is divided into 4 parts with 1 part shaded. Therefore 41 is shaded. Write the fraction that is shaded.
....................
....................
....................
....................
.................... .................... .................... Mahobe Resources (NZ) Ltd
47
Maturing Mathematician
FRACTIONS What fraction of each shape is shaded?
......................
......................
......................
......................
......................
......................
......................
......................
......................
......................
Maturing Mathematician
48
Mahobe Resources (NZ) Ltd
............
Shade in each of these shapes to show the
3 4 ............ 2 5 ............
1 3 ............ 1 4 ............
2 3 ............
1 2 ............
Circle each shape below that is half shaded.
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49
Maturing Mathematician
FRACTIONS Shade the shape to show the fraction.
one half two thirds one quarter one fifth one tenth five sixths Maturing Mathematician
50
Mahobe Resources (NZ) Ltd
Colour each fraction. Compare the two rectangles and fill in the missing sign with greater than (>), less than (<) or equals (=).
2 4 ...............
1 8 ...............
1 4 ...............
3 8 ...............
3 4 ...............
1 2 ...............
4 8 ...............
1 2 ...............
2 3 ...............
1 2 ...............
3 5 ...............
3 4 ...............
Mahobe Resources (NZ) Ltd
51
Maturing Mathematician
ESTIMATING NUMBERS Write what you think the number in each of the boxes would be.
0
10
30
40 60
80
150
250
400
500
Mark on the number line below where you think the following numbers would be: 5, 12, 27, 33 and 39.
0
Maturing Mathematician
10
20
52
30
40
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HALF WAY BETWEEN Write in the numbers that are halfway between.
1
5
3
9
10
50
30
90
100
500
300
900
4
10
1
7
40
100
10
70
400
1000 100
700
2
10
2
6
52
60
92
96
182
190
332
336
Mahobe Resources (NZ) Ltd
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Maturing Mathematician
DIVISIONS BETWEEN Write the missing numbers on each number line.
0
100
0
30
0
80
0
20
0
60
0
70
0
100
0
90
Maturing Mathematician
54
Mahobe Resources (NZ) Ltd
MONEY EQUIVALENTS Different countries have different types of coins. Here are the most popular. Draw a line to show each equivalent value.
50 20 20 20
25
50 50 20 10 Mahobe Resources (NZ) Ltd
C
C
$1 one
10
C
20
C
C
10
C
5 5 5 C 5 5 5
C
C
C
55
20
50
10 10 5 Maturing Mathematician
MONEY EQUIVALENTS Draw a line to show each equivalent value of coins.
20
C
20
20 C 20 10
C
20 20 20 20
10 C
C
10
C
50
10 5 20 5 50 20 25 Maturing Mathematician
C C 56
5
50
C
$1
C
5 10 5
one
Mahobe Resources (NZ) Ltd
ADDING MONEY 10 10 5 5 5
+
25
$1
$1
one
one
20
+
50 20
10
20 20 +
10 $1
one
one
20 Mahobe Resources (NZ) Ltd
= ................................
50
5 5 = ................................
10
$1
= ................................
+ 50
2050 57
= ................................ Maturing Mathematician
SUBTRACTING MONEY 20 10 5
-
20 = ................................ 20 25 5
10 10 10 5 5 5 5 10 10 10 $1
$1
one
one
20
- 50
50 20
= ................................
10
$1 one
one
Maturing Mathematician
20
5 5
= ................................ $1
$1
50 = ................................
50 10 - 50
20
20 10
one
50 58
20 20 10
= ................................ Mahobe Resources (NZ) Ltd
NUMBERS and PATTERNS
SUDOKU
Complete the pattern and the rule.
8 ........, 10 12 14 ........, 16 ........, 18 20 2, 4, 6, ........, ........, ........, ........, 22 ....... Add 2 to the previous number
Rule = ..........................................................................
5, 10, 15, 20 ......., 25 ......., 30 ......., 35 ......., 40 ......., 45 ......., 50 ......., 55 .......
Add 5 to the previous number
Rule = ..........................................................................
91 100, 99, 98, 97 ......., 96 ......., 95 ......., 94 ......., 93 ......., 92 ......., .......
Subtract 1 from previous number
Rule = ..........................................................................
10 100, 90, 80, 70 ......., 60 ......., 50 ......., 40 ......., 30 ......., 20 ......., .......
Subtract 10 from previous number
Rule = ..........................................................................
512 1024 16 32 1, 2, 4, 8, ......., ......., 64 ......., 128 ......., 256 .........., ..........., ............ Double the previous number
Rule = .......................................................................... The sum of any two adjacent numbers is the number directly above. Fill in all the missing numbers
100
100
70 30 50 20 10 40 10 10 0
55 45 30 25 20
20 10 15 5
1 2 3 4 5 7 6 8 9
5 7 6 3 8 9 4 2 1
4 8 9 1 2 6 5 3 7
3 1 2 7 4 5 9 6 8
6 9 5 8 1 3 7 4 2
7 4 8 6 9 2 1 5 3
8 3 1 5 7 4 2 9 6
2 6 4 9 3 1 8 7 5
9 5 7 2 6 8 3 1 4
1 2 3 5 7 9 8 6 4
9 4 6 2 3 8 5 7 1
5 7 8 1 4 6 3 2 9
3 6 2 8 4 7 1 8 5 3 6 9 7 4 9 1 5 2 8 9 4 7 3 6 5 1 6 2 9 8 2 3 7 4 1 5 9 2 1 6 7 4 4 5 3 9 8 1 6 7 8 5 2 3 3 5 4 6 7 1 2 1 9 6 4 2 8 3 7 2 8 5 3 9 1 4 1 5 7 9 2 6 6 3 2 1 8 4 7 8 7 9 3 6 5 4 2 4 1 8 5 6 9 5 6 3 9 1 7 8 9 8 7 2 4 3 5
6
5
LEARNING THE 4s
To multiply by 2: Double the number.
To multiply by 4 : Add the number 4 times. or Double the number, then double again.
10 5 5 = .................... 5H2 =...............+............... 12 12 = .................... 24 12H2 =...............+............... 15 15 = .................... 30 15H2 =...............+............... 36 18 18 = .................... 18H2 =...............+............... 23 23H2= ............... 23 + ............... 46 ....................
34 34H2= ............... + 34 ............... 68 ....................
47 47H2= ............... + 47 ............... 94 ....................
55 55H2= ............... 55 + ............... 110 ....................
4H12
12 doubled is 24 24 doubled is 48 4H12 = 48
12............ 4H3 = ............
88 4H22 = ............ ............
28............ 4H7 = ............
100............ 4H25 = ............
36............ 4H9 = ............
128 4H32 = ............ ............
52............ 4H13 = ............
136............ 4H34 = ............
60............ 4H15 = ............
188............ 4H47 = ............
72............ 4H18 = ............
220 4H55 = ............ ............
Even Numbers
FINDING MULTIPLES When you multiply a number by another the result is a multiple. e.g. Multiplying 3 H 5 = 15 therefore 15 is a multiple of 3. The first few multiples of the 3 are 3, 6, 9, 12, 15, 18, ...
40............ 5H11 = ............55............ 5H8 = ............ 70............ 5H15 = ............75............ 5H14 = ............ 90............ 5H17 = ............ 85............ 5H18 = ............ 100............ 5H19 = ............95............ 5H20 = ............ 105 5H22 = ............110 ............ 5H21 = ............ ............ 130 115............ 5H26 = ............ ............ 5H23 = ............ 125 140 5H28 = ............ ............ 5H25 = ............ ............ 150 155 5H30 = ............ ............ 5H31 = ............ ............
22 65 4780 34 13 Circle all 59 71 96 the even numbers
49 7H7 = ............... 6H8 =
48 ...............
81 9H9 = ...............
Circle each multiple of 5.
Circle all the 47 2070 35 60 82 96 14 numbers that end in a zero or five
56 8H7 = ...............
Circle each multiple of 10.
92
80 65 Circle all the 50 28 numbers that end 70 43 30 in a zero. 12 Mahobe Resources (NZ) Ltd
11
Use your finger calculator to multiply the following.
Find each of the multiples.
Circle each multiple of 2.
Odd Numbers
30............ 5H9 = ............ 45............ 5H6 = ............
9
8
9 7 6 8 5 2 3 4 1
7
LEARNING THE 2s 4 4 = .................... 8 4H2 =...............+...............
8 5 4 3 9 1 7 2 6
60 6H10 = ............... 15
59
Use your finger calculator to multiply the following.
56 7H8 = ...............
70 7H10 = ...............
72 9H8 = ...............
54 9H6 = ...............
64 8H8 = ...............
48 8H6 = ...............
63 9H7 = ...............
54 6H9 = ...............
90 9H10 = ...............
36 6H6 = ...............
80 8H10 = ...............
63 7H9 = ...............
72 8H9 = ...............
42 6H7 = ...............
81 9H9 = ...............
42 7H6 = ...............
16
16
Maturing Mathematician
NUMBERS 0 TO 100
Fingers Multiplication by 9 Use the fingers method to calculate these 9 x multiplications.
Multiplication by 9: Method 2
27 9H3=...............
Count and write the correct number in each box.
This is called the one less = nine method. Step ONE: Subtract 1 from the number you are multiplying 9 by. This is the first digit. Step TWO: The two digits that make up the answer add to give 9. Calculate the second digit.
72 9H8=...............
9 H 4 = 36 3+6=9
4-1=3
45 9H5=...............
18 9H2=...............
81 9H9=...............
90 9H10=...............
54 9H6=...............
27 9H3=...............
63 9H7=...............
72 9H8=...............
18 9H2=...............
45 9H5=...............
81 9H9=...............
90 9H10=...............
54 9H6=...............
ARITHMETIC Use the diagrams to complete the sums.
28
24 17 33 45
+7
-7
8 2515 22 56 18 32 37 35 42 28 9 15 44 38 45 52 9 15 28 37 44 56 82 50 50 26 37 41 + 43 + 52 +30 +27 45 93 89 56 77 86
41 ......... + 5 = 46 ............... 46 5 = 41 .......... - ..........
Put the circled numbers above in order - smallest to biggest
................................................................................... Complete these additions
44 60 ......... + 16 = ............... 60 16 = ............... 44 .......... - ..........
+
ARITHMETIC Fill in the missing numbers.
5 45 ............ + 5= 50 6 + 87 ............= 93 2 48 22 46 + ............= ............ + 7= 29 8 +53 ............= 61 7 + 27= 34 73 + 4 ............= 77 65 ............ + 3= 68 ............ 33 8 90 ............ - 3= 30 98 - ............= 58 ............ - 2= 56 77 - 5 ............= 72 50 7 21 ............ - 6= 44 28 - ............= 1 6 2 9 38 84 22 8 34 + ............= 39
1.
1. 20 - 1
3. 6 + 3
2. 32 - 4
4. 25 + 11 + 2
4. 40 - 6
5. 32 + 52
5. 87 - 5
6. 6 + 16
7. 12 - 4
1 10
10
10 10 1 1 1 1 1
=
=
1
Maturing Mathematician
=
10
10 10 10 1 1 1 1 1
=
12 27 12 = ............... 15 27 - .......... 15 + .......... = ...............
24 ......... + 8 = 32 ............... 32 8 = 24 .......... - .......... 20 9 2 1 6 40 1 2 9
1.
1.
5, 10, 15, ....., 25
1.
100 - 78
3.
8, 6, 4, ....., 0
2.
100 - 4
4.
1, 2, 4, 8, ....., 32
4.
100 - 90
5.
10, 20, 30, .....
5.
100 - 58
6.
3, 6, 9, ....., 15
7.
100 - 91
2.
3.
4.
5.
6.
7.
+
= 30 = 20
+
-
-
+
100 = ............... 60 40 = ...............
= ...............
Write down the number that each picture represents.
342
423
.....................
4 17 1 6 3 10
3 6 9 12 14 15
188
297
.....................
.....................
620
.....................
Circle 3 numbers that add up to 50
9 13 22 12 2 15
20 18 11 25 45 32 5
4.
7.
If
24
1 1 1
10
.....................
5.
6.
+
Circle 2 numbers that add up to 20
2.
3.
10
=
23
= 50
15 419 18 11 3 5
10 1 1 1 1 1 1 10
22
21
1. 10 + 6
1
5 21 5 = 16 21 - .......... 8 = ............... 25 17 + .......... 8 = 17 25 - ..........
17 22 27 32 37 27 42 37 52 47 47 57
82
10
16 + .......... = ...............
+5
-5
33 43 53 63
10 10
=
20
NUMBER RELATIONSHIPS 31 41 51 61
41 39 52 26
19
Complete the tables.
+2
1 1 1 10 1 1 1 10 10 1 1 1
1
18
29 39 49 59
56
Remember - these methods only work up until 9x10. Find a calculator and write out the 9 times table up to 30. Can you see a pattern emerging?
63 9H7=...............
-2
47
and
20 5 32 44 11 2 8 10
+ = 50 + + = 36
25+12=37 + = ..........
then
25
60
187
.....................
234
.....................
109
.....................
27 Mahobe Resources (NZ) Ltd
Write down the number that each picture represents.
PLACE VALUE
PLACE VALUE
Write the number of objects in each place-value table.
Write the correct number.
H
331
T
57
544
.....................
10 10
100
135
.....................
H
T
U
1 23 .....................
H
T
U
41 8
296
.....................
422
.....................
H
333
500
.....................
.....................
28
T
U
345
100 100 100 100
1 1 1 1
100 10 10 10 10 100 10 10 10 10 10
290 .......................................................
1 1 1 1
100 100 100
100 100 10 10 1 1 1 1 1 100 100 10 1 1 1 1
704 .......................................................
439 .......................................................
100 100 100 100 10 10 100 100 10 10 1 1 1 1 100 100 10 10 1 1
10 10 1 1 10 1 10
100 100
243 .......................................................
866 .......................................................
29
1 1 1 1
328 .......................................................
100 10 10 100 100 10 10 100 100 10 10 1 1
562 .......................................................
279
167
.....................
100 100 10 100 10
1 1 1 1 1
10
U
30
PLACE VALUE
NUMBERS to 1000
NUMBERS to 1000
Write the number and the number word.
Write each sum and then write the number word.
Draw the correct number of beads and write the number formed.
H
T
O
H
342
T
624
O
H
Six hundred and twenty four
H
T
T
906
H
T
O
451
Four hundred and fifty one
Five hundred and sixty three
H
31
T
H
O
500+80+4=584 five hundred and eighty four
O
Nine hundred and six
O
563
O
Six hundred and ninety three
three hundred and forty two
H
T
693
H
T
T
H
300+40+2=342 H
400+60+1=461
O
T
H
O
700+20+5=725 H
T
500+60+9=569 200+50+6=256
Five hundred and sixty nine
T
H
O
T
O
5 hundreds, 8 tens, 0 ones
580
H
O
T
O
1 hundred 5 tens, *20 ones
7 hundreds, 2 tens 9 ones
729
Two hundred and fifty six
O
435
228 T
T
4 hundreds, 3 tens, 5 ones
....................................................
H
O
H
O
629
Seven hundred and twenty five
O
T
6 hundreds, 2 tens, 9 ones
Three hundred and forty two
O
Four hundred and sixty one H
T
*20 ones = 2 tens
32
170
33
NUMBERS to 1000
NUMBERS to 1000
PARTITIONING NUMBERS
Draw the correct number of beads and write the number formed.
Which numbers have been labelled?
Write in the missing digits.
a H
T
H
O
927 ones
T
724
H
O
22 tens, 16 ones ....................................................
236
H
T
T
O
30 tens 16 ones
316
H
O
1 ten, 80 ones
90
O
150
160
170
e f
c d 180
190 200 210
g
h
220 230 240
i 250
72 tens, 4 ones
927
H
T
b
T
O
3 tens, 15 ones
34
45
Mahobe Resources (NZ) Ltd
one hundred and sixty four a = 164 ........................................................................................... 172 one hundred and seventy two b = ........................................................................................... 189 one hundred and eighty nine c = ........................................................................................... one hundred and ninety five d = 195 ........................................................................................... 207 two hundred and seven e = ........................................................................................... 213 two hundred and thirteen f = ........................................................................................... 221 two hundred and twenty one g = ........................................................................................... 236 two hundred and thirty six h = ........................................................................................... 249 two hundred and forty nine i = ...........................................................................................
35
61
452 348 601 794
= 4 0 0 = 300 = 600 = 70 0
+50 + 40 + 0 + 90
+ + + +
2 8 1 4
Now, write in the missing numbers.
351 = 3 0 0 + 50 + 1 867 = 8 0 0 + 6 0 + 7 422 = 400 + 2 0 + 2 105 = 1 0 0 + 0 + 5 Finally, write the answers.
400 + 50 700 + 60 900 200
+ + + +
8 2 3 10 36
= = = =
4 58 76 2 9 03 210
Maturing Mathematician
ADDITION
36
Arithmetic is always easier when the sum is broken into smaller bits.
26 + 18 = 20+6 + 10+8
Which is easier to calculate? or
+
40 + 15
= 30 + 14 = 44 18
47
30+ 9 + 10 + 8
40 + 17 65
40+
=
+
26
5 + 20+ 6 80 + 11 = 91
60+
20+
12
+
+
72
81
= 44
6 + 50 + 4
20+
80
=
+
5
7E 3
6
25
57
70 + 10
=
9 + 30 + 8
54
+
=
87
50+
80 60
2E C 8
7 4 E
3
5E 5 8E 2
5 6 8 11
+ + + +
4= 9 5= 11 7= 15 10= 21
33 35 17
1 + 3 + 2 + 8 + 9 + 6 + 4 = ............... 5 + 7 + 3 + 9 + 8 + 2 + 1 = ............... 5 + 2 + 5 + 5 = ...............
+
43
19
7 + 10 + 9 16
+
=
76
48
40
71 + 29 =
100
46 + 14 =
60
55 + 35 =
90
35 + 15 =
50
42 + 28 =
70
4 +40 + 8
90 + 12
=
102
39
ADD TO 100
11 + 12= 23 7 + 9 + 8= 17 5 + 6 + 7= 13 12 + 10 + 12= 22 13 +
9= 16 7= 12 8= 20 7= 20
Fill in the blanks.
95 =100 +...............
6 + 14= 20 10 + 15= 25 9 + 11= 20 17 + 20= 37 15 + 5=20 18 + 22= 40 17 + 13=30 22 + 28=50
85 =100 +...............
97
+............... =100
10
20 2 + 9 + 8 + 1 = ...............
=
23 + 17 =
Find pairs that add up to 10 to help you answer these.
10
57 30 + 13
5 +20+ 5
50+
27
38
Calculate the following.
Make each pair of number cards add up to 10.
E
+
=
+
6 +20 + 7
10+
38
MENTAL STRATEGIES 1E 9
16
40 + 17 55
70 + 17 50+
=
29
Write the answers.
40+
9
40 + 14
42
29
+
54
37
6 4E
+
49
29
+ 20+
=
+
8 +20 + 9
20+
9 +20 + 9 60 + 18 = 78
9 +40 + 4 50 + 13 = 63 25
54
28
40+
10+
=
70 + 10
+
17
5 + 10 + 7
49
3 + 40+ 8
19
7 +20 + 5
57 60
26
25
+
55 30 + 12
48
70 + 11
+
20+
=
+
30+
Write in the missing numbers and find the answers.
+
25
6 + 10 + 9
30+
33
39
19
93
26 + 34=60 23 + 27= 50 32 + 48=80 15 + 55= 70
+............... =100
91
+............... =100
88
+............... =100
Treat each 9 as a 10 then take away the extra 1s at the end.
7 + 10 - 1 = 16 7 + 9 = .................................................................. 14 + 9 = .................................................................. 28 + 9 = .................................................................. 35 + 9 = ..................................................................
14+10-1=23 28+10-1=37 35+10-1=44
16 + 24= 40 48 + 52=100 29 + 38= 67 28 + 32= 60 27 + 33= 60 14 + 27= 41 46 + 24=70 32 + 28= 60 81 + 19= 100 35 + 15= 50 79 + 21=100 57 + 43= 100
SUBTRACTION
52
7 = 66
52 -
73 - 3 - 4 70 - 4 = 66
91
Write in the missing numbers and find the answers.
65
-
9 =
65 - 5 60 52
4 4 = 56
52 - 2 50 -
6 6 = 44
44 Maturing Mathematician
-
9 = 43
75
2-7 50 - 7 = 43 -
1
91 -
56
8 = 44
-
43 Write the answers.
Arithmetic is easier when the sum is broken down into smaller bits.
-
80
+............... =100
42
40
73
94
+............... =100
90 82
6 =
75 -
85
88 88 -
6 = 76
82 - 2 - 4 80 91 91 -
-
1
4 = 76 9 =
96 - 8 =
5-3 70 - 3 = 67
52 - 9 =
8
-
9
=
=
79
1 80 - 1 = 79 63 - 5 = 58 63 - 3 - 2 60 - 2 = 58
5 - 5 = 85
-
-
67
-
82
57
8 90 - 8 = 82
57 -
-
45
62
8
-
-
10
8
=
49
7- 1 50 - 1 = 49
75 - 6 =
88 43 69
68 54 35
74 - 6 = 61 - 7 = 44 - 9 =
Use a strategy to find the answers.
55
-
27
=
28
- 39
88 - 30 58 -
28
=
15
8
3- 5 20 - 5 = 15
23 -
5 - 2 30 - 2 = 28
88
-
43 -20 -
55 - 20 - 7 35 -
43
=
49
73
-
35
= 38
5 43 - 3 - 2 40- 2 = 38
73 - 30 -
9
8-1 50 - 1 = 49 46
Mahobe Resources (NZ) Ltd
............ Have an adult check your answer 3 4 ............
FRACTIONS
Fraction Man is here to introduce...
Shade in each of these shapes to show the
What fraction of each shape is shaded?
This square is divided into 4 parts with 1 part shaded. Therefore 41 is shaded.
3
3
4
5 ......................
10 ......................
3
4 ......................
9 ......................
Write the fraction that is shaded.
2 5 ............
1 3 ............
2 5
....................
2 3
1 2
....................
....................
3 4 1 5
1 2
2 4
....................
3 4
....................
5= 1 10 ......................2
5= 1 15...................... 3
5= 1 20 ......................4
1 4 ............
2 3 ............
16 = 4 20 5 ......................
2= 1 5 10......................
2
5 ......................
1 2
............ Circle each shape below that is half shaded.
....................
48
47
49
ESTIMATING NUMBERS
FRACTIONS Colour each fraction. Compare the two rectangles and fill in the missing sign with greater than (>), less than (<) or equals (=).
Shade the shape to show the fraction.
one half
Write what you think the number in each of the boxes would be.
5
0
two thirds
2 4 ...............
3 < ............... 8
1 4 ...............
1 > ............... 8
one quarter
3 4 ...............
one fifth
4 8 ...............
1 2 > ...............
1 2 ...............
=
36
30
10
40 60
68
80
210 240250
150
170
400
425 445 470 485 500
Mark on the number line below where you think the following numbers would be: 5, 12, 27, 33 and 39.
one tenth
10
0 2 3 ...............
five sixths
>
1 2 ...............
50
3 5 ...............
<
3 4 ...............
20
5 12
40
30
27 33 39 52
51
HALF WAY BETWEEN
DIVISIONS BETWEEN
MONEY EQUIVALENTS
Write in the numbers that are halfway between.
Write the missing numbers on each number line.
Different countries have different types of coins. Here are the most popular. Draw a line to show each equivalent value.
1 10 100 4 40 400 2 52 182
3 30 300 7 70 700 6 56 186
5
3
50
30
500
300
10
1
100
10
1000 100 10
2
60
92
190
332
6 60 600 4 40 400 4 94 334
53 Mahobe Resources (NZ) Ltd
50
100
9
0
90
0
900
0 10 20 30 40 50 60 70 80
7 70 700 6 96 336
0 0
10
20
4 8 12 16 12 24 36 48
30
C
C
$1
50 20 20 20
C
C
20
C
C
10
C
C 5 5 5
C
C
20 60
25
0 7 14 21 28 35 4249 56 63 70 0 0
25 50 75 15 30 45 60 75 54
63
100 90
50 50 20 10
one
10 20
50
5 5 5
10 10 5
55 Maturing Mathematician
MONEY EQUIVALENTS Draw a line to show each equivalent value of coins.
20
C
C
20
20 C 10 20
C
20 20 20 20
10 C
C
C
C
$1
C
C
5 10 5
10
50
10 5 20 5 50 20 25
5
50 one
56
ADDING MONEY 10 10 5 5 5
+
25
$1
$1
one
one
20
+
50
10
20
20 20 +
10
10 $1
$1
one
one
20
0.60 = ................................
50
2.80 = ................................
5 5 = ................................
1.40
+ 50
2050 57
3.40 = ................................ SUBTRACTING MONEY 20 10 5
0.15
-
20 = ................................ 20 5 25
10 10 10 10 55 5 5 1010 $1
$1
one
one
20
- 50
50 20
0.30 = ................................
50 10 - 50
20
10
$1 $1
$1
one
one
20
one
50
20 10
50
1.00 = ................................
5 5
0.50 = ................................ 20 20 10
0.20 = ................................
58
Maturing Mathematician
64
Mahobe Resources (NZ) Ltd
MightY Math MATURING MATHEMATICIAN for 7 - 9 year olds Book 1: Sailing Into Mathematics Builds an awareness of numbers and number relationships. It covers methods of multiplication, number patterns, ordinals and counting up to 1000, adding and subtracting strategies, fractions and money calculations. By the end of this book children will have more confidence when manipulating larger numbers.
Book 2: Sailing On With Mathematics Introduces more number sequences, arithmetic strategies, measurement and fractions. By the end of this book children will have gained confidence with arithmetic and will recognize the value of each digit that makes up a number.
Book 3: Sailing Away With Mathematics Reinforces all the work covered in the previous two Maturing Mathematician books. There are more arithmetic strategies, more fractions and more measurement. By the end of this book children will be confident in their ability to manipulate numbers.
The MIGHTY MATH series is a structured, easy-to-follow series of fun activities designed to stimulate and challenge.
Beginner Mathematician (for 4 - 6 year olds), look for the RED books. Developing Mathematician for (5 - 7 year olds), look for the YELLOW books. Advancing Mathematician for (6 - 8 year olds), look for the BLUE books. Maturing Mathematician for (7 - 9 year olds), look for the GREEN books.
MAHOBE Give your children a powerful head start at school. Make sure any Math book that you purchase has the Mighty Math logo and is published by: Mahobe Resources (NZ) Ltd.
Are you looking to give your child a powerful head start at school?
Introduce your child to mathematics with
Mighty Maths.
This is a structured, easy-to-follow series of fun activities designed to stimulate and challenge the advancing mathematician. This book covers: methods of multiplication C number patterns C ordinals and counting up to 1000 C adding and subtracting strategies C fractions C money calculations C By the end of this book children will have a better awareness of numbers and number relationships and more confidence when manipulating larger numbers. Choose Mighty Maths and observe a marked improvement in your child’s mathematical ability. Success and confidence in mathematics will lead to an increase in motivation and an enjoyment of learning.
Mighty Maths reinforces the mathematics that children are studying at school. Study habits begin at home, complement school work and have an enormous impact on future academic achievement.
Mighty Maths Maturing Mathematician for 7 - 9 year olds
BOOK 1
ISBN 1-877216-87-9
9 781877 216879
MAHOBE
