Sailing into Mathematics

MightY Math

for 7-9 year olds Maturing Mathematician BOOK 1

Sailing Into

Mathematics Kim Freeman

From the publisher - Mahobe Resources (NZ) Ltd We hope you enjoy these sample pages from the Mighty Math series. The actual eBook is 64 pages and can be purchased from our website www.mahobe.co.nz, from many other ebook websites or other book websites. It provides a structured, easy-to-follow series of fun activities to stimulate and challenge the maturing mathematician. The full book contains pages on methods of multiplication, number patterns, ordinals and counting up to 1000, adding and subtracting strategies, fractions and money calculations. Go hard, play fair and enjoy your mathematics!

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.co.nz © Mahobe Resources (NZ) Ltd. ISBN10: 1877216879 ISBN13: 9781877216879

MAHOBE

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

What is found in this book? In this book you look at: Methods of Multiplication, Addition and Subtraction.

5H 4 = 20 30 20

half of 4 = 2 add the zero

39

+

10

2 H 3 = 6 50

18

8 H 7 = 56

30+ 9 + 10 + 8 40 + 17

40

= 57 Money

Fractions

20

50

20 10

10 = $1 one

Maturing Mathematician

4

10 Mahobe Resources (NZ) Ltd

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

LEARNING THE 4s To multiply by 4 : Add the number 4 times. or Double the number, then double again.

4H 12 12 doubled is 24 24 doubled is 48 ˆ 4H 12 = 48

22 = ........................ 4H 3 = ........................ 4H

25 = ........................ 4H 7 = ........................ 4H

32 = ........................ 4H 9 = ........................ 4H

34 = ........................ 4H 13 = ........................ 4H

47 = ........................ 4H 15 = ........................ 4H

55 = ........................ 4H 18 = ........................ 4H Mahobe Resources (NZ) Ltd

9


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.

If the number is even, take half the number and put a zero after it.

5H 4 = 20 5H 16 = 80 half of 16 = 8 add the zero

half of 4 = 2 add the zero

2.

If the number is odd, subtract 1 from the number, halve it Then put a five after it.

5H 7 = 35 5H 13 = 65 7 - 1 = 6 half of 6 = 3


13 - 1 = 12 half of 12 = 6 add the 5

add the 5

10

Mahobe Resources (NZ) Ltd

Even Numbers

Odd Numbers

5H 6 = ........................ 5H 9 = ........................

5H 8 = ........................ 5H 11 = ........................

5H 14 = ........................ 5H 15 = ........................

5H 18 = ........................ 5H 17 = ........................

5H 20 = ........................ 5H 19 = ........................

5H 22 = ........................ 5H 21 = ........................

5H 26 = ........................ 5H 23 = ........................

5H 28 = ........................ 5H 25 = ........................

5H 30 = ........................ 5H 31 = ........................ Mahobe Resources (NZ) Ltd

11


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


13


Step FOUR: Multiply the folded fingers.

2 H 3 = 6

Step FIVE: Finally, add the two numbers together.

50 + 6 = 56

8 H 7 = 56

You have now found the answer.

7

H 9 40 20 30 50 60 10 3H 1=3 7


14

H 9 = 63 Mahobe Resources (NZ) Ltd

Use your finger calculator to multiply the following.

7H 7 = ...............

6H 8 = ...............

9H 9 = ...............

8H 7 = ...............

6H 10 = ............... Mahobe Resources (NZ) Ltd

15


Use your finger calculator to multiply the following.

7H 8 = ............... 7H 10 = ...............

9H 8 = ............... 9H 6 = ...............

8H 8 = ............... 8H 6 = ...............

9H 7 = ............... 6H 9 = ...............

9H 10 = ............... 6H 6 = ...............

7H 9 = ............... 8H 10 = ...............

6H 7 = ............... 8H 9 = ...............

7H 6 = ............... 9H 9 = ............... Maturing Mathematician

16


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 3 = 27 Mahobe Resources (NZ) Ltd

17


Fingers Multiplication by 9 Use the fingers method to calculate these 9 x multiplications.

9H 3=...............

9H 8=...............

9H 5=...............

9H 7=...............

9H 2=............... 9H 9=...............

9H 10=............... 9H 6=............... Maturing Mathematician

18


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?

9H 3=............... 9H 7=...............

9H 8=............... 9H 2=...............

9H 5=............... 9H 9=...............

9H 10=............... 9H 6=............... Mahobe Resources (NZ) Ltd

19


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


50

26

21

+

77

45 86


ARITHMETIC Use the diagrams to complete the sums.

16 + .......... = ............... 21 - .......... = 16 17 + .......... = ............... 25 - .......... = 17

......... + 5 = ............... .......... - .......... = 41 ......... + 16 = ............... .......... - .......... = ............... Maturing Mathematician

22


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


23

2.

3.

4.

5.

6.

7.


= 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


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


Write down the number that each picture represents.

.....................

.....................

.....................

.....................

..................... .....................

.....................

..................... Mahobe Resources (NZ) Ltd

27


PLACE VALUE Write the number of objects in each place-value table.


29

H

T

U

H

T

U

H

T

U

H

T

U


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


PLACE VALUE Write the number and the number word.

H

T

O

H

T

O

342 three hundred and forty two

H

T

H


T

O

O

31

H

T

O

H

T

O


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

35


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


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 + 14 = 44 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

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


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


FRACTIONS Shade the shape to show the fraction.

one half two thirds one quarter one fifth one tenth five sixths Maturing Mathematician

50


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 ...............


51


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


10

20

52

30

40


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


53


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


54


MONEY EQUIVALENTS Different countries have different types of coins. Here are the most popular. Draw a line to show each equivalent value.

$1

C C

50

one

20 20 20

10

C 20 20 C 10

25

50 50 20 10 Mahobe Resources (NZ) Ltd

C C 50

5 5 5 C C 5 5 5

C C 10 10 5 55


ADDING MONEY 10 10 5 5 5

+

25

$1

$1

one

one

20

+

50 20

10

20 20 +

10 $1

one

one


= ................................

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


20

5 5

= ................................ $1

$1

50 = ................................

50 10 - 50

20

20 10

one

50 58

20 20 10

= ................................ 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: C methods of multiplication C number patterns C ordinals and counting up to 1000 C adding and subtracting strategies C fractions C money calculations 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

Sailing into Mathematics

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