International Primary Maths Student's Book 5

59993_Book.indb i

28/07/2016 14:40

Contents Number 1 Whole numbers 1

1

2 Whole numbers 2

9

3 Decimals 1

13

4 Decimals 2

17

5 Fractions

21

6 Percentages

25

7 Ratio and proportion

29

8 Addition and subtraction 1

33

9 Addition and subtraction 2

37

10 Addition and subtraction 3

45

11 Multiplication and division 1

49

12 Multiplication and division 2

57

13 Multiplication and division 3

65

Geometry 14 2D shape, including symmetry

73

15 3D shape

77

16 Angles

81

17 Position and movement

85

59993_Book.indb iii

28/07/2016 14:40

Measure 18 Length

93

19 Mass

97

20 Capacity

101

21 Time

105

22 Area and perimeter

109

Handling data 23 Handling data

59993_Book.indb iv

113

28/07/2016 14:40

Unit

1

Lesson 1: Counting on and back (1)

Whole numbers 1

Key words

• step • sequence • count on • count back

• Count on and back in steps of equal size

Discover

Number

Workbook page 2

Counting forwards and backwards in steps helps you understand the pattern and sequence of number.

137

+

4

+

+

4

4

Learn You can use a number line to explore forwards and backwards counting sequences.

You can start at any point on the line and count on or back in whole numbers or decimals.

Count forward in 1s 0

1

2

3

4

5

6

7

8

Count backwards in 2s 9 10 11 12 13 14 15 16 17 18 19 20

Example Count back from 43 in steps of 3. Is 28 in this sequence?

22

25

28

31

34

37

40

43

Put your finger on 43 and count back in 3s: 43, 40, 37, 34, 31, 28, 25, 22....yes, 28 is part of this sequence.

1

59993_Book.indb 1

28/07/2016 14:40

Unit

1

Whole numbers 1

Workbook page 4

Lesson 2: Number sequences Number

• Describe number sequences and find the rule

Discover

Key words

• step • rule • sequence • value • term • common d ifference

The black keys on the piano are arranged in a sequence, 3, 2, 3, 2 … .

Learn A sequence is an ordered list of numbers called terms. Each term has a value.

Every sequence has a rule. Once you know the rule, you can work out the next term in the sequence.

A sequence is enclosed within curly brackets.

Use a comma to separate each term.

1st term

{ 2 , 4 , 6 , 8 , 10 , 12 , … } The three dots mean the sequence continues.

3rd term

2nd term

Example There are eight terms in this sequence.

2

9 +7

16 +7

23 +7

30 +7

37 +7

44 +7

51 +7

The values in the sequence are {2, 9, 16, 23, …} The rule is ‘add 7’.

2

59993_Book.indb 2

28/07/2016 14:40

Unit

Workbook page 6

Lesson 3: Place value (1)

1

Whole numbers 1

• place value • digit • hundred th ousands • ten thousa nds

• Know what each digit represents in a five- or six-digit number

Discover

Place value helps you understand the value of a digit in a number.

Number

Key words

21 409 g or 21 940 g

Learn The value of a digit depends on its place, or position, in the number.

Each place has a value of 10 times the place to its right.

Example

tens

units

× 10

hundreds

× 10

thousands

× 10

ten thousands

× 10

hundred thousands

Value of 3 digit: 300 000 (three hundred thousands)

× 10

3

0

7

4

8

2

Value of 0 digit: 0 (zero ten thousands)

Value of 7 digit: 7000 (seven thousands) 3

59993_Book.indb 3

28/07/2016 14:40

Unit

1

Whole numbers 1

Workbook page 8

Lesson 4: Place value (2)

Key words

Number

• place value • digit • partition

• Use place value to partition any number up to one million

Discover Knowing the value of each of the digits in a number is very important, because adding and subtracting often need you to exchange one value for another.

tens

units

tens

units

30

4

20

14

34 can be expressed as 2 tens (20) and 14 units.

Learn To exchange one value for another it is important to know how to split a number into thousands, hundreds, tens and units.

This 6-digit number has been partitioned into its separate place values.

634 129 = 600 000 + 30 000 + 4000 + 100 + 20 + 9

Example Arrow cards can be used to show how numbers can be split into separate place values, then recombined.

438 129 = 400 000 + 30 000 + 8000 + 100 + 20 + 9 4 0 3 0 8 1 0 0 2 0 9

4 0 0 0 0 0 3 0 0 0 0 1 0 0

8 0 0 0 2 0

9

4

59993_Book.indb 4

28/07/2016 14:41

Unit

1

Lesson 5: Multiplying and dividing by 10 or 100

Whole numbers 1

Key words

• place value • multiply • divide

• Multiply and divide whole numbers by 10 or 100

Discover

Number

Workbook page 10

Multiplying and dividing by 10 or 100 can help you to convert metric measurements and find percentages.

×10

×100

mm

cm

÷10

m

÷100

Learn Multiply by 10: Move all digits one place value to the left.

Multiply by 100: Move all digits two place values to the left.

Example HTh TTh

2

2 5

Divide by 10: Divide by 100:

Th 2 5 3

H 5 3 8

T 3 8 0

U 8 0 0

× 10 × 100

Move all digits one place value to the right.

Move all digits two place values to the right.

Example HTh TTh

Th 7

H 5 7

T 0 5 7

U 0 0 5

÷ 10 ÷ 100 5

59993_Book.indb 5

28/07/2016 14:41

Unit

1

Whole numbers 1

Workbook page 12

Lesson 6: Rounding

Key words

Number

• round • rounding d igit • nearest 10 • nearest 10 0 • nearest 10 00

• Round 4-digit numbers to the nearest 10, 100 or 1000

Discover The exact number of fans at a football match was 56 327, but the newspaper says there were 56 330.

They have rounded the number to the nearest 10.

Match Report

Attendance: 56 330

Learn

To round If the digit is: a number, • 5 or greater, round up look at the digit to the right of the place • less than 5, the whole number position you are remains the same. rounding to.

Include place holder zeros as needed.

Example Round 3862 to the nearest hundred.

3862 is between 3800 and 3900.

3862 3800

3900

Look at the number to right of the 8, which is 6.

6 is greater than 5, so round up to 3900.

Replace the rest of the digits with placeholder zeros.

6

59993_Book.indb 6

28/07/2016 14:41

Unit

Workbook page 14

1

Whole numbers 1

Lesson 7: Comparing and ordering • Use the > and < signs to order and compare numbers up to a million

Discover Place value can help you to put large numbers in order.

The diameter of Earth, Uranus and Neptune can be put in order by looking at the ten thousands place.

Number

Key words

• place value • digit • thousands • hundreds • tens • units

Earth 12 756 km < Neptune 49 528 km < Uranus 51 118 km.

Venus Mercury

Mars Earth

Uranus Jupiter

Neptune

Saturn

Learn

We can compare whole numbers with the same number of digits.

• Compare digits in each place position, starting on the left.

• If the left-most digit is the same, compare digits in the next place to right.

• When two numbers have different digits in the same place, the number containing the larger digit is the larger number.

Example HTh TTh

4 3 4

Th

H

T

U

5 7 7

1 8 3

3 9 5

7 8 2

47 352 > 45 137 > 37 898

37 898 is the smallest number; then comparing the next digit (thousand place) 47 352 is the larger number.

7

59993_Book.indb 7

28/07/2016 14:41

Unit

1

Whole numbers 1

Workbook page 16

Lesson 8: Odds, evens and multiples (1) Number

• Recognise odd and even numbers and multiples of 5, 10, 25, 50 and 100

Discover

Key words

• odd • even • multiple

The door numbers on the blue doors are multiples of 25 but not 50.

125

175

150

110

Learn Numbers with 00, 25, 50 or 75 in the tens and units positions are multiples of 25.

Numbers with 00 or 50 in the tens and units positions are multiples of 50.

Numbers which end in 1, 3, 5, 7 or 9 are odd numbers.

50

25 00

multiples of 25

50

00

multiples of 50

75

Example Which of the following numbers are multiples of 25 but not 50: 200, 650, 2275, 4300, 6625?

Multiples of both 25 and 50 have 00 or 50 in the tens and unit positions.

Multiples of 50 but not 25 have 25 or 75 in the tens and unit positions.

So, only 2275 and 6625 are multiples of 25 but not 50.

8

59993_Book.indb 8

28/07/2016 14:41

2

Unit

Workbook page 18

Lesson 1: Whole numbers

°C

We use negative numbers to describe a value on a scale that goes below zero.

The temperature on this thermometer reads −5 °C.

• negative n umber • positive nu mber • step • sequence • count on • count back

Number

Key words

• Describe and continue number sequences, including negative numbers

Discover

Whole numbers 2

30

20

10

0

–5°C –10

How do temperature and money both use negative numbers?

Learn Positive numbers are greater than zero.

Negative numbers are less than zero.

–10

–6

–2

0

2

6

10

Count back from 10 in steps of 4. Is −4 in this sequence?

Place your finger on 10 and count back in 4s to check.

9

59993_Book.indb 9

28/07/2016 14:41

2

Unit

Whole numbers 2

Workbook page 20

Number

Lesson 2: Positive and negative numbers

Key words

• negative n umber • positive nu mber • order • thermomete r • temperature • degrees Ce lsius (°C)

• Order and compare negative and positive numbers on a number line and temperature scale

Discover In golf, the player with the lowest score wins.

Sometimes it can be a negative score.

Position Name Score 1st Jason –5 Day 2nd Jordan –3 Spieth 3rd Rory –1 McIlroy 2 4th Bubba Watson 4 5th Louis Oothuizen

Learn Writing numbers on a number line makes it easier to order positive and negative numbers.

Numbers on the left are smaller than numbers on the right.

Numbers on the right are greater than numbers on the left.

Example –14

–3

–15 –14 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1

2 0

1

2

8 3

4

5

6

7

8

9

10

Placing numbers on the number line shows that: −14 < −3 < 2 < 8 10

59993_Book.indb 10

28/07/2016 14:41