Nelson International Mathematics Workbook 6

Name:

2nd edition

Division rules

24

Writing numerals

5

Measuring instruments

25

Revising place value

6

Changing from one unit to another

26

Comparing and ordering numbers

7

Revising fractions

27

Rounding numbers

8

Numbers below 0

9

Mixed numbers and improper fractions

28

Working with calendars

10

Revising time

11

Properties of 3D shapes

12

3D shapes and their nets

13

Making equivalent fractions 29 Compare and order fractions

30

Compare and order mixed numbers

31

Place value to thousandths 32

Investigate the nets of open boxes

14

15

16

Subtracting whole numbers 17 More subtraction

18

Multiplication facts

19

More multiplication facts

20

Multiply by 10, 100 and 1000

21

Division facts

22

Dividing whole numbers

23

Rounding decimals

33

Sorting data

34

Grouped data

35

Graphs from tables

36

Line graphs

37

More line graphs

38

Unusual graphs

39

More unusual graphs

40

Multiply and divide decimals by 10 and 100

41

More operations with 10 and 100

42

43

Halving decimals

44

Dealing with discounts

46

Perimeter

47

More perimeter

48

Factors

49

Prime numbers

50

Multiplication by multiples of 10 51 Multiplying pairs of multiples of 10 and 100

52

61

Checking your calculations 62 Increase in prices

63

Revising coordinates

64

Extending the grid

65

Matching shapes

66

Timed division

67

Division â&#x20AC;&#x201C; rounding the remainder

68

Ratio

69

Proportion

70

Investigating multiplication 71 Making sense of bar graphs 72

Calculating the size of angles

53

More missing angles

54

Angles in a triangle

55

Calculating angles in triangles

56

Angles of rotation

57

Percentages

58

Percentages, fractions and decimals

59

More percentages of amounts

60

Making sense of line graphs 73 Shape patterns

74

Number machines

75

Number patterns

76

Area of combined shapes

77

Estimating area on a grid

78

Dividing decimal amounts

79

This is a chimpu. Write a few sentences explaining how it is used to record a number.

4 strings = 4 digits

______________________________________________ Studentâ&#x20AC;&#x2122;s own answers. However, they should mention ______________________________________________ that the chimpu works using place value, with one

4 thousands 2 hundreds 7 units

8 tens

4287

________________________________________________________________________________ the units and the next string, for hundreds the beads are threaded onto the units, tens and ________________________________________________________________________________ hundreds strings. In other words, the number of strings indicates which place you are dealing with.

2

Write the number represented on each chimpu.

2242 ___________ 3

2331 ___________

4302 ___________

2059 ___________

Draw your own chimpu to show how each number would be represented.

Own work

2008 4

4079

1489 + 2167

52 614

Writing numerals 1

The table shows how the numerals we use today have changed over time.

Today 600 years ago 1000 years ago 1200 years ago 2300 years ago a Write these numbers as they would appear today.

4007 ___________

3587 ___________

8534 ___________

34 009 ___________

b If you lived 1200 years ago, how would you have written these numbers?

2

123

809

1267

8952

91 207

___________

___________

___________

___________

___________

There is a theory that our numerals developed according to the number of angles they contain. Look at the examples and complete the table.

No angle

1 angle

3 angles

Students to discuss and then draw their own ideas

7 angles

5

Revising place value 1

Write these numbers in figures on the place value chart:

a three hundred and twelve b nine thousand, three hundred and seventeen c ninety-nine thousand, four hundred and forty-six d four-hundred-and-five thousand, three hundred and fifty-two e nine-hundred thousand and eight f forty thousand, three hundred and four g seventy-six thousand and thirty-five h five-hundred and seventy-two thousand, three hundred and ninety-seven i

three-hundred thousand, nine hundred and sixteen

j

nine-hundred and ninety-nine thousand, nine hundred and ninety-nine. Hundred thousands

Ten thousands

Thousands

Hundreds

Tens

Units

3

1

2

9

3

1

7

9

9

4

4

6

0 0

5 0

3 0

5 0

2 8

f

4

0

3

0

4

g

6 2

0 3

3 9

5 7

a b c d e

4 9

h

5

7 7

i

3

0

0

9

1

6

j

9

9

9

9

9

9

2

Work with a partner. Say each number out loud.

3

If you add 1 to the last number you get 1 000 000.

a Do you know what this number is?

one million

Studentsâ&#x20AC;&#x2122; verbal activity Millions 1

b How could you show this number on a place value chart? 6

Hundred Ten Thousands Hundreds thousands thousands 0 0 0 0

Tens

Units

0

0

see Student Book page 5

Comparing and ordering numbers 10 000

1

Estimate where each of the following numbers will fit onto the number line. Make a mark to show where you think the number lies and write the number next to your mark.

a 1750

b 7512

c 1925

d 4306

e 7861

f 3295

g 1682

h 3750

i

9999

j

9300

k 8200

l

7099

2

Write in digits, the number that is:

a 1000 more than 3451 ___________ 4451 b 1000 less than 3451 ___________ 2451 c 5000 more than 4500 ___________ 9500 d 8000 less than 10 000 ___________ 2000

3

What is the biggest number you can write and say? Write it here in digits and read it aloud to your partner.

Studentsâ&#x20AC;&#x2122; own work

0

Studentsâ&#x20AC;&#x2122; own work, Allow them to check each otherâ&#x20AC;&#x2122;s number lines and to discuss whether or not their estimates are reasonable. see Student Book page 6 7

Rounding numbers 1

Complete the table by rounding each number to the value shown. Number

To the nearest 10

To the nearest 100

To the nearest 1000

4770 3460

4800 3500

5000 3000

7654

8880 7650

8900 7700

9000 8000

3211

3210

3200

3000

9876 12 987

9880 12 990

9900 13 000

10 000 13 000

14 897

14 900

14 900

15 000

19 811

19 810

19 800

20 000

122 456 342 183

122 460 342 180

122 500 342 200

122 000 342 000

665 581

665 580

665 600

666 000

316 479

316 480

316 500

316 000

1 223 720 3 213 990

1 223 700 3 214 000

1 224 000 3 214 000

4765 3456 8876

1 223 718 3 213 987

2

Numbers are often rounded. How would you round these numbers:

a 2 846 123 population

___________________________ 3 million

b \$12 643 071 in debt

___________________________ \$12.5 million

c \$19.99 for a CD

___________________________ \$100

d 123 407 attend a cricket match.

___________________________ 125 000

see Student Book page 7 8

Numbers below 0 1

Fill in each number in the correct place on the number lines. The divisions are in units of one, see Student Book page 9 for a reminder.

-5

-7

e –5, –4, –3, –2, –1

2

-1

0

0

-2 -1

0

-2

0

-4

-6 -5

-3

-1

2

4

2

4 5

0

-5 -4 -3 -2 -1

-7 -6

5 6

3

0

0

-2

-5

f 7, 5, 3, –2, 1, –1, –5

h –3, –5, 6, –1, 4, –6, 7

-3

-5 -4

d –4, –2, 4, 2, 5, –5

g 2, 4, 6, 7, –2, –4, –6, –7

-3 -2

-6

b 2, 4, –3, –6, –2 c –1, –3, –5, –7

-2 -1

-6

a 3, –2, 5, 6, –6, –1

0

Draw and label arrows on the thermometer to show the following temperatures:

1

5

3 2

4

6 7

4

6 7

°C 50

a 12 °C

40

b –4 °C

30 20

e 7 degrees above –2 °C

19°C 12°C 5°C -4°C

f 9 degrees below –12 °C.

-21°C

–20

c 15 degrees warmer than 4 °C d 6 degrees colder than –1 °C

7

10 0 –10

-7°C

–30

see Student Book page 9 9

Working with calendars You will need a calendar for this year to complete these activities.

1

How many years have passed since this day in the year 2000? ______________________________________________________________________

2

On what date do the following fall this year:

a the last day of January

______________

b the third Tuesday in March

______________

c the start of the school year

______________

d the last Friday in August

______________

e the first day of Spring?

______________

3

Look at the month of October.

In this section, all the answers will depend on the current year. In 2013, for example, the answer is 2013â&#x2C6;&#x2019;2000 = 13 years. Make sure the students have a calendar available to them and check the answers with the students

a On what day does the month begin?

______________

b How many Fridays are there in October this year?

______________

c How many weeks and days are there in October?

______________

4

How many weeks and days have passed since:

a the beginning of the year

______________

______________

c the first day of school?

______________

5

What will the day and date be:

a five days from now

______________

b three weeks from today

______________

c in twelve weeksâ&#x20AC;&#x2122; time?

______________

6

How long is it until the end of the year? Write this in:

a months and weeks

______________

b weeks and days

______________

c days.

______________

7

Write down three important holidays in your country. Then write the day and date on which these holidays will fall this year. ______________________________________________________________________ ______________________________________________________________________ see Student Book page 12

10

Revising time 1

Complete the following:

a 1 hour = ________________ minutes 60 b 2 minutes = ________________ seconds 120 minutes c 240 seconds = ________________ 4 d

1 – 2

minute = ________________ seconds 30

e

1 – 4

hour = ________________ minutes 15

f 48 hours = ________________ days 2

2

a

e

3

Here are some 24-hour times. Draw the hands on the clocks to show how these times would appear on an analogue clock. Write a.m. or p.m. next to each clock. 11 12 1 10 2 9 3 4 8 7 6 5

11 12 1 10 2 9 3 4 8 7 6 5

b

a.m.

f

p.m.

11 12 1 10 2 9 3 4 8 7 6 5

11 12 1 10 2 9 3 4 8 7 6 5

c

a.m.

g

p.m.

11 12 1 10 2 9 3 4 8 7 6 5

11 12 1 10 2 9 3 4 8 7 6 5

d

a.m.

11 12 1 10 2 9 3 4 8 7 6 5

a.m.

h

p.m.

11 12 1 10 2 9 3 4 8 7 6 5

p.m.

What time is it right now? Write it as a digital 24-hour time and an a.m. or p.m. time. ________________________ Student’s own work

________________________

see Student Book page 13 11

Properties of 3D shapes 1

Write the name of each 3D shape below it. The correct names are given in the table below if you get stuck.

a

b

c

__________ cone

__________ cylinder

__________

__________

f

2

d

__________ square-based __________ pyramid

g

e

__________ cuboid

__________ sphere

__________

__________

h

i

__________ triangular

__________ triangular

__________ hexagonal

__________ cube

__________ prism

__________ pyramid

__________ prism

__________

Complete this table to summarise the properties of these solids. Shape

Number of faces

Number of vertices

Number of edges

Cube Cuboid

6 6

8 8

12 12

Cone

2

1

1

Cylinder

3

0

2

Sphere

1

0

0

Triangular pyramid

4 5

4 5

6 8

5 8

6 12

9 18

Square-based pyramid Triangular prism Hexagonal prism

see Student Book page 17 12

3D shapes and their nets Simon built the 3D shapes in the right-hand column using the flat shapes shown in the left-hand column.

1

Draw lines to match each set of flat shapes to the correct 3D shape. Flat shapes Base

Other faces

Base

Other faces

3D shapes

a

b

Base

Other faces

c

Base

Other faces

d

Base

Other faces

e

Base

Other faces

f

see Student Book page 18 13

Investigate the nets of open boxes Zorina wants to make a set of boxes with five square faces like this one to store her button collection.

This is an investigation. Allow the students to cut out and fold up the nets using grid paper if they struggle. Remind them that any net with four blocks arranged like a square (as in the second diagram) cannot be folded up. Colour all the possible nets that she could use.

The 12 shapes above can be fitted together to fill this grid exactly. Draw the shapes to show how this can be done.

see Student Book page 19 14

Fill in the numbers 1 to 6 in the circles so that each side of the triangle adds up to the number in the centre.

a

2

1 1

6

c

6

4

10

3

2

b

5

2

12

5

6 1

4

3

3

11

4

2

5

Fill in the numbers 1 to 9 in the circles so that each side of the triangle adds up to the number in the centre.

a

b

1 9 4 3

7

1

6

3 8

17

5

7 2

c

9

7

6 8

20

4

6

2

1 5

9

3 5

23

4

2

8

alternatives possible 3

In these grids, each column, row and diagonal adds to the same total. The total is given above each grid. Fill in the missing numbers to complete the squares.

a

b 36

c 66

d 36

87

18

4

14

28

14

24

14

3

19

32

20 35

8

12

16

18

22 26

17

12

7

33

29

25

10 20

6

20

30

5

21

10

22 38

27

16

see Student Book page 20 15

The sum of two numbers is shown on a number line. Find the missing number in each pair.

a 201 +

500

349 525

223 +

b

87 +

160 550

600

625

377

191 +

550

103

650

600

675

700

459

650

+ 497

725

516

109 +

463

500

2

575

589

+ 415

425 +

700

750

372

800

+ 328

+ 111

750

775

97 +

703

800

325 850 214 +

900

686

Find the sum of:

199 b 232 + 153 385 c 315 + 1002 1317 d 487 + 82 569 e 659 + 194 853 f 215 + 870 1085 g 955 + 144 1099 h 389 + 1041 1430 a 52 + 147

3

Find the missing values in these sums.

1

5 0 2 7 0+ 4 2 0

3 9 3 6 5 6 1 0 +

9 5 4 6

5 0 4 6 4 7+ 1 1 5 1 see Student Book page 21

16

Subtracting whole numbers 1

Subtract:

17

c 451 – 442 9 d 657 – 428 229 31 e 251 – 139 1 1 2 f 625 – 473 152 g 856 – 296 560 h 4035 – 3999 36 i 6000 – 3999 2001 j 1248 – 249 999

a 35 – 18

b 325 – 294

50 - 25 = 25

2

Subtract 25 from the difference between 90 and 40.

3

What is the difference in value between 12 ten-cent coins and 12 five-cent coins? 12 # 10 = 120; 12 # 5 = 60; Difference = 60 cents

4

Nick buys a car for \$2350 then resells it for \$1800. How much less is that? \$550

5

Approximately how many hundred dollar bills would you need to buy items costing \$249, \$87 and \$515?

6

8 or 9

You are given the number sentence 773 + 583 = 1356. Use these numbers to complete these two different subtractions. =

1356 - 583 = 773

=

1356 - 773 = 583

Make up subtractions to give each of the following answers. You may need to work out the missing values on the number line before you start. Students’ own values

621 –

1000 –

7 52

7 51

7 50

7

2

49

49

2

48

7

47

7 46

7

2

45

7

45

44

2

44

7

41

2

41

7

see Student Book page 23 17

More subtraction 1

Job used the additions on the right to check the answers to his subtraction homework. Draw a line to match each addition to a subtraction.

Allow students to discuss the strategies.

Check: 850 – 200 = 821 – 177 = 673 – 147 =

644 + 177

902 – 300 = 1000 – 778 = 748 – 549 = 643 – 230 =

526 + 147 222 + 778

230 + 199 2

650 + 200 = 850 413 + 230 = 643 602 + 300 = 902 = 600 + 100 + 40 + 70+ 7 + 4 = 700 + 110 + 11 = 810 + 11 = 821 = 600 + 60 + 13 = 673 = 900 + 90 + 10 = 900 + 100 = 1000 = 230 + 200 - 1 = 430 - 1 = 429

Look at the addition sums again. What strategies did Job use to work out each answer?

see Student Book page 24 18

Multiplication facts Can you complete each column in one minute? Write the answers only. One-week multiplication and division facts revision Day 1

Day 2

Day 3

Day 4

5 × 6 = 30

10 × 5 = 50

60 ÷ 10 = 6

12 ÷ 12 =

63 ÷ 7 = 9

36 ÷ 9 =

3 × 6 = 18

9×6=

32 ÷ 4 = 8

54 ÷ 6 =

8×2 =

16

4×2 =

15 ÷ 3 =

5

49 ÷ 7 =

7

30 ÷ 3 =

10

6 × 6 = 36

4×4 =

16

8×7 =

56

6

12 ÷ 4 =

3

8 × 9 = 72

3×9 =

27

6×3=

30 ÷ 5 =

6

6×7 =

9×7 =

63

64 ÷ 8 =

36 ÷ 4 =

9

9×9 =

81

42 ÷ 7 =

72 ÷ 6 =

12

8x3=

54 9 8

2×8=

16 9

63 ÷ 7 =

6 × 7 = 42

5

40 ÷ 8 =

40

10 × 11 =

110

10 × 9 = 90

8×5=

12 × 12 = 144 54 ÷ 9 =

6

2 × 8 = 16

9 × 6 = 54

3 × 9 = 27

18

56 ÷ 8 = 7

4 × 8 = 32

42

72 ÷ 8 = 9

3 × 8 = 24

6 × 5 = 30

8

6 × 5 = 30

6 × 8 = 48

12 × 8 = 96

50 ÷ 5 = 10

81 ÷ 9 =

10 × 10 = 100 40 ÷ 5 = 8

24

6×9 =

54

4×6 =

64

9×6=

54

27 ÷ 3 =

7 4 × 8 = 32

18 ÷ 3 =

6

10 ÷ 2 =

9

7×4 =

28

7×7 =

45 ÷ 9 =

5

6×8=

9

42 ÷ 7 =

63 40 ÷ 4 = 10

7×9 =

40 ÷ 10 =

48

48 ÷ 6 = 8

24

6

6 × 9 = 54

10 × 10 =

8 × 5 = 40

8

5 × 9 = 45

9 × 8 = 72

40 ÷ 5 =

64 ÷ 8 =

42 ÷ 6 =

81 ÷ 9 =

8

28 ÷ 7 = 4

7 × 5 = 35

5 9 × 8 = 72

4 × 9 = 36

7 × 6 = 42

1

9

36 ÷ 6 = 8x8 =

4

Day 5

4

6

90 ÷ 10 = 9÷9 =1 9 x 11 =

99 4

49

4 × 9 = 36

32 ÷ 8 =

5

56 ÷ 7 = 8

5 × 7 = 35

24 ÷ 8 = 3

100 7 × 8 = 56

9 × 4 = 36

144 ÷ 12 =

25 ÷ 5 =

9

12 3 × 12 = 36

see Student Book page 25 19

More multiplication facts 1

Complete these multiplication targets as quickly as you can. Swap with a partner and check each other’s answers.

a

44

9

36

×11

5

2

1 10

d

84

4

1

68

85

45

8

10

170

136

18

17

×18 36

1

153

126

4

72

64

36

171

114

133

190

38

7 2

×19 36

9 10

108

144

32

6

128

9 2

96

19

6

180

8

1 2

10

×16 36 6

5

7

9 1

90

48

7 3

10

i

3

8

1 12

4

135

54

16 1

9

162 9

160

120

1 17

26

80

104

9 2

5

2

30

8

130

f

8

150

144

10

39

60

×15 36

×13 36

3

5

65

7 5

4

4

10

3

2

34

51

×17 36

75

7

h

5

7

15 1

52

84 72

120

3

28

126

6

105

2 9

14

4

1 12

1

6 10

12

90

78 6

7

6 8

5

102

108

98

×14 36

1 19

1

7

10

36

×12

91

13

2

5

e

6

24

8

9

33

42 3

60

66

3 7

77

56

g

3 4

6

22

70

48

c

96

36

8

10

140

88

1

4

55

b

11

99

4

76

8

152

3 5

57

95

see Student Book page 26 20

Multiply by 10, 100 and 1000 1

Complete the table. Time yourself to see how quickly you can do all these multiplications. ×10

×100

×1000

9

90

900

9000

17

170

1700

17 000

28

280

2800

28 000

39

390

3900

39 000

66

660

6600

66 000

89

890

8900

89 000

101

1010

10 100

101 000

145

1450

14 500

145 000

865

8650

86 500

865 000

435

4350

43 500

435 000

234

2340

23 400

234 000

1234

12 340

123 400

1 234 000

4076

40 760

407 600

4 076 000

5999

59 990

599 900

5 999 000

9800

98 000

980 000

9 800 000

Mark: It took me ________________ to complete the table.

2

Swap with a partner. Check each other’s answers. Write a mark out of 15 at the bottom of each column.

Students’ own work see Student Book page 27 21

Division facts Can you complete each column in four minutes? Write the answers only. One-week division with remainders revision Day 1

Day 2

Day 3

Day 4

Day 5

60 ÷ 7 = 8 r4

35 ÷ 3 = 1 1 r2

48 ÷ 5 = 9 r3

19 ÷ 2 = 9 r1

11 ÷ 3 = 3 r2

54 ÷ 5 = 10 r4

35 ÷ 2 = 17 r1

19 ÷ 5 = 3 r4

27 ÷ 4 = 6 r3

11 ÷ 7 = 1 r4

36 ÷ 10 = 3 r6

35 ÷ 4 = 8 r3

23 ÷ 6 = 3 r5

27 ÷ 5 = 5 r2

11 ÷ 4 = 2 r3

73 ÷ 8 = 9 r1

35 ÷ 6 = 5 r5

33 ÷ 6 = 5 r3

37 ÷ 5 = 7 r2

11 ÷ 6 = 1 r5

46 ÷ 5 = 9 r1

35 ÷ 8 = 4 r3

23 ÷ 7 = 3 r2

27 ÷ 4 = 6 r3

23 ÷ 3 = 7 r2

41 ÷ 4 = 10 r1

35 ÷ 9 =3 r8

33 ÷ 7 = 4 r5

37 ÷ 7 = 5 r2

29 ÷ 3 =

50 ÷ 6 = 8 r2

60 ÷ 9 = 6 r6

43 ÷ 8 = 5 r3

27 ÷ 6 = 4 r3

29 ÷ 5 = 5 r4

50 ÷ 7 = 7 r1

40 ÷ 6 = 6 r4

53 ÷ 8 = 6 r5

37 ÷ 8 = 4 r5

29 ÷ 8 = 3 r5

33 ÷ 2 = 16 r1

40 ÷ 7 = 5 r5

43 ÷ 9 = 4 r7

47 ÷ 8 = 5 r7

29 ÷ 7 = 4 r1

19 ÷ 4 = 4 r3

50 ÷ 7 = 7 r1

53 ÷ 9 = 5 r8

47 ÷ 5 = 9 r2

29 ÷ 9 = 3 r2

37 ÷ 5 = 7 r2

13 ÷ 6 = 2 r1

43 ÷ 10 = 4 r3

47 ÷ 10 =

49 ÷ 3 = 16 r1

13 ÷ 8 = 1 r5

53 ÷ 10 = 5 r3

47 ÷ 3 = 15 r2

14 ÷ 3 =

49 ÷ 6 = 8 r1

13 ÷ 5 = 2 r3

80 ÷ 9 = 8 r8

19 ÷ 3 = 6 r1

17 ÷ 2 = 8 r1

50 ÷ 7 = 7 r1

13 ÷ 10 =

14 ÷ 9 = 9 r5

29 ÷ 2 = 14 r1

23 ÷ 2 =

17 ÷ 2 = 8 r1

23 ÷ 10 = 2 r3

35 ÷ 8 = 4 r3

17 ÷ 4 = 4 r1

23 ÷ 4 = 5 r3

88 ÷ 10 =

1 r3

8 r8 99 ÷ 10 = 9 r9 25 ÷ 8 = 3 r1 4 r1

9 r2

4 r7 29 ÷ 10 = 2 r9 4 r2 1 1 r1

70 ÷ 8 = 8 r4

9÷2=

80 ÷ 9 = 8 r8

15 ÷ 4 = 3 r3

25 ÷ 7 = 3 r4

17 ÷ 6 = 2 r5

23 ÷ 6 = 3 r5

42 ÷ 5 = 8 r2

26 ÷ 3 = 8 r2

35 ÷ 7 = 5

27 ÷ 6 = 4 r3

19 ÷ 7 = 2 r5

43 ÷ 6 = 7 r1

26 ÷ 5 = 5 r1

25 ÷ 6 = 4 r1

27 ÷ 8 = 3 r3

31 ÷ 7 = 4 r3

39 ÷ 4 = 9 r3

26 ÷ 6 = 4 r2

35 ÷ 6 = 5 r5

11 ÷ 2 = 5 r1

31 ÷ 9 = 3 r4

see Student Book page 30 22

Dividing whole numbers 1

÷2 764

945

95 21

191

382

÷3

÷2

÷3

315

÷3

35

105

Answers will vary as students may round different numbers 2 Complete the table. Do any working you need to do on and do different working. scrap paper. Actual answers are: Calculation 348 ÷ 7

Estimate by rounding

Own work

343 r5

288 ÷ 9

32

256 ÷ 8

32

785 ÷ 5

157

976 ÷ 8

122

245 ÷ 7

35

810 ÷ 9

90

102 ÷ 3

34

888 ÷ 2

444

954 ÷ 3

318

Check using inverse operation

see Student Book page 30 23

Division rules 1

Do the divisions. Write the answers in the blocks.

2

Colour blocks with the same answers to match, join them with lines and find a path to the stars. Colour the stars to match the colours.

Red

Green

Blue

Yellow

Brown

Orange

Purple

500 ÷ 4

68 ÷ 2

256 ÷ 8

220 ÷ 10

125

34

32

122

288 ÷ 9

244 ÷ 2

488 ÷ 4

272 ÷ 8

32

122

122

34

156 ÷ 4

260 ÷ 20

105 ÷ 3

250 ÷ 2

39

130

35

125

650 ÷ 5

140 ÷ 4

117 ÷ 3

195 ÷ 5

130

35

39

39

102 ÷ 3

375 ÷ 3

390 ÷ 3

245 ÷ 7

34

125

130

35

976 ÷ 8

96 ÷ 3

625 ÷ 5

910 ÷ 7

122

32

125

130

210 ÷ 6

78 ÷ 2

170 ÷ 5

224 ÷ 7

35

39

34

32

see Student Book page 32 24

Measuring instruments 1

Write the measurement shown on each instrument. Include the correct units of measurement.

1 cm 2

3

4

5

6

7

97 cm 98

4.5 cm or 45 mm ____________________

99

1m

0 70

kg

35 °C 10 30 °C

kg 1

2

1 m____________________ and 0.5 cm or 100.5 cm

0

3

1

60

20 50

25 °C

30

20 °C

2

40

____________________ 2.4 kg

____________________ 62 kg

15 °C 10 °C

1

2 Litre

0

10

12

13 °C 5 °C

3

_________________ 14 °C

4

____________________ 2.4 l

2

11

____________________ 12.5 °C

Shade each measuring jug to show where the level would be if you added 150 ml to each one. Write the amount of liquid in each jug below it in ml and in litres. 1000 ml 900 800 700 600 500 400 300 200 100 0

570 ml __________ 0.57 l __________

1000 ml 900 800 700 600 500 400 300 200 100 0

500 ml __________ 0.5 l __________

see Student Book page 34 25

Changing from one unit to another Complete the tables to show equal measurements with different units.

8000

Grams

4000

Kilograms

4

8

Metres

1500

3050

1.5

Kilometres Kilometres

4

3.05 7.5

12 500

9500

9.5

12.5

4750

9460

125 000

6500

6.5

125

10 500

13 250

13.25

4.75

9.46

10.5

12.75

88.69

90.09

120.50

Metres

4000

7500

12 750

88 690 90 090 120 500

Millilitres

3500

5540

12 760

34 090 49 909

Litres

3.5 km

5.54

12.76

m

34.09

49.909

cm

1

100

1000

0.004

4

400

4000

0.05

50

5000

50 000

0.05

50

5000

50 000 cl

l

83.149

mm

0.001

kl

83 149

ml

1

1000

1 000 000

10 000 000

0.002

2

200

2000

0.0004

0.4

40

400

0.0005

0.5

50

500 see Student Book page 36

26

Revising fractions 1

Shade each shape to show the given fraction.

a

b

c

3 – 8

2 – 3

1 – 8

d

e

5 –– 12

f

9 –– 10

g

h

7 –– 8

2

3 –– 4

7 –– 10

Shade the given fraction of each group.

a

b

c 1 – 3

1 – 4

1 – 5

d 1 – 3

e

f

1 – 5 1 – 6

see Student Book page 41 27

Mixed numbers and improper fractions 1

Sort the fractions in the box into the correct columns of the table. 5 – 6

7 –8

7

2 –4

17 –– 5

–2

9 — 12

–3

18 — 10

8— 12

4 –9

–8

–7

1 —

3 –5

11 –– 5

15 –– 3

11 — 12 9 – 4

1

5

7

8

2

25

Proper fractions

3

— 9 10

3

5

Mixed numbers

2

Improper fractions 15 3 18 10 8 7 17 5 9 4 11 5 3 2

1 21 8 121 9 103 4 95 7 78 2 34 3 52

1 3 5 6 11 12 7 8 2 5 9 12

2

1

1–2

1 – 3

Write each fraction in the correct place on the number line.

a

0

1 – 2

7

1 2

1

b 1–8

c 2 –4

1

1

d

7 8

14 –– 8

2

1 68

1

e 3 –8

3

2 41

3

Use dots to mark four more fractions on the number line. Students’ own work

4

Swap with a partner and write each marked fraction as a mixed number and as an improper fraction.

4

3 81

Students’ own work

see Student Book page 42 28

Making equivalent fractions 1

Colour each fraction a different colour. 1 – 3

–1 2

2

3

1 – 4

3 – 4

1 – 5

4 – 5

Find the fractions that are equivalent to each fraction above and colour them to match. 2 – 4

20 —– 100

12 — 48

2 — 10

3 – 9

4 — 16

5 — 10

24 — 32

50 —– 100

750 —— 1000

9 — 40

75 —– 100

10 — 30

6 — 24

90 —– 100

4 — 20

27 — 36

11 — 22

15 — 45

100 —– 400

6 — 30

3 — 15

5 — 13

9 — 27

200 —— 1000

500 —— 1000

23 — 46

3 – 6

8 — 10

7 — 14

800 —— 1000

9 — 12

18 — 24

200 —– 600

36 — 45

16 — 20

33 —– 100

9 — 10

12 — 48

2 – 6

9 — 18

2 – 8

10 — 50

12 — 24

100 —– 300

4 — 16

12 — 24

15 — 30

4 – 8

5 — 20

Make as many equivalent fractions as you can for each.

Students’ own work

1 – 2

3 – 4 1 – 4

see Student Book page 45 29

Compare and order fractions 1

Circle all the fractions that are smaller than the given fraction.

a

2 – 3

b

4 —

2

1 – 4

–1

11

2

4 —

7 —

–3

–3

15

12

4

8

15 — 30 1 – 3

Circle all the fractions that are greater than the given fraction.

a

–2

–1 3

1 – 2

2 – 9

4 – 6

–3

b

5 – 8

–2 3

9 — 12

1 – 2

–5 9

19 — 24

3

3

4

Write the fraction shown by the arrow on each number line.

a

b

1 2

0

1

c

2 7

1

e

2 1 8 4

5 8

8 8

0

4

1

1 2

5 6

0

1

d

5 7

0

1 6

3 1 12 4

6 1 12 2

8 3 12 4

11 12

0

f

1 1 4

0

3 4

1 1

1 21 2

Draw your own divisions on the number line and locate the following fractions on it: 3 – 4

1 – 4

1 – 2

8 – 8

5 – 8

3 – 8

–1 8

Students’ own work 0

1

see Student Book page 46 30

Compare and order mixed numbers 1

Complete the number line. 2 5

1 5

3 5

5 5

4 5

0

2 a

1

1 51

7 5

8 5

9 5

10 5

11 5

12 5

13 5

14 5

15 5

125

1 35

1 45

2

2 51

2 52

2 35

2 45

3

13 —

> 21–5

d

=

h 1–5

Fill in <, > or =. –7

> 1

5

4

>

e 1–5

3

6 5

b 12 — 5

3 – 4

11 — 5

1

f 2–5

12 — 30

–9

< 3 114 — 4

<

90 —

3

–9

45

c

4

g 1 –5 12 — 8

8

5

–3

19 —

7

20

–9

9 – 5

> 1–25 1

5

>

6 – 7

20 — 19

a Circle the fractions that are smaller than 1. b Write the fractions that are greater than 1 as mixed numbers. 12

9

1

9

90

1

20

1

3=3 8 =18 30 = 2 2 45 = 2 19 = 1 19 ________________________________________________________________________________

________________________________________________________________________________ c Write the mixed numbers in order from smallest to greatest. 1

1

1

1 19 18 2 22 3 ________________________________________________________________________________ ________________________________________________________________________________

4

a Simplify these improper fractions and show their positions on the number line: 14 — 6

30 — 5

28 — 6

72 — 12

39 — 12

14 6

0

1

= 2 62

2

39 12

= 3 123

3

28 6

= 4 64

4

30 5

=6

72 12

=6

5

6

b Write the fractions as mixed (or whole) numbers in order from greatest to smallest. 14

39

28

30

72

6 12 6 5 12 ___________ ___________ ___________ ___________ ___________

see Student Book page 47 31

Place value to thousandths 1

Draw beads on each abacus to show the decimal fraction given.

a 26.456

H

T

b 37.206

U .

t

h

th

d 42.32

H

T

j

T

U .

t

h

th

T

U .

t

h

th

H

T

U .

t

h

th

H

T

U .

t

h

th

t

h

th

H

T

H

i

U .

t

h

th

k 129.098

U .

H

T

U .

t

h

th

U .

t

h

th

U .

t

h

th

U .

t

h

th

f 345.234

h 99.993

1.234

H

T

e 28.9

g 38.904

H

H

c 389.4

U .

t

h

th

0.456

H

l

T

T

40.125

H

T

see Student Book page 48 32

Rounding decimals 1

Complete the table. Rounded to nearest hundredth

Rounded to nearest tenth

Rounded to nearest whole number

12.452

12.45

12.5

12

23.976

23.98

24.0

24

14.299

14.30

14.3

14

45.004

45.00

45.0

45

93.901

90.90

93.9

94

116.667

1 16.67

1 16.7

1 17

0.9823

0.98

1.0

1

1.0457

1.05

1.1

1

Number

2

3

Naresh made some mistakes when he tried to round these decimal fractions to the nearest whole number. Find his mistakes and correct them.

1 1.474 = 1.5 __________

3 2.644 = 2 __________

13 12.509 = 14 __________

26 25.919 = 29 __________

4 3.788 = 37 __________

Challenge Using this frame:

â&#x20AC;˘

99.999 a What is the biggest possible number you can make? ________________________ b What is the biggest possible number you can make using five different digits 98.765 (no repeats). ________________________ c What is the smallest possible number you can make using any digits except 0? 1 1.1 1 1 (repeating digits) or 12.345 (with no repeats) ________________________ d What is the highest possible number with three decimal places that will round off to 49.999 50 if it is rounded to the nearest whole number? ________________________

see Student Book page 50 33

Sorting data 1

Sam threw a die 20 times. Complete this frequency table to show how often Sam threw each number. Score

2

Tally

Frequency

1

4

2

4

3

4

4 5

3 3

6

2

Here is a list of the number of times each student in a class left the room during a school day. 0 1 0

2 6 0

1 0 0

0 2 1

1 0 1

4 1 3

3 3 2

1 1 1

2 2 0

0 4 0

2 3 2

0 2 0

Complete this frequency table to summarise the data. Number of times student left the room

Tally

Frequency

0

12

1 2

9 8

3

4

4

2

5

0

6

1

Total

36 see Student Book page 52

34

Grouped data 1

A clinic measured the mass of 30 children to the nearest kilogram. The masses are given here. 42 41 40

36 34 33

24 26 29

33 20 38

32 28 37

43 31 39

28 43 22

33 19 38

42 31 40

50 33 41

Complete this frequency table to sort the data. Mass in kilograms

2

Tally

Frequency

16–20

2

21–25

2

26–30

4

31–35

8

36–40

7

41–45

6

46–50

1

Total

30

30 a How many children were weighed? ____________________ 8 b How many children weighed between 31 kg and 35 kg? ____________________ 1 c How many children weighed 46 kg or more? ____________________ 31-35 d What mass range has the most children in it? ____________________ 27, 28, 29 or 30 e If your mass was in the 26–30 kg range, what could you weigh? 26, ___________________ 8 f How many children weighed less than 31 kg? ___________________ 31-35 because 30.5 g Jessie weighs 30.5 kg. Which group would she be in? Why? ___________________ rounded to the nearest whole number is 31 _______________________________________________________________________________ see Student Book page 53 35

Graphs from tables 2

60

30

50

25

40

20

30

0 \$5 n ha

et or

M

Amount spent

9 \$4 9.9

0-

\$3

9.9

9 9.9

0-

-\$ .00

\$4 0.0

Number of people in family

\$10

6-8

\$2

19 .9

9.9 -\$

3-5

.00

0-2

\$0

0

\$3 0.0

0 9

5

0-

10

9

10

9

20

0.0

15

\$2

Frequency

Frequency

1

see Student Book page 55 36

Line graphs These measurements show the changing height of a tree in the botanical gardens over 18 years. Age in years

2

4

6

8

10

12

14

16

18

Height in cm

45

90

100

140

170

190

200

210

230

1

Changing height of a tree

Draw a line graph to show the data. Donâ&#x20AC;&#x2122;t forget to give the graph a heading.

240 220 200

Height in cm

180 160 140 120 100 80 60 40 20 0 0

2

2

4

6

8 10 12 14 16 18 20 Age in years

a What is the scale on the vertical axis? ____________________ 20 cm b What is the time interval on the horizontal axis? ____________________ 2 years c How much taller did the tree grow from when it was 8 years old until it was 14 years old? ____________________ 60 cm

3

a How tall the tree was when it was 1 year old. ____________________ approx 20 cm b Its height at 5 years. ____________________ approx 95 cm

approx 245 cm c How tall the tree is likely to be when it is 20 years old. ____________________ see Student Book page 56 37

More line graphs This table shows how much money Anna had in her bank account at the end of each month for a year. Month Balance (\$)

F

M

N

D

100 130 200 180 150 160 120 100 145 100 90

60

2

A

M

J

Complete this line graph to show the data. You will need to decide on a vertical scale.

This table shows how much Mae-Ling had in her bank account at the same time. Use a different colour to show this data on the same graph. Month Balance (\$)

J

F

J

A

S

O

Annaâ&#x20AC;&#x2122;s balance (\$) Mae-Lingâ&#x20AC;&#x2122;s balance (\$)

Balance in account

1

J

M

220 200 180 160 140 120 100 80 60 40 20 0

A

J

M

F M A M J J Month

J

J

A

S

A

O

S O N D

N

D

90 120 150 140 150 145 130 140 120 130 140 150

3

When did the two girls have the same amount in the bank? ____________________ May

4

In which months did Anna have more money in the bank than Mae-Ling? _____________________________________ January, February, March, April, June and September

5

Which girl increased her balance over the year? ____________________ Mae-Ling see Student Book page 57

38

Unusual graphs This graph shows how much water is used to produce some of the food people eat. Water used to produce food

litres 217

15 497

255 909 1334

1egg 1kg potatoes

1kg maize

2291 3046

1kg wheat 1kg rice 1kg chicken

1kg beef

Draw a bar graph to show the same data. Think carefully about the scale before you do this. Studentsâ&#x20AC;&#x2122; own work

see Student Book page 58 39

More unusual graphs The pictures on this page show the outlines of six tall towers of the world. The name of each tower and its height in metres is given in the table. Use this information and the outlines to draw an unusual but accurate graph comparing their heights. Height in metres

553

b Ostankino Tower, Russia

537

c KFVS TV Tower (USA)

511

d Oriental Pearl Tower (China)

468

435

f Menara KL (Malaysia)

421

a

b

c

d

e

f

600 550

Height in metres

500 450 400 350 300 250 200 150 100 50 0

a

b

c

d

e

f

see Student Book page 59 40

Multiply and divide decimals by 10 and 100 Do these in your head. Write the answers only. One-week mental practice Day 1

Day 2

Day 3

25.44

Day 4

3.4 × 10

34

254.4 ÷ 10

0.2 × 10

2

254.4 ÷ 100 2.544 10 × 4.55

10 × 2.3

23

1.3 × 10

45.5

1.3 × 100

12.2 × 10

122

25.44 × 100 2544 10 × 9.332

14.2 ÷ 10

1.42

245 × 10

2450

10 × 9.81

2.45 × 10

24.5

10 × 10.01

24 ÷ 10

2.4

93.32

98.1 100.1

2.6 × 10

Day 5

13 130 26

0.005 × 100 0.5

204 ÷ 10

2.04

2.45 × 100

245

100 × 2.3

230

0.006 × 100

0.5 × 100

50

36.5 ÷ 10

3.65

100 × 4.5

450

12.5 ÷ 10

7.9 × 100

790

365 ÷ 10

36.5

100 × 90.07 9007 125 ÷ 100

0.3 × 10

3

365 ÷ 100

0.2 ÷ 10

0.02

3.65 × 10

3.65 36.5

1.23 × 100

1230

3.65 × 100

4.24 × 100

424

2.6 × 10

0.007 × 100

0.7

26

525 ÷ 100

5.25

1230

100 × 2.1 210

240

100 × 2.4

154.6 ÷ 10

15.46

3.42

34.2 ÷ 10

455.5

0.38

125 ÷ 10

12.5

12.7 × 10

0.4 × 10

4

19.34 × 10

1.25

0.4 × 100

40

12 ÷100

0.12

1.3

25 ÷ 100

0.25

0.345 × 100

34.5

246 ÷ 10

24.6

10001 ÷ 100 100.01 19.7 ÷10

125 ÷ 10

4.3 × 10

430 43 4.3

456 ÷ 100

12.345 × 10 123.45 9000 ÷100

90

929

1.76 ÷10

19.7 0.176

32.6 × 100

3260

12.3 ÷10

1.23

342 ÷ 100

3.42

125 ÷ 100

1.25

43 ÷ 10

2.45 × 10

24.5

43 ÷ 100

0.43

2345 ÷100 23.45 1945 ÷ 100

2.45 × 100

245

4.3 ÷ 10

0.43

10 ÷ 100

0.1

250

2.5 × 100 13 ÷10

193.4

45

4.3 × 100

4.56

127

0.45 × 100

0.12 × 100

2.3

19.65

1965 ÷ 100

3.8 ÷10

45.2 ÷ 10

23 ÷ 10

34.5

1.25

4300

12 12.5

0.6

345 ÷10

0.23

43 × 100

4.52

370

2.3 ÷10

4555 ÷ 10

23.95

37

0.23

52.5

239.5 ÷ 10

3.7 × 10

23 ÷ 100

525 ÷ 10

0.04 ÷10

0.004

365

100 × 12.3

27

3.7 × 100

260

2.6 × 100

2.7 × 10

205 ÷ 100

19.45

2.05

92.9 × 10

342 ÷ 10

34.2

342 × 100 34 200

see Student Book page 60 41

More operations with 10 and 100 1

2

Complete each table. 22

282

1435

14.7

1187

231

8

× 10

220

28.2

14.35

147

1 1.87

2310

0.8

÷ 10

2.2

0.282

0.1435

1.47

0.1 187

23.1

0.008

22

2.82

1.435

14.7

1.187

231

0.08

× 10

220

28.2

14.35

147

1 1.87

2310

0.8

× 100

2200

282

143.5

1470

1 18.7

23 100

8

207

31

7

19

147

2081

2100

÷ 10

20.7

3.1

0.7

1.9

14.7

208.1

210

÷ 100

2.07

0.31

0.07

0.19

1.47

20.81

21

Work out what number (10 or 100) is missing from these number chains. Write the numbers in the boxes.

a

×

10

0.7

b

÷

10

7

×

10

12.5

c 42.3

100

0.7

÷

100

125

÷

×

100 4.23

100

÷

70

×

1000

1.25

×

×

1000 423

7000

÷ 10 000 125

÷

100

1000

×

100 12.5

1.25

× 4.23

70

100

÷ 423

10 42.3

see Student Book page 61 42

2

Join pairs of decimals to make 1. 0.88

0.65

0.7

0.1

0.4

0.99

0.35

0.8

0.3

0.72

0.6

0.9

0.01

0.2

0.75

0.45

0.37

0.63

0.12

0.28

0.25

0.55

Complete the number chain by filling in the missing values.

a

14

13.5

b

+0.2

14.8 –

3

33.8

3

+0.8

+0.5

0.7

30.8

+0.4

+0.6

15 –

15.4 –

0.2

30.1

+1.7

16

16.3

0.7

29.9

+0.3

1.2

29.2

18

0.7

28.0

27.3

Anna says 7 + 8 = 15, so 0.7 + 0.8 = 0.15. Use this number line to show why Anna is wrong.

+0.8

0.7

0

4

1.5

1

Can you find three different ways to complete this puzzle? 15.5

+ +

+ +

10.4

+ 4.5

10.6

15.5

+ + + 10.4

Students’ own work 15.5

+ +

4.5 10.6

2

+ +

10.4

4.5 10.6

see Student Book page 65 43

Halving decimals 1

Halve the number at each step to find the missing numbers in each division tree.

a

b 29

2

42.4

14.5

2

2

7.25

2

21.2

10.6

2

3.625

2

5.3

13.7

c

2 d

2

2.65

15.2

6.85

2

2

3.425

2

1.325

7.6

2

3.8 see Student Book page 68

44

 

All sides equal in length



Opposite sides equal in length





Both pairs of opposite sides parallel



   

 

 

 



 

One pair of opposite sides parallel



No sides parallel

2

Kite



Trapezium

Rectangle

Has four sides

Property

Rhombus

Square

Shape

Parallelogram

Complete this table by ticking the blocks that apply to each shape.

Four right angles





Opposite angles equal



 





Fill in the missing shape names in these sentences.

a A ____________________ is a shape with four sides. quadrilateral* b A ____________________ square, rectangle, is a quadrilateral with 2 pairs of parallelogram, rhombus parallel sides. c A ____________________ square, rhombus is a parallelogram with 4 equal sides. d A ____________________ square, rectangle is a parallelogram with right angles. is a parallelogram with 4 equal sides e A ____________________ square and 4 right angles. has one pair of parallel sides. f A ____________________ trapezium has two pairs of equal sides, but g A ____________________ kite no parallel sides. *

square, rectangle, parallelogram, rhombus, trapezium, kite

see Student Book page 72 45

Naming quadrilaterals You can use a pin-board and elastic bands to help you complete this activity. Draw an example of the named shapes on the pin-boards. Make sure you end up with 15 different shapes. Studentsâ&#x20AC;&#x2122; own work

1

Square

2

Rectangle

3

Kite

4

Parallelogram

5

Rhombus

6

Kite

7

Trapezium

8

Rectangle

9

Rhombus

10

Square

11 Parallelogram

12 Trapezium

13

Rectangle

14 Rectangle

15 Kite

see Student Book page 73 46

Perimeter 1

a Fill in the missing side lengths on each shape. b Calculate the perimeter of each shape.

A

20 cm

P= 7 cm

B

25 cm

P= 5 cm

5 cm

3 cm

C

13.8 cm

P=

D

3.2 cm

4.6 cm 2.1 cm

(All sides equal)

E

P=

10.6 cm 15 m

F

9 cm

2m

6m

18 cm 8 cm

76 cm

P=

2

9m

20 cm

42 m

P=

The perimeter of each shape is given. Use this to work out the lengths of the missing sides.

a

b

17 cm

32 mm

c

5.5 m

40 mm

12 cm

13 cm

14 cm perimeter = 56 cm

20 mm 18 mm

4m

25 mm

perimeter = 135 mm

perimeter = 19 m

see Student Book page 77 47

More perimeter A rectangle has a perimeter of 24 units. Draw different rectangles on the grid to show some possible lengths for the sides.

see Student Book page 78 48

Factors 1

Complete the grids to show all the pairs of factors for each number.

a

b

8

1 2

d

46

1 2

g

2

e

60 30 20 15 12 10

f

48

h

72

72 36 24 18 12 9

20 10 5

100

1 100 2 50 4 25 5 20 10 10

48 24 16 12 8

1 2 3 4 6 8

20

1 2 4

24 12 8 6

1 2 3 4 6

46 23

60

1 2 3 4 5 6

1 2 3 4

8 4

c

24

i

40

1 2 4 5

40 20 10 8

Use your tables to find the common factors of:

a 24 and 48 ____________________ 1, 2, 3, 4, 6, 8, 12, 24 b 20, 60 and 100 ____________________ 1, 2, 4, 5, 10, 20

see Student Book page 80 49

Prime numbers Eratosthenes was a Greek mathematician who lived over 2000 years ago. He found a way of sorting out prime numbers, from other numbers. His method is called the sieve of Eratosthenes. Follow the instructions to find the prime numbers between 1 and 100 in the same way as he did.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99 100

• Cross out 1. • Colour 2 then cross out all other multiples of 2. • Colour 3 then cross out all the other multiples of 3. • Colour the next number that is not coloured or crossed out, then cross out all the multiples of that number. • Keep doing this until all the numbers are either coloured or crossed out. The coloured numbers are the prime numbers. List them here. You should have 25 numbers on your list.

2 _____ 3 _____ 5 _____ 7 _____ 1 1 _____ 13 _____ 17 _____ 19 _____ 23 _____ _____ 29 _____ 31 _____ 37 _____ 41 _____ 43 _____ 47 _____ 53 _____ 59 _____ 61

67 _____ 71 _____ 73 _____ 79 _____ 83 _____ 89 _____ 97 _____ see Student Book page 81 50

Multiplication by multiples of 10 Complete each set of multiplications. What patterns can you see in the answers? Write a rule for the pattern.

1

8 × 2 = 16

6 × 3 = 18

9 × 4 = 36

8 × 20 = 160

6 × 30 = 180

9 × 40 = 360

8 × 200 = 1600

6 × 300 = 1800

9 × 400 = 3600

8 × 6 = 48

6 × 8 = 48

9 × 5 = 45

8 × 60 = 480

6 × 80 = 480

9 × 50 = 450

8 × 600 = 4800

6 × 800 = 4800

9 × 500 = 4500

Pattern: __________________________________________________ Students’ own pattern explanation ___________________________________________________________

2

80 × 2 = 160

60 × 3 = 180

90 × 4 = 360

80 × 20 = 1600

60 × 30 = 1800

90 × 40 = 3600

80 × 200 = 16 000

60 × 300 = 18 000

90 × 400 = 36 000

80 × 2000 = 160 000

60 × 3000 = 180 000

90 × 4000 = 360 000

80 × 6 = 480

60 × 8 = 480

90 × 5 = 450

80 × 60 = 4800

60 × 80 = 4800

90 × 50 = 4500

80 × 600 = 48 000

60 × 800 = 48 000

90 × 500 = 45 000

80 × 6000 = 480 000

60 × 8000 = 480 000

90 × 5000 = 450 000

Pattern: __________________________________________________ Students’ own pattern explanation ___________________________________________________________ see Student Book page 83 51

Multiplying pairs of multiples of 10 and 100 Complete the multiplication table as quickly as you can. Try to work mentally as much as possible. Ă&#x2014;

10

20

30

50

90

200

400

800

10

100

200

300

500

900

2000

4000

8000

20

200

400

600

1000

1800

4000

8 000

16 000

30

300

600

900

1500

2700

6000

12 000 24 000

40

400

800

1200

2000

3600

8000

16 000 32 000

60

600

1200

1800

3000

5400

12 000 24 000 48 000

100

1000

2000

3000

5000

9000 20 000 40 000 80 000

400

4000

8000

12 000 20 000 36 000 80 000 160 000 320 000

800

8000

16 000 24 000 40 000 72 000 160 000 320 000 640 000

1000

10 000 20 000 30 000 50 000 90 000 200 000 400 000 800 000

2000

20 000 40 000 60 000 100 000 180 000 400 000 800 000 1 600 000

110

1 100

2200

3300

5500

9900

150

1500

3000

4500

7500

13 500 30 000 60 000 120 000

220

2200

4400

6600

1 1 000

19 800 44 000 88 000 176 000

1100

11000

22 000 33 000 55 000 99 000 220 000 440 000 880 000

22 000 44 000 88 000

see Student Book page 84 52

Calculating the size of angles 1

Calculate the missing angles. Write the size in degrees on each drawing. Check by measuring.

a

b

138°

42º

107°

c

73º

d

93°

42º

1 13°

54º

33º

25º

e

f

40º

132°

76º

132º 97º

147°

96º

2

Measure angle p. Calculate angle q.

a

b

c

30°

45°

q

p q

45°

60°

130° p

q

59°

p

see Student Book page 89 53

More missing angles 1

Calculate the missing angles. Write the size in degrees on each drawing. Check by measuring.

a

b 112º

90°

90º

90°

90°

68° 1 12°

142°

c

38°

68°

d

138º

38º

42°

42°

142° e

f

147° 33°

33º

138° 168° 12°

12º

168°

147° g

h

45° a

30º

45°

90º

90°

a

80º b

90°

90° 70°

45°

b

45°

see Student Book page 90 54

Angles in a triangle Measure the angles in each triangle. Write the size in the correct place. Add them up to check that you get 180°.

1

2

50° + _____ 90° + _____ 40° = _____ 180° _____ 3

78° + _____ 37° + _____ 65° = _____ 180° _____ 4

32° + _____ 33° + _____ 65° = _____ 180° _____ 5

38° + _____ 66° + _____ 76° = _____ 180° _____ 6

50° + _____ 90° + _____ 40° = _____ 180° _____ 7

36° + _____ 1 14° + _____ 30° = _____ 180° _____ 8

1 15° + _____ 33° + _____ 32° = _____ 180° _____

45° + _____ 38° + _____ 97° = _____ 180° _____ see Student Book page 91 55

Calculating angles in triangles Calculate the missing angles in these triangles. Write your answers on the drawings.

1

2

25º

77° 53º

50º

136°

19º

3

4 74º

1 10° 53º 35º

53°

35º

5

6

69° 90°

42º 21º

48° 7

90°

8 75º

42°

120º

45°

60°

115º

147°

9

10

50°

50º

33º

75° 55º

120º

60°

70°

110º

see Student Book page 92 56

Angles of rotation Draw the position of each shape to show where it will be after the rotation described. Use the dot on the shape as the point of rotation.

1

90º clockwise

2

90º clockwise

3

90º anti-clockwise

4

90º anti-clockwise

5

90º clockwise

6

90º anti-clockwise

see Student Book page 93 57

Percentages 1

Colour the number of squares given. Complete the statements next to each block.

a

50

% coloured

50

% not coloured

b

50 squares c

90

% coloured

10

% not coloured

d

18

% coloured

82

% not coloured

0

25

% coloured

75

% not coloured

3

f

% coloured

h

% not coloured

100 squares

27 squares

% not coloured

% coloured

97

% not coloured

25

% coloured

75

% not coloured

3 squares

100

i

20

25 squares

18 squares g

% coloured

80 squares

90 squares e

80

every 4th square

27

% coloured

73

% not coloured

1

j

99

% coloured % not coloured

1 square see Student Book page 94

58

Percentages, fractions and decimals The number line represents one whole. Write the fractions, decimals and percentages in the correct position on the number line. You can write on both sides of the line.

15% 4 – 5 30%

0.2

20% 2 – 5 80%

6 –– 20

90% 25% 60% 0.6

100%

1

90%

0.9

80% 75%

4 5 3 4

60%

0.6

1 – 2

40% 1 2

50%

50%

75%

40%

2 5

30% 25%

6 20 1 4

20% 15%

0.2

0

1 – 4

3 – 4 0.9

100% see Student Book page 95 59

More percentages of amounts Divide and colour each strip using the percentages given. If the percentages do not add up to 100%, leave part of the strip uncoloured.

1

50% yellow, 50% green

2

75% yellow, 25% blue

3

20% yellow, 70% red

4

45% yellow, 50% green

5

25% yellow, 25% red, 50% green

6

14% yellow, 29% red, 57% blue

7

12% yellow, 15% red, 19% green

8

24% yellow, 30% red, 22% green

see Student Book page 98 60

Dealing with discounts 1

2

Complete this chart. Original price

Percentage discount

Money off

Sale price

\$75

10%

\$7.50

\$67.50

\$40

5%

\$2.00

\$38.00

\$52

10%

\$5.20

\$46.80

\$125

20%

\$25.00

\$100

\$60

50%

\$30.00

\$30

\$245

20%

\$49.00

\$196

\$339

33.3%

\$113.00

\$226

\$850

25%

\$212.50

\$637.50

\$1260

15%

\$189.00

\$1071

\$2612

5%

\$130.60

\$2481.40

Write the new price if each item is discounted by 20%. Was: \$20.00 Now: \$16.00

Was: \$14.50 Now: \$1 1.60

Was: \$55.00 Now: \$44.00

Was: \$19.99 Now: \$15.99

Was: \$120.00 Now: \$96.00

Was: \$75.99 Now: \$60.79

see Student Book page 99 61

For each of the following lists:

a Estimate the total cost. b Estimate the change you would get from \$10. c Use a calculator to work out the exact total. d Check your total by adding in reverse order. List A \$4.10 4 × \$0.97 2 × \$3.15 \$6.59 Estimated total: ____________ Estimated change: ____________ Exact total: ____________ \$20.87

Change: \$79.13 List C 3 × \$3.79 2 × \$1.49 \$1.98 4 × \$1.54 Estimated total: ____________ Estimated change: ____________ Exact total: ____________ \$22.49

Change: \$77.51 List E 5 × \$2.47 \$1.69 6 × \$1.78 \$5.79

List B \$56.09 2 × \$2.20 \$2.76 \$1.95 10 × \$1.06 Estimated total: ____________ Estimated change: ____________ Exact total: ____________ \$75.80

Change: \$24.20 List D 6 × \$2.47 \$2.75 \$4.70 4 × \$0.99 \$3.80

Estimated total: ____________ Estimated change: ____________ Exact total: ____________ \$30.03

Change: \$69.97

Estimated total: ____________ Estimated change: ____________ Exact total: ____________ \$30.51

Change: \$69.49 2

Calculate how much change you would get from \$100. see Student Book page 101

62

Increase in prices

Studentsâ&#x20AC;&#x2122; own work

see Student Book page 102 question 3 63

Revising coordinates 8

D

7

I

6

C G

5

y-axis

H F N

4

A

3

M

J

2

E

B P

1

O 0

K 1

2

L

3

4

5

6

7

8

x-axis 1

Fill in the names of the two axes and mark the origin on the graph.

2

Plot these points on the graph. Label each one with the correct capital letter.

3

A (1, 3)

B (2, 2)

C (5, 6)

D (4, 7)

E (8, 4)

F (7, 5)

G (3, 5)

H (6, 6)

I (0, 6)

J (0, 2)

K (3, 0)

L (5, 0)

M (4, 3)

N (6, 4)

O (0, 0)

P (6, 1)

Add your own points, Q, R and S to the grid. Write the coordinates of each letter here. Studentsâ&#x20AC;&#x2122; own work Q (___, ___)

R (___, ___)

S (___, ___)

see Student Book page 109 64

Extending the grid Plot the points A to Z on the grid. Label each point with a capital letter. A (1, 3)

B (2, –2)

C (–2, –2)

D (4, 2)

E (–2, 2)

F (–4, –2)

G (4, 4)

H (4, 0)

I (–2, 1)

J (–4, 5)

K (1, –4)

L (–5, –5)

M (4, –4)

N (0, 1)

O (0, 0)

P (–5, 4)

Q (3, 1)

R (–4, –3)

S (5, –2)

T (2, 5)

U (–2, 5)

V (3, –5)

W (5, 5)

X (–4, 1)

Y (–5, –3)

Z (3, –3) y 6

J

U

P

T

5

W G

4

A

3

E X

I

D

2 1

N

Q

O –5

–4

F Y

R

–3

–2

C

–1 0 –1

1

2

5 x

4

S Z

–3

–5

3

B

–2

–4

L

H

K

M V

–6

see Student Book page 110 65

Matching shapes Grid A

1 y 6

F'

5

b Write the coordinates of each vertex before and after reflection

A

4 3

G' E'

2

a Draw the reflection of each shape about the x-axis.

D

B

Before reflection

After reflection

A

3, 4

3, -4

B

5, 2

5, -2

C

3, 0

3, 0

D

1, 2

1, -2

E

-2, -2

-2, 2

F

-4, -5

-4, 5

G

-5, -3

-5, 3

1 –5 –5 –4 –3 –2 –1 0 –1 E –2 G –3

1

C 3 4

2

5

D'

B'

–4

A'

–5

F

x

–6

Grid B y 6

2

5 4

A

3

C

2 C

1

–5 –5 –4 –3 –2 –1 0 B 1 –1

The shapes on the grid were translated 2 blocks to the right and 3 blocks down to get these positions. Draw each shape in its original position (before translation).

A 2

3

4

5

x

–2

D

–3 –4 D

B

–5 –6

see Student Book page 114 66

Timed division Do each of these sets of divisions mentally as quickly as you can. Time yourself and write down how long it takes you. Set A

Set B

Set C

Set D

Set E

34 ÷ 2 = 17

40 ÷ 4 = 10

90 ÷ 10 = 9

32 ÷ 8 = 4

3.2 ÷ 8 = 0.4

68 ÷ 2 = 34

400 ÷ 4 = 100

400 ÷ 10 = 40

320 ÷ 8 = 40

320 ÷ 80 = 4

12 ÷ 3 = 4

4000 ÷ 4 =1000 1000 ÷ 10 =100 34 ÷ 8 = 4 r2

120 ÷ 3 = 40

28 ÷ 4 = 7

450 ÷ 10 = 45

49 ÷ 7 = 7

4.9 ÷ 7 = 0.7

76 ÷ 2 = 38

280 ÷ 4 = 70

860 ÷ 10 = 86

490 ÷ 7 = 70

490 ÷ 70 = 7

75 ÷ 3 = 25

2800 ÷ 4 = 700 740 ÷ 10 = 74

50 ÷ 7 = 7 r1

5.0 ÷ 7 = 0.71

280 ÷ 2 = 140

36 ÷ 4 = 9

36 ÷ 10 = 3.6

63 ÷ 9 = 7

6.3 ÷ 9 = 0.7

240 ÷ 3 = 80

360 ÷ 4 = 90

49 ÷ 10 = 4.9

630 ÷ 9 = 70

630 ÷ 90 = 7

612 ÷ 2 = 306

364 ÷ 4 = 91

99 ÷ 10 = 9.9

65 ÷ 9 = 7 r2

6.5 ÷ 9 = 0.72

612 ÷ 3 = 204

3600 ÷ 4 = 900 123 ÷ 10 = 12.3 72 ÷ 8 = 9

7.2 ÷ 8 = 0.9

270 ÷ 3 = 90

3640 ÷ 4 = 910 145 ÷ 10 = 14.5 72 ÷ 9 = 8

7.2 ÷ 9 = 0.8

270 ÷ 2 = 135

52 ÷ 4 = 13

234 ÷ 10 = 23.4 720 ÷ 8 = 90

720 ÷ 80 = 9

110 ÷ 2 = 55

520 ÷ 4 = 130

976 ÷ 10 = 97.6 720 ÷ 9 = 80

720 ÷ 90 = 8

360 ÷ 3 = 120

528 ÷ 4 = 132

1230 ÷ 10 = 123 73 ÷ 8 = 9 r1

7.3 ÷ 8 = 0.9125

3.4 ÷ 8 = 0.425

5200 ÷ 4 =1300 1045 ÷ 10 = 74 ÷ 9 = 8 r2 104.5 1000 ÷ 2 = 500 5280 ÷ 4 = 1340 1009 ÷ 10 = 77 ÷ 7 = 1 1 100.9 1500 ÷ 3 = 500 72 ÷ 4 = 18 5 ÷ 10 = 0.5 77 ÷ 11= 7

7.4 ÷ 9 = 0.82

1200 ÷ 2 = 600 724 ÷ 4 = 181

1.5 ÷ 10 = 0.15 770 ÷ 7 = 1 10

770 ÷ 70 = 1 1

7500 ÷ 3 =2500 728 ÷ 4 = 182

2.9 ÷ 10 = 0.29 78 ÷ 7 = 1 1 r1

7.8 ÷ 7 = 1.1 1

360 ÷ 2 = 180

7600 ÷ 2 =3800 7280 ÷ 4 = 1820 9.7 ÷ 10 = 0.97 78 ÷ 11= 7 r1

7.7 ÷ 7 = 1.1 7.7 ÷ 11= 0.7

7.8 ÷ 11= 0.709

_______ minutes _______ minutes _______ minutes _______ minutes _______ minutes Which set was easiest for you? Tell your partner why. see Student Book page 115 67

Division – rounding the remainder 1 a

Divide. Write the answers as mixed numbers.

685 ÷ 6

b

1 14 1/685 d

2

832 ÷ 5 166 1/5

685 ÷ 7

685 ÷ 8

c

97 6/685 e

832 ÷ 6 138 2/3

85 1/137 f

832 ÷ 9 92 1/208

Divide. Write the answers as decimal fractions.

a

247 ÷ 5 49.4

b

247 ÷ 2 123.5

c

247 ÷ 4 61.75

d

819 ÷ 5 163.8

e

819 ÷ 2 409.5

f

819 ÷ 4 204.75

3

Divide. Round the answers to the closest whole number.

a

925 ÷ 4 231

b

876 ÷ 6 146

c

408 ÷ 9 45

d

321 ÷ 4 80

e

209 ÷ 5 42

f

807 ÷ 10 81

g

697 ÷ 7 100

h

297 ÷ 3 99

i

912 ÷ 10 91

see Student Book page 118 68

Ratio Colour each shape according to the instructions. Complete the statements under each shape.

1

2

Colour 4 green for every 8 yellow. yellow to green = _____ 2 to _____ 1 green to yellow = _____ 1 to _____ 2

Colour 1 green for every 5 yellow. yellow to green = _____ 5 to _____ 1 green to yellow = _____ 1 to _____ 5

3

4

Colour 3 green for every 7 yellow. yellow to green = _____ 7 to _____ 3 green to yellow = _____ to _____ 3 7

Colour 3 green for every 3 yellow. yellow to green = _____ 1 to _____ 1 green to yellow = _____ to _____ 1 1

5

6

Colour 9 green for every 1 yellow. yellow to green = _____ 1 to _____ 9 green to yellow = _____ 9 to _____ 1

Colour 1 green for every 4 yellow. yellow to green = _____ 4 to _____ 1 green to yellow = _____ 1 to _____ 4

7

8

Colour 1 green for every 2 yellow and 5 red. green to yellow = _____ 1 to _____ 2 red to green = _____ 5 to _____ 1 red to yellow to green = _____ 5 to _____ 2 to _____ 1

Colour 4 green for every 8 yellow and 2 red. yellow to green = _____ 2 to _____ 1 green to red = _____ 2 to ____ 1 red to yellow to green = _____ 1 to _____ 2 to _____ 4

see Student Book page 123 69

Proportion What proportion of each shape is shaded? Draw lines to match the shapes to the fractions that show the proportion shaded.

1

2 – 5

2

1 – 4 3

1 – 2

4

6 – 6 5

1 – 5

6

2 – 3 7

1 – 3

8

2 – 7 see Student Book page 126 70

Investigating multiplication 1

a Fill in the missing values. 5 × 25 =

and 5 × 100 ÷ 4 =

8 × 25 =

and 8 × 100 ÷ 4 =

12 × 25 =

and 12 × 100 ÷ 4 =

18 × 25 =

and 18 × 100 ÷ 4 =

25 × 25 =

and 25 × 100 ÷ 4 =

This is an open-ended investigation. Allow the students to discuss and share their ideas.

b What do you notice about the answers? c Why does this work? ______________________________________________________________________ ______________________________________________________________________

2 i

Look at these three methods that students used to find 2567 × 36. 2567 × 10 = 25 670 2567 × 10 = 25 670 2567 × 10 = 25 670 2567 × 5 = 12 835 2567 × 1 = 2 567 92 412

ii 2567 × 25 = (2567 × 100) ÷ 4 = (256 700) ÷ 4 = 641 175 2567 × 10 = 25 670 2567 × 1 = 2 567 64 175 + 25 670 + 2567 = 92 412 iii

2567 36 × 15 402 77 01 92 412 a Write notes next to each calculation to explain what each student did. b Which of these methods seems easiest to you? Why? see Student Book page 127 71

Making sense of bar graphs 1

Roll a die 30 times. Record your scores in this frequency table. Studentsâ&#x20AC;&#x2122; own work Score

Tally

Frequency

1 2 3 4 5 6 Total

2

Draw a bar graph on this grid to show your results.

Studentsâ&#x20AC;&#x2122; own work

see Student Book page 131 72

Making sense of line graphs Jessieâ&#x20AC;&#x2122;s baby brother is weighed each week at the clinic and his mass (in kg) is recorded on a table. Week Mass (kg)

1

0

1

2

3

4

5

6

7

8

9

10

2.1

2.1

2.2

2.3

2.4

2.5

2.3

2.6

2.8

3.0

3.2

Draw a line graph to show this data.

3.5 3 Mass (kg)

2.5 2 1.5 1 0.5 0

0

1

2

3

4

5 6 Week

7

8

9

10

2

The baby was ill one week. Which week do you think it was? Why? ________________________________________________________________ Week 5 - Week 6 because the baby lost weight between Week 5 and ________________________________________________________________ Week 6 ________________________________________________________________

3

Use your graph to estimate how much the baby weighed when he 1 was 9â&#x20AC;&#x201C;2 weeks old. ________________________________________________________________ 3.1 kg ________________________________________________________________ see Student Book page 132 73

Shape patterns Complete the table for each shape pattern. Pattern A Number of triangles

Number of rods used

Pattern

1 2 3 4

3 6 9 12

1#3 2#3 3#3 4#3

Number of X shapes

Number of rods used

Pattern

1 2 3 4

4 8 12 16

1#4 2#4 3#4 4#4

Number of squares

Number of rods used

Pattern

1 2 3 4

4 8 12 16

1#4 2#4 3#4 4#4

Number of squares

Number of rods used

Pattern

1 2 3 4

4 7 10 13

1#3+1 2#3+1 3#3+1 4#3+1

Pattern B

Pattern C

Pattern D

see Student Book page 137 74

Number machines Fill in the missing inputs and outputs. a

c

e

Input 2 9 7 1

12 19 47

+4

6 13 11 10

–3

9 16 44

62

59

12 10

×4

48 40

×10

13 47

9 100

g

b

Output

1.3 4.7

3.5 9

i 200 400 600

800

÷4

Input 4 12 138 400 509

f

25 30

h

59 60 45 100

–9

19 23

12.6 13.5

35 90

1.85 2.64

50 j 100 150

200 215

50 120

11 19 145 407 536

+7

d

68 69 54 109

36 400

200

Output

×8

152 184 200 240

×100

1260 1350

÷10

20 21.5

185 264

5 12

see Student Book page 138 75

Number patterns 1 a

b

Complete each pattern. Use a calculator if you need to. 3

6

12

24

48

96

192

8

15

24

35

48

63

80

4

16

64

256

1024

4096

16 384

30

300

3000

30 000

300 000

3 000 30 000 000 000

92

83

c

d

e

101

f

100

g

10

h

128

2

75

125

100

64

100

1000

32

65

74

16

150

125

56

175

8

4

150

1 000 000

10 000 100 000 2

47

10 000 000

1

Tell your partner what rule you used to complete each pattern.

a) double b) +7, +9, +1 1 ...

e) -9 f) +25 in two separate sequences

c) #4

g) #10

d) #10

h) รท2 see Student Book page 140

76

Area of combined shapes Work out the lengths of any missing sides. Divide the shapes into rectangles and calculate the area of each one.

1

2

14 cm

2m

5 cm 10 cm

7m

8 cm 5 cm

5m

100 cm2

6 cm

3

12 m

34 m2

6m

4

120 cm 20 cm

40 m

30 m

60 cm

60 m

2280 m2 5

4m

5m

50 cm

4400 cm2 6

10 cm

3m 4m

3 cm

8m

4 cm

4 cm

6 cm 2

92 m 7

42 cm2 8

70 cm

3m

30 cm 40 cm

4m

100 cm

4m 3m 4m 3m

72 m2

40 cm

5800 cm2 Note that there are different ways of breaking up the shapes, including working out the larger area and subtracting a cut-out section see Student Book page 147 77

Estimating area on a grid 1

Estimate the area of each shape. Each square represents 1 cm2. • Put a circle in the full squares. Count them and write the number. • Shade all the half squares. Count the halves, divide the total by 2 and write the number. • Tick any areas that are greater than half a square. Count them and write the number. • Add the numbers to find the approximate total area. Write it with the correct units.

A

2

B

C

Complete each shape so it has the approximate area given.

A

13 cm2

B 15 cm2

C 12 cm2

D 20 cm2

see Student Book page 148 78

Dividing decimal amounts 1

Measure the length of each line accurately in centimetres. Write the lengths next to the lines.

B

12.5 cm A

C

25.5 cm 10.5 cm

D

5.8 cm 2

Divide line A into ten equal parts. Write the length on each part.

2.55 cm

3

Divide line B into five equal parts. Write the length on each part.

2.5 cm

4

Divide line C into three equal parts. Write the length on each part. 3.5 cm

5

Divide line D into two equal parts. Write the length on each part.

2.9 cm see Student Book page 154 79

Nelson international maths workbook 6 answers
Nelson international maths workbook 6 answers