Nelson International Mathematics Workbook 6
Name:
2nd edition
Contents Task done Page
Task done Page
Traditional counting systems 4
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
Addition and subtraction facts
15
Adding whole numbers
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
Contents Task done Page
Adding and subtracting decimals
43
Halving decimals
44
Dealing with discounts
Properties of quadrilaterals 45 Naming quadrilaterals
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
Task done Page
52
61
Checking your calculations 62 Increase in prices
63
Revising coordinates
64
Extending the grid
65
Matching shapes
66
Timed division
67
Division – 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
Traditional counting systems 1
This is a chimpu. Write a few sentences explaining how it is used to record a number.
4 strings = 4 digits
______________________________________________ Student’s own answers. However, they should mention ______________________________________________ that the chimpu works using place value, with one
4 thousands 2 hundreds 7 units
8 tens
______________________________________________ string for each place, for units, beads are threaded ______________________________________________ onto a single string, for tens, the beads are threaded on
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
Students’ 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.
Students’ own work
0
Students’ own work, Allow them to check each other’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 2013−2000 = 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
______________
b your last birthday
______________
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 weeks’ 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
Addition and subtraction facts 1
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
Adding whole numbers 1
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.
Use the additions to find the missing answers to the subtractions.
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
Follow the division chains. Fill in the missing answers. ÷2
÷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
Actual answer
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
Answer these questions about your table.
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
$2
Frequency
Frequency
1
see Student Book page 55 36
Line graphs These measurements show the changing height of a tree in the botanical gardens over 18 years. Age in years
2
4
6
8
10
12
14
16
18
Height in cm
45
90
100
140
170
190
200
210
230
1
Changing height of a tree
Draw a line graph to show the data. Donâ&#x20AC;&#x2122;t forget to give the graph a heading.
240 220 200
Height in cm
180 160 140 120 100 80 60 40 20 0 0
2
2
4
6
8 10 12 14 16 18 20 Age in years
Answer these questions about your graph.
a What is the scale on the vertical axis? ____________________ 20 cm b What is the time interval on the horizontal axis? ____________________ 2 years c How much taller did the tree grow from when it was 8 years old until it was 14 years old? ____________________ 60 cm
3
Use your graph to estimate:
a How tall the tree was when it was 1 year old. ____________________ approx 20 cm b Its height at 5 years. ____________________ approx 95 cm
approx 245 cm c How tall the tree is likely to be when it is 20 years old. ____________________ see Student Book page 56 37
More line graphs This table shows how much money Anna had in her bank account at the end of each month for a year. Month Balance ($)
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
Tower a CN Tower (Canada)
553
b Ostankino Tower, Russia
537
c KFVS TV Tower (USA)
511
d Oriental Pearl Tower (China)
468
e Milad Tower (Iran)
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
Adding and subtracting decimals 1
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
Properties of quadrilaterals 1
All sides equal in length
Opposite sides equal in length
Adjacent 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
Checking your calculations 1
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.
Students’ answers will vary.
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