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CAMBRIDGE
Primary Mathematics
Pakistan edition
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Based on Single National Curriculum 2020
Workbook 3
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Supplementary reading material
Cherri Moseley & Janet Rees
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anthology and reproduction for the purposes of setting examination questions.
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Contents
Contents
How to use this book
5
Thinking and working mathematically
6
1
Numbers to 1000
2
Addition and subtraction
22
22
27
31
3
Multiplication and division
34
34
39
43
4
3D shapes
47
47
5
Measurement, area and perimeter
53
53
59
65
3.1
3.2
3.3
4.1
Addition
Subtraction
Roman numerals
Exploring multiplication and division
Connecting 2×, 4× and 8×
Connecting 3×, 6× and 9×
3D shapes
Measurement
2D shapes and perimeter
Area
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5.1
5.2
5.3
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2.1
2.2
2.3
Hundreds, tens and ones
Comparing and ordering
Estimating and rounding
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1.1
1.2
1.3
8
8
13
17
6
Fractions of shapes
72
72
7
Statistics: tally charts and frequency tables
79
79
8
Time
85
85
6.1
7.1
8.1
Fractions and equivalence of shapes
Statistics
Time
3
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Contents
9
9.1
9.2
9.3
More addition and subtraction
Addition: regrouping tens and reordering
Subtraction: regrouping tens
Complements
10 More multiplication and division
106
106
109
113
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10.1 Revisiting multiplication and division
10.2 Playing with multiplication and division
10.3 Extending multiplication and division
90
90
96
101
11 More fractions
118
118
123
128
12 Measures
132
132
139
146
11.1 Fractions of numbers
11.2 Ordering and comparing fractions
11.3 Calculating with fractions
12.1 Mass
12.2 Capacity
12.3 Temperature
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13 Time (2)
13.1 Time
13.2 Timetables
14 Angles and movement
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14.1 Angles, direction, position and movement
155
155
162
171
171
15 Graphs
182
182
193
16 Pattern and symmetry
198
198
205
17 Looking forward: 4-digit numbers
17.1 Numbers to 10,000
17.2 Addition and subtraction with 4-digit numbers
210
210
215
Acknowledgements
224
15.1 Pictograms and bar charts
15.2 Carroll diagrams
16.1 Shape and symmetry
16.2 Pattern and symmetry
4
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How to use this book
How to use this book
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This workbook provides questions for you to practise what you
have learned in class. There is a unit to match each unit in
your Learner’s Book. Each exercise is divided into three parts:
• Focus: these questions help you to master the basics
• Practice: these questions help you to become more confident in
using what you have learned
• Challenge: these questions will make you think more deeply.
2
Addition,
subtraction and money
You might not need to work on all three parts of each exercise.
2.1 Addition
You will also find these features:
Exercise 2.1
Important words that
Focus
you will use.
decompose
exchange
regroup
single
1 Numbers to 1000
Complete each addition. Show how you found
total.
Workedeach
example
1
M
1
compose
24 + 5 =
Step-by-step examples showing a
way to solve a problem.
SA
48 + 9 =
2
Draw beads on the abacus to show this 3-digit number.
42 + 5 =
2 0
3
6 0 0
100s 10s
1s
Draw six beads on the 100s tower to stand for 600.
37 + 8 =
1.1 Hundreds, tens and ones
100s 10s
1s
There are often
4 What 3-digit numbers are represented below?
a
many different
Complete each addition. Show how you found each total.
ways to solve a
123 + 6 =
153 + 5 =
problem.
These questions will help you
+ 7 =of thinking
develop your254
skills
and working mathematically.
Draw two beads on the 10s tower to stand for 20.
100s 10s
1s
Draw three beads on the 1s tower for 3.
b
100s 10s
235 + 8 =
5
22
10
1s
100s
623
Together, the beads represent the 3-digit
10s 623. 1s
number
What is the value of the ringed digit in each 3-digit number?
1 64
23 7
31 5
128
4 52
381
Practice
6
Write the numbers in the next row of the 1 to 1000 strip.
351
352
353
354
355
356
357
358
359
5360
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Thinking and Working Mathematically
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Thinking and Working
Mathematically
There are some important skills that you will develop as you
learn mathematics.
Specialising
is when I give an
example of something
that fits a rule or
pattern.
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Characterising
is when I explain how
a group of things are
the same.
Generalising
is when I
explain a rule or
pattern.
Classifying
is when I put things
into groups.
6
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Thinking and Working Mathematically
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Critiquing
is when I think about
what is good and what
could be better in my
work or someone
else’s work.
Improving
is when I try to
make my work
better.
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Conjecturing is
when I think of an idea
or question to develop
my understanding.
Convincing
is when I explain my
thinking to someone else,
to help them
understand.
7
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1
Numbers to 1000
1.1 Hundreds, tens and ones
represent
Focus
1
Here is the last row of a 100 square. Write the numbers in
the next row, which is the first row of the 101 to 200 square.
91
92
101
93
94
95
96
97
a
b
201
SA
112
3
98
99
100
Complete these pieces from a 1 to 1000 number strip.
M
2
digit
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Exercise 1.1
c
132
Draw a representation of 316.
How will you show the value of each digit?
8
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1.1 Hundreds, tens and ones
4
What 3-digit numbers are represented below?
b
5
100s
10s
1s
What is the value of the ringed digit in each 3-digit number?
23 7
1 64
4 52
Practice
1 2 8
M
31 5
3 8 1
Write the numbers in the next row of the 1 to 1000 strip.
SA
6
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a
351
352
353
354
355
356
357
358
359
360
9
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1 Numbers to 1000
Worked example 1
Draw beads on the abacus to show this 3-digit number.
2 0
3
100s 10s
1s
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6 0 0
Draw six beads on the 100s tower to stand for 600.
100s 10s
1s
Draw two beads on the 10s tower to stand for 20.
1s
M
100s 10s
Draw three beads on the 1s tower for 3.
1s
SA
100s 10s
623
Together, the beads represent the 3-digit
number 623.
10
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1.1 Hundreds, tens and ones
7
Draw beads on each abacus to show each 3-digit number.
3 0 0
5
7 0
7 0 0
9 0
7
8
1s
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100s 10s
100s 10s
1s
Which three-digit number is represented on each abacus?
100s 10s
1s 100s 10s
1s
9
M
Write this 3-digit number in words.
200
300
400
500
SA
100
600
700
800
900
10
20
30
40
50
60
70
80
90
1
2
3
4
5
6
7
8
9
11
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1 Numbers to 1000
Challenge
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10 Complete these pieces, which come from a 1 to 1000 number strip.
500
899
11 Write the missing numbers on each worm.
217
M
157 167 177
422
452 462
SA
763 773 783
12 Read along each row to find three 3-digit numbers.
5
4
6
Read down each column to find another
three 3-digit numbers.
Write each number in words.
3
1
8
9
7
2
12
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1.2 Comparing and ordering
13
When you have two
different digit cards, you can make
two different 2-digit numbers. So when
you have three different digit cards, you
must be able to make three different
3-digit numbers.
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Is Arun correct? How do you know?
1.2 Comparing and ordering
Focus
Complete these pieces, which come from a 1000 square.
SA
1
M
Exercise 1.2
190
230
350
inequality, inequalities is greater than, > is less than, < symbol
13
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1 Numbers to 1000
2
Compare these numbers and complete the sentences.
100s
10s
1s
2
4
9
1
7
3
.
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is less than
is greater than
.
Write the statements in question 2 using the symbols < and >.
4
Order these numbers from smallest to greatest.
M
3
79
236
64
142
SA
327
smallest
5
greatest
Estimate the value of each number marked on the number line.
0
100
200
300
400
500
600
700
800
900
1000
14
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1.2 Comparing and ordering
Practice
7
Use < and > to write two inequalities about these numbers.
100s
10s
1s
4
5
6
4
6
5
Order these numbers from greatest to smallest.
968
689
greatest
98
96
896
smallest
Mark the numbers from question 7 on the number line.
M
8
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6
100
200
300
400
500
600
700
800
900
1000
SA
0
Challenge
9
Compare these numbers. Write some inequalities using < or >.
100s
10s
1s
5
7
4
7
5
3
5
4
7
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1 Numbers to 1000
10 Yusef looks at the place value grid in question 9 and writes:
547 < 753 > 574
753 < 547 < 574
Write some more inequalities like those written by Yusef.
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11 What could the missing digit be in each of these inequalities?
634 < 6
1
765 >
83
257 > 25
372 <
72
12 Order the heights of these towers from shortest to tallest.
Name of tower
Lakhta Centre
Location
Height in metres
St Petersburg
462
Chicago
442
Burj Khalifa
Dubai
828
Petronas Tower 1
Kuala Lumpur
452
SA
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Willis Tower
Shanghai Tower
Shanghai
632
Lotte World Tower
Seoul
555
shortesttallest
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1.3 Estimating and rounding
13 Write the digits 1 to 9 anywhere in the grid.
0
100
200
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Read across and down the grid to find six 3-digit numbers.
Mark each number on the number line.
300
400
500
600
700
800
900
1000
1.3 Estimating and rounding
Focus
Estimate how many stars there are in the box.
SA
1
M
Exercise 1.3
estimate gram (g)
range round, rounding
17
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1 Numbers to 1000
2
Estimate how many grains of rice are on the middle spoon.
400 – 600
PL
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100 – 200
4
Round each number to the nearest 10.
271
138
397
404
M
3
Round each number to the nearest 100.
164
325
250
SA
449
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1.3 Estimating and rounding
Practice
5
Class 3 used this table to check their estimates of the
number of beans in different plastic bags.
Number of beans
Mass of beans
200
300
400
500
600
10 grams
15 grams
20 grams
25 grams
30 grams
35 grams
M
700
5 grams
PL
E
100
40 grams
900
45 grams
1000
50 grams
SA
800
6
a
Samira estimated that her plastic bag had 300 to 400 beans.
They weighed 18 grams. Is this a good estimate?
b
Pedro’s beans weighed 31 grams.
What range would be a good estimate for his beans?
Round each amount to the nearest $10.
$537
$695
$808
$772
19
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1 Numbers to 1000
Round each amount to the nearest 100 kilograms.
150 kilograms
kilograms
555 kilograms
kilograms
444 kilograms
kilograms
501 kilograms
Challenge
8
PL
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7
kilograms
Round the height of each tower to the nearest 10 metres
and then to the nearest 100 metres.
Name of tower
St Petersburg
M
Lakhta Centre
Location
462
Chicago
442
Burj Khalifa
Dubai
828
Petronas Tower 1
Kuala Lumpur
452
SA
Willis Tower
Shanghai Tower
Shanghai
Lotte World Tower Seoul
9
Height in Nearest
Nearest
metres 10 metres 100 metres
632
555
Which towers are the same height when their heights are
rounded to the nearest 100 metres?
10 Zara rounds a number to the nearest 10 and then to the
nearest 100. Her answer both times is 500.
What could her number be?
20
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1.3 Estimating and rounding
11 Follow the rounding instructions.
What do you notice about the results of rounding to 100?
323 645 809
747 558 178
Round to
nearest 10
Round to nearest 100
M
Round to nearest 100
PL
E
952 216 448
SA
12 In a shop, all prices are rounded to the nearest Rs10.
Would all the customers be happy about the changes in price?
21
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2
Addition and
subtraction
Exercise 2.1
Focus
1
PL
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2.1 Addition
compose
decompose
exchange
regroup
single
Complete each addition. Show how you found each total.
42 + 5 =
48 + 9 =
37 + 8 =
SA
M
24 + 5 =
123 + 6 =
153 + 5 =
254 + 7 =
235 + 8 =
2
Complete each addition. Show how you found each total.
22
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2.1 Addition
3
Estimate and then complete each addition to find the total.
estimate =
112 + 26 =
+20
132
164 + 28 =
+20
164
4
PL
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112
estimate =
184
Cheng did not have enough time to finish his calculations.
Complete them both for him.
a
315 + 232
estimate: 320 + 230 = 550
SA
=
M
= 300 + 10 + 5 + 200 + 30 + 2
b
247 + 218
estimate 250 + 220 =
= 200 + 40 + 7 +
=
23
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2 Addition and subtraction
Practice
6
Read across or down the grid to find a 2-digit number.
Add 6 to each number. Show how you found your totals.
4
3
7
8
Complete each addition. Show how you found each total.
246 + 3 =
171 + 7 =
269 + 9 =
M
345 + 8 =
The baker made 246 small cakes and 26 large cakes.
How many cakes did the baker make all together?
SA
7
PL
E
5
Estimate and then find the total. Show your method.
24
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2.1 Addition
8
A market stall has 38 apples left.
A box of 148 apples are delivered.
How many apples are on
the stall now?
359 children and 218 adults
visited the play park today.
How many people visited the
play park today?
M
9
PL
E
Estimate, then calculate.
Show your method.
SA
Estimate and then calculate.
Show your method.
10 Estimate the total, then use an empty number line to help
you add 414 and 268.
25
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2 Addition and subtraction
Challenge
11 The addition machine adds 56 to each number in the grid.
Estimate and then complete the answer grid.
How will you find the totals?
122 225 413
134 229 516
+ 256
total
M
estimate
PL
E
430 328 117
++
12 Marina spilt some ink on the ones digits in her number sentence.
32
+ 14
= 475
SA
What could her calculation have been? Find all the possible answers.
26
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2.2 Subtraction
2.2 Subtraction
Exercise 2.2
Focus
Complete each subtraction. Show how you found each answer.
38 − 5 =
64 − 7 =
2
PL
E
1
49 − 7=
25 − 8=
Complete each subtraction. Show how you found each answer.
238 − 4=
M
169 − 6 =
243 − 7=
SA
134 − 8 =
3
Estimate and then complete each subtraction.
184 – 42 =
–40
144
361 – 33 =
estimate = 180 –
184
estimate = 360 –
331
=
361
=
27
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2 Addition and subtraction
4
Emyr did not have enough time to finish his calculation.
Complete them both for him.
estimate: 460 − 250 =
estimate: 370 − 220 =
No regrouping needed.
Regroup 373 into 300 + 60 + 13.
373 = 300 +
− 246 = 200 + 40 + 6
=
Practice
5
+
PL
E
458 = 400 + 50 + 8
− 217 = 200 + 10 + 7
=
Sort these subtractions into the table.
47 − 3
72 − 17
87 − 29
93 − 8
54 − 5
61 − 15
76 − 23
57 − 7
No regrouping needed to find
the answer
SA
M
Change a ten for 10 ones
to find the answer
6
The shop has 268 metres of rope.
Minh buys 5 metres.
How much rope does the shop have now?
HARDWARES
The next day, Loki buys 8 metres of rope.
How much rope is left in the shop now?
28
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2.2 Subtraction
7
763 children attend Blue
Haven School. 38 children
are away today. How many
children are in school today?
8
PL
E
Estimate and then find the
answer. Show your method.
There are 362 people on the train. At the first station, 47 people get
off and no one gets on. How many people are on the train now?
SA
M
Estimate and then find the answer. Show your method.
9
763 children attend Blue Haven School. 427 of them are girls.
How many boys are there?
Estimate and then calculate. Show your method.
29
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2 Addition and subtraction
10 Estimate and then use an empty number line to help you find the
difference between 426 and 483.
Challenge
PL
E
11 The subtraction machine subtracts 37 from each number in the grid.
Estimate and then complete the answer grid.
How will you find the totals?
228
691
154
545
472
989
863
366
M
179
+ 256
total
SA
estimate
+
12 Ahliya spilt some ink on the ones digits in her number sentence.
55
+ 31
= 232
What could her calculation have been? Find all the possible answers.
30
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2.3 Roman numbers
2.3 Roman numbers
Exercise 2.3
Focus
Join the Roman numerals and the matching numbers.
VIII
4
1
III
IV
3
8
2
I
7
5
V
VII
Write the value of each representation in Roman numerals and
the numbers we use today.
SA
2
II
VI
M
6
PL
E
1
10
1
31
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2 Addition and subtraction
Practice
4
a
4
c
8
b
16
d
19
Write these Roman numbers using the numbers we use today
a
III
b
IX
c
XVII
d
XIV
Look out for examples of Roman numerals at home. You might
see them on a clock face, at the end of a television programme
or film, in books, in newspapers, when numbering things like
sporting events or kings and queens, or somewhere else.
You could ask an adult to help you. Draw what you saw.
SA
M
5
Write these numbers using Roman numerals
PL
E
3
32
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2.3 Roman numbers
Challenge
Here is a clockface using Roman numerals. Which number is different
from what you would expect?
7
Draw the hands on the analogue clocks to match the digital clocks.
SA
M
PL
E
6
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3
Multiplication and
division
Exercise 3.1
Worked example 1
PL
E
3.1 Exploring multiplication
and division
Draw a ring around the multiples of 10.
commutative
multiple
pattern
sequence
term
term-to-term rule
(recursion rule)
M
23, 147, 60, 194, 220, 381, 600, 425,
276, 390
array
23, 147, 60, 194, 220, 381, 600, 425, Multiples of 10 always have 0 in
276, 390.
the ones place.
23, 147, 60 , 194, 220 , 381, 600 ,
SA
425, 276, 390 .
I can see 60, 220, 600 and 390 with
0 in the ones place. They are all
multiples of 10, so I need to draw
a ring around each of them.
Focus
1
Draw a ring around all the multiples of 5.
15, 72, 125, 230, 86, 157, 390, 269, 95, 414
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3.1 Exploring multiplication and division
Mosego sorted the
numbers from 20 to 40
into the correct places
in the table. Finish
Mosego’s work by
putting numbers 35
to 40 in the correct
places in the table.
numbers 20 to 40
multiples of 2
multiples of 5
20, 22, 24, 26, 28,
30, 32, 34
20, 25, 30
PL
E
2
Which numbers can not be added to the table? Why?
Write the fact family for this array.
M
3
=
SA
×
4
÷
=
×
=
÷
=
=
×
=
÷
=
×
=
÷
Write the multiplying by 10 facts shown here.
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3 Multiplication and division
100s
10s
7
1s
7
0
100s
1
10s
1
9
1s
9
0
Practice
Describe the multiples of 2, 5 and 10.
Use the words ‘odd’ and ‘even’.
PL
E
5
M
How are multiples of 2 and 10 the same?
How are the multiples of 5 different?
I am an odd number. I am > 70 but < 80. I am a multiple of 5.
Which number am I?
7
Which multiplication facts from the 1, 2, 5 and 10 multiplication
tables have only four facts in their fact family?
SA
6
Write the fact family for one of these facts.
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3.1 Exploring multiplication and division
This machine multiplies numbers by 10. Complete the grid
to record the numbers after they come out of the machine.
74
9
56
6
82
29
17
38
5
3
94
61
Challenge
9
×
× 10
PL
E
8
I am an even number. I am > 374 but < 386.
I am a multiple of 2, 5 and 10. Which number am I?
10
SA
M
The multiplication
fact 1 × 1 = 1 is special because all
the numbers in the fact family are the
same and there isn’t another fact
family like that.
Find a different special multiplication fact from the
1, 2, 5, 10 fact families. Explain why it is special.
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3 Multiplication and division
PL
E
11 Binh has ten 65 cm lengths of timber.
What is the total length of timber that Binh has?
12
M
0 × 10 = 10, because
multiplying by 10 makes any number
ten times larger.
SA
Do you agree with Arun? Why?
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3.2 Connecting 2 ×, 4 × and 8 ×
3.2 Connecting 2 ×, 4 × and 8 ×
Exercise 3.2
Focus
Which multiplication fact is represented below?
four
four
four
PL
E
1
×
=
2
Write the multiplication table for 4, up to 4 × 10 = 40.
3
Colour all the multiples of 8. What do you notice about these numbers?
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
22
23
24
25
26
27
28
29
30
32
33
34
35
36
37
38
39
40
46
47
48
49
50
21
SA
31
M
1
41
4
42
43
44
45
There are six spiders on a plant. Write and solve
the multiplication fact to find out how
many spiders’ legs are on the plant.
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3 Multiplication and division
Worked example 2
The term-to-term rule is ‘add 4’.
Start at 2. What are the next five numbers in the sequence?
How could you describe the numbers in this sequence?
2, 6,
,
,
,
,
,
PL
E
,
2,
The term-to-term rule tells me what to do to
find the next number in the sequence.
,
2+4=6
2, 6, 10, 14, 18, 22
Now I can add 4 to that number to find
the next number and keep going to find
the rest of the sequence.
6 + 4 = 10
10 + 4 = 14
M
14 + 4 = 18
18 + 4 = 22
SA
All the numbers are even. They are all 2 more (and 2 fewer) than
a multiple of 4. The first two numbers have 1-digit, all the others
are 2-digit numbers.
5
The term-to-term rule is ‘add 4’. How could you describe the
numbers in this sequence?
Start at 3. What are the next five numbers in the sequence?
3,
,
,
,
,
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3.2 Connecting 2 ×, 4 × and 8 ×
Practice
6
What is the third multiple of 4?
What is the seventh multiple of 4?
What are the next five multiples of 4?
,
40,
PL
E
7
,
,
,
8
Describe the pattern of the multiples of 4.
9
What is the fifth multiple of 8?
M
What is the ninth multiple of 8?
10 Write the missing multiplication facts.
SA
4 × 4 = 16
2×2=4
double →
double →
halve →
halve →
8 × 8 = 64
2 × 7 = 14
11 What is the term-to-term rule in the sequence below? Find the
missing numbers. How could you describe the numbers in
this sequence?
7, 15,
,
,
,
The term-to-term rule is
.
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3 Multiplication and division
Challenge
12 Complete the multiplication grid.
×
2
4
10
20
8
3
5
6
PL
E
13 A pear costs Rs8.
Write the multiplication fact that tells you
the cost of seven pears.
9
SA
$4
M
14 A white T-shirt costs Rs4.
Write the multiplication fact that tells you the cost of 8 T-shirts.
15 Tara’s father bought six pieces of timber,
each measuring 4 metres long.
What is the total length of timber that
Tara’s father bought?
16 Choose a term-to-term rule, a start number and an
end number. Write your sequence. Describe the numbers in
your sequence.
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3.3 Connecting 3 ×, 6 × and 9 ×
3.3 Connecting 3 ×, 6 × and 9 ×
Exercise 3.3
counting stick
Focus
Use the number line to help you find the multiples of 3.
+3
PL
E
1
0 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
3,
,
,
,
,
,
, 30
Use the number line in question 1 to help you find the
multiples of 6. Use the pattern to help you continue to 60.
6,
3
,
,
,
,
,
,
,
M
2
,
,
, 60
Write the missing multiplication facts.
3×2=6
SA
3 × 6 = 18
double →
6 × 4 = 24
halve →
6×1=6
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3 Multiplication and division
4
Multiply the numbers in the bricks next to each other to find
the number for the brick above.
a
b
5
3
1
9
1
2
PL
E
1
The term-to-term rule is add 9. How could you describe the
numbers in this sequence?
Start at 8 and write the next five numbers in your sequence.
8,
,
,
,
6
M
Practice
Multiply the numbers in the bricks next to each other to find
the number for the brick above.
SA
a
1
7
,
6
1
b
3
1
9
Ruby the red kangaroo jumps 9 metres in each jump.
How far does she travel with seven jumps?
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3.3 Connecting 3 ×, 6 × and 9 ×
8
Write the missing multiplication facts.
6 × 3 = 18
3 × 10 = 30
double →
9
6 × 9 = 54
together
→
PL
E
halve →
3×0=0
+ 3× and
6×
8 × 5 = 5 × 5 + 3 × 5 = 25 + 15 = 40
SA
M
Draw a picture to show how you can add the multiplication
tables for 5 and 4 together to find 9 × 6.
Challenge
10 102, 108, 114 and 120 are multiples of 3 and 6.
Which multiples of 3 and 6 are they?
102
108
114
120
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3 Multiplication and division
11 The term-to-term rule is – 9.
Start at 100. What are the next five numbers in the sequence?
How could you describe the numbers in this sequence?
,
100,
,
,
,
PL
E
Is 1 part of this sequence?
12 Zara finds it hard to remember the multiplication
table for 9. She says that she can use the
multiplication table for 10, then subtract 1
from the product for each 9.
SA
M
Do you agree? Why?
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4
3D shapes
4.1 3D shapes
Exercise 4.1
Worked example
prism
PL
E
apex
A pyramid has a flat base and flat sides. The sides are triangles.
They join at the top, making an apex.
Draw a ring around the shapes that are not pyramids.
b
d
e
c
M
a
f
SA
Look at the sides and surfaces of the shapes.
Look for an apex.
a
b
c
d
e
f
b, d and f are not pyramids because they do not have an apex.
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4 3D shapes
Focus
1
A prism has identical ends and flat faces.
The shape at the ends gives the prism a name.
PL
E
This is a rectangular prism.
Ring the shapes that are prisms. Write their names underneath.
a
M
SA
d
b
g
c
e
f
h
i
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4.1 3D shapes
2
For each shape, write its name and the number of vertices
that it has. Use these words to help you.
cube
triangle-based pyramid
Name
Name
Number of vertices
Number of vertices
Name
SA
Name
Number of vertices
3
a
cylinder
Name
M
Number of vertices
triangular prism
PL
E
square-based pyramid
triangular prism
Number of vertices
Name
Number of vertices
Trace over the dashed lines to show 3D shapes.
Write their names underneath.
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4 3D shapes
Sketch two of your own shapes.
c
Tick the shapes that are prisms.
Practice
4
PL
E
b
For each shape, write whether it is a prism or a pyramid.
a
M
e
c
f
SA
d
b
5
Draw and name the 3D shapes.
a
I have six faces and eight vertices.
I have 12 edges and my faces are all the same shape.
What am I?
b
I have six faces and eight vertices. I have 12 edges.
Four of my faces are rectangles, the other two are squares.
What am I?
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4.1 3D shapes
c
I have five faces and six vertices. I have nine edges.
If you cut me in half, my end face will remain the same.
Two of my faces are the same, one is curved.
What am I?
d
I have one smooth surface and 0 vertices. I have 0 edges.
Sketch a cube.
M
6
PL
E
What am I?
SA
Sketch a cuboid.
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4 3D shapes
Challenge
7
Complete the table.
Number of
faces
3D shape
Number of
edges
Number of
vertices
hexagonal prism
PL
E
triangular prism
octagonal prism
triangular-based pyramid
8
Look around you. Find two 3D shapes that are cylinders,
two that are prisms and two that are neither.
SA
M
Draw them.
9
Sketch this shape.
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5
Measurement,
area and perimeter
Exercise 5.1
centimetre (cm)
Focus
1
PL
E
5.1 Measurement
Use a ruler.
kilometre (km)
line segment metre (m)
Estimate and then measure each of these line segments.
a
estimate:
measure:
estimate:
measure:
SA
b
measure:
M
estimate:
c
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5 Measurement, area and perimeter
2
Draw line segments of lengths 2 cm, 5 cm and 7 cm. Label them.
PL
E
d
Measure and record the radius and diameter of each circle in
centimetres. Use a ruler.
a
M
b
radius
cm
diameter
SA
cm
3
cm
radius
diameter
cm
Find the length of the objects, to the nearest centimetre.
a
71
72
73
74
75
76
77
78
79
80
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5.1 Measurement
b
13
14
19
20
21
c
Practice
16
18
19
20
21
22
23
24
25
26
27
28
Complete the sentence. Round the answer to the
nearest centimetre.
2
3
4
SA
1
5
The length of the pencil is about
5
17
M
4
15
PL
E
12
6
7
8
9
10
cm.
Measure and record the radius and diameter of
this circle in centimetres. Use a ruler.
Round your measurements to the nearest
centimetre or half centimetre.
radius
diameter
cm
cm
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5 Measurement, area and perimeter
a
Estimate the height of each picture.
Estimate:
7
measure:
estimate:
measure:
Draw and measure a person shorter than Arun.
M
b
PL
E
6
Draw a ring around the correct answers.
300 cm
b
1
How many centimetres are in 3 metres?
SA
a
350 cm
2
35 cm
1
How many centimetres are in 5 m?
550 cm
575 cm
c
500 cm =
m
d
250 cm =
m
e
Which is more:
3
4
4
525 cm
500 cm
m or 700 cm?
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5.1 Measurement
Challenge
aFind the lengths of the key and paper clip, to the
nearest centimetre.
1
2
3
Length of key:
4
5
6
7
cm Length of paper clip:
cm
Use this ruler to measure four things in your house.
0
M
b
PL
E
8
1
2
3
4
5
6
7
8
9
10 11
12 13 14
15
SA
Round the measurements to the nearest centimetre.
Draw and label what you have found.
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5 Measurement, area and perimeter
9
a
Collect four objects that you estimate to be 20 cm long.
Draw them and then measure them.
How close were your estimates?
b
Find four objects that you estimate to be half the length
of the others.
PL
E
Draw them and then measure them.
How close were your estimates?
10 Use what you know about circles to help you complete this table
without measuring
Circle
a
radius
diameter
30 Km
b
28 m
c
11 cm
M
11 Ali swims 8 diameters of a circular pool. The radius of the pool is 50
metres. How far does Ali swim?
12 Complete the number sentences.
3
a
5 m=
c
250 m =
e
Write three number sentences of your own.
cm
SA
4
km
b
10 m =
d
750 m =
cm
km
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5.2 2D shapes and perimeter
5.2 2D shapes and perimeter
Exercises 5.2
irregular shape
Focus
perimeter
1
polygon
PL
E
Inside each grid, draw a quadrilateral.
Write ‘regular’ or ‘irregular’ below each shape.
quadrilateral
a
regular shape
b
a
What is the perimeter of this quadrilateral?
SA
2
d
M
c
4 12 cm
1
4 2 cm
Tip
Add the whole numbers first
and then the fractions.
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5 Measurement, area and perimeter
b
Draw a square with a perimeter of 16 cm. Use your ruler.
What is the perimeter of this triangle?
M
c
PL
E
How long is each side?
SA
4 cm
3
a
b
stimate the length of each side. Use a ruler
E
to measure.
I estimated
cm.
I measured
cm.
How close was your estimate?
3 cm
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5.2 2D shapes and perimeter
c
How many centimetres were you away from
the measurement?
cm
d
Work out the perimeter of the shape.
cm.
PL
E
The perimeter is
Show how you worked that out.
Practice
4
Draw three regular shapes and draw three irregular shapes.
Label them.
a
g
5
M
c
e
f
SA
d
b
Write two differences between regular and irregular shapes.
Sana says it is easier to find the perimeter of a square than an irregular
quadrilateral. Explain why Sana might think this.
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5 Measurement, area and perimeter
a
Measure this square.
PL
E
6
The perimeter is
b
Halve its measurements and draw it here.
The perimeter is
c
cm.
cm.
Double its measurements and draw it here.
cm.
SA
M
The perimeter is
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5.2 2D shapes and perimeter
a
Estimate the lengths of these sides.
PL
E
7
estimate:
measure:
b
My estimate was
c
What is the perimeter of the square?
Show how you worked that out.
M
away from the measured length.
Challenge
aDraw three squares that have sides the same length but
look different.
SA
8
b
Draw three triangles with sides the same length but look different.
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5 Measurement, area and perimeter
9
a
This pentagon has sides of 16 metres.
b
PL
E
What is its perimeter? Show how you worked out
the answer.
Use a ruler to draw a rectangle. Choose the length of it sides.
Calculate the perimeter.
SA
M
10 a Estimate the length of these sides, then use a ruler
to measure them.
estimate:
measure:
b
Calculate the perimeter of the octagon.
c
If each line is made 2 cm longer, what will be the perimeter?
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5.3 Area
5.3 Area
Exercises 5.3
area
Worked example
square units
PL
E
How many squares are inside this shape?
1
Focus
1
M
This shape has been made with 6 squares: 5 whole squares and
2
3 half squares.
How many squares are inside each shape?
b
SA
a
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5 Measurement, area and perimeter
Complete the triangle.
PL
E
2
Its area is
3
square units.
Find the areas and perimeters of these shapes.
Shape
a
SA
c
Perimeter
M
b
Area
d
e
What is the area and perimeter of the next shape in the series?
Draw it.
f
What do you notice about the numbers that you have
written for the area and the perimeter?
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5.3 Area
Practice
Estimate and calculate the area of these shapes.
b
d
e
c
PL
E
a
f
a
estimate:
b
estimate:
measure:
c
estimate:
measure:
d
estimate:
measure:
e
estimate:
measure:
f
estimate:
measure:
M
measure:
SA
4
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5 Measurement, area and perimeter
5
Draw lines to join the pairs of shapes that have the same area.
b
d
6
a
c
PL
E
a
e
f
Work out the area and the perimeter of these shapes.
Area
Perimeter
SA
M
Square
b
Can you predict the area and the perimeter of the next
shape in the series?
c
What do you notice about the area and the perimeter of 16 squares?
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5.3 Area
Challenge
7
Estimate then measure the length of the sides of these shapes.
Then calculate the area of each shape.
b
Estimate:
Measure:
Measure:
Area:
d
SA
c
Estimate:
M
Area:
PL
E
a
Estimate:
Estimate:
Measure:
Measure:
Area:
Area:
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5 Measurement, area and perimeter
f
Draw a shape that has an area less than the smallest
area of the shapes a to d.
a
Draw a rectangle with an area of 12 square units.
PL
E
Which shape has the largest area?
Use the squared paper to help you.
SA
M
8
e
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5.3 Area
1
Draw any shape with an area of 13 square units.
2
If the area of a square is 25 square units.
a
How long are each of its sides?
b
How long is the perimeter? Show your working.
SA
9
M
PL
E
b
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6
Fractions of
shapes
Exercise 6.1
Worked example 1
PL
E
6.1 Fractions and equivalence
denominator
of shapes
equal
equivalent
fifths
numerator
This rectangle has four equal parts.
tenths
M
thirds
It is divided into quarters. One part is called one-quarter.
Colour three-quarters.
b
How many quarters are not coloured?
SA
a
a
b
There is one-quarter not coloured.
Count the empty
squares to find the number
that are not coloured.
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6.1 Fractions and equivalence of shapes
Focus
1
For each shape, shade the fraction shown below it.
a
b
c
PL
E
one-third
two-fifths
three-tenths
How many squares are not coloured for each shape?
a
c
Which fractions are shown here?
Count the number of parts in each whole shape.
b
c
d
SA
a
M
2
b
3
The dots have been joined to make more triangles.
Number the equal parts of the triangle.
There are
equal parts.
Each part is called a
There are four
.
that make a whole.
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6 Fractions of shapes
Practice
4
Tip
Divide these shapes into
two equal parts.
PL
E
Count the number of small
squares in each shape.
Use what you know about multiples
3 and 5 to work out the number of
squares that you will need.
SA
M
Draw shapes that can be divided into three equal parts.
Draw shapes that can be divided into five equal parts.
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6.1 Fractions and equivalence of shapes
5
Colour two different ways to show one-third of this rectangle.
PL
E
Colour two different ways to show one-fifth of this square.
SA
M
Colour two different ways to show four-tenths in this rectangle.
Tip
Work out what one-tenth is first.
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6 Fractions of shapes
6
Draw equivalent fractions to match the ones on the left.
Use fifths and tenths.
a
b
PL
E
1
2
1 whole
c
2
5
d
M
8
10
SA
Challenge
7
Write the fractions.
a
b
c
d
e
Draw these fractions.
f
2
4
g
2
3
h
4
5
i
8
j
10
1
2
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6.1 Fractions and equivalence of shapes
This is a third of a shape.
Draw two different whole shapes.
b
What if it was one-fifth of a whole shape?
Draw two different whole shapes.
PL
E
a
SA
M
8
c
This is one-tenth of a whole shape.
Draw two different shapes that it could be.
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6 Fractions of shapes
9
Put a tick in the box if the fractions are equivalent.
Put a cross in the box if they are not equivalent.
a
PL
E
b
c
d
SA
g
f
M
e
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PL
E
7
Statistics: tally
charts and frequency
tables
7.1 Statistics
Exercise 7.1
Focus
1
chance
frequency table
survey
Complete the tally chart using the data.
M
17 triangles, 25 squares, nine pentagons, 24 circles
Tally
SA
Shape
a
What is the total number of shapes?
b
Which shape is there the most of?
c
Which shape is there the fewest of?
d
Which two shapes total 42?
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7 Statistics: tally charts and frequency tables
2
Use the tally chart in question 1 to make a frequency table.
Draw the shapes.
3
Frequency
PL
E
Shape
Fill in the missing parts of this table.
Ways of travelling
walk
bus
car
Frequency
1
6
M
bike
Tally
SA
Practice
4
Complete the tally chart to show the numbers of vertices
in each shape.
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7.1 Statistics
Number of vertices
Tally
0
1
2
4
5
PL
E
3
Write three different things that the tally chart shows you.
1
2
3
M
This frequency table shows the number of sweets in 20 bags.
Number of sweets
Frequency
23
1
24
4
25
9
26
3
27
3
SA
5
Use the data in the frequency table to write three questions
for your partner.
1
2
3
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7 Statistics: tally charts and frequency tables
This table shows the colour of the cars parked outside
the school.
white
purple
black
purple
black
green
red
green
blue
white
purple
white
yellow
blue
white
blue
black
green
green
yellow
blue
yellow
black
blue
PL
E
6
Complete the table to show the car colours.
Colour
Tally
blue
black
red
yellow
green
purple
M
Frequency
white
Write three questions about the data in the table for
your partner to answer.
SA
1
2
3
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7.1 Statistics
Challenge
7
Nasif does a survey. He asks his classmates what kind of
pet they have. He records the data like this.
Pets
Tally
Frequency
cat
fish
PL
E
26
8
rabbit
4
horse
3
other
10
Total
42
Trang is ill and cannot go to school. She counts and
records the number of people in cars travelling down
her street in 2 hours.
Number of people in each car
Number of cars
1
41
2
54
3
32
4
20
5
3
SA
8
M
Nasif has made three mistakes.
Find his mistakes and correct them.
a
How many cars went past Trang’s house?
b
How many people in total travelled in those cars?
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7 Statistics: tally charts and frequency tables
9
These are the results of a survey of the most popular rides
at the funfair from 3 p.m. to 4 p.m.
a
Complete the tally chart and frequency table.
Ride
Tally
Frequency
bumper cars
Ferris wheel
helter skelter
roller coaster
teacups
waltzers
23
14
28
21
M
drop tower
PL
E
carousel
pirate ship
b
27
Write three questions for your partner to answer.
SA
1
2
3
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8
Time
8.1 Time
analogue clock
Exercise 8.1
Worked example 1
PL
E
digital clock
minute
Write these times in words.
a
4:02
a
4:02
4:00 can be written in words as two minutes past four.
b
5:12
5:12 can be written in words as twelve minutes past five.
c
8:30
8:30 can be written in words as half past eight or thirty
minutes past eight.
c
8:30
Write these times in words.
a
6:01
b
3:30
c
12:14
d
8:45
SA
1
5:12
M
Focus
b
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8 Time
3
Write these times in digital form.
a
half past eight
b
thirty-four minutes past two
c
four o’clock
d
forty-two minutes past six
PL
E
2
Fill in the empty digital clocks.
11 12 1
10
2
a
9
7 6
5
4
M
8
3
11 12 1
10
2
b
9
7 6
5
4
SA
8
3
c
11 12 1
10
2
9
8
3
7 6
5
4
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8.1 Time
Practice
Draw the hands on the clocks to show the correct time.
a
b
11 12 1
10
2
9
8
3
7 6
5
9
4
8
1:35
5
11 12 1
10
2
c
3
7 6
5
9
4
d
11 12 1
10
2
8
9
3
7 6
5
11 12 1
10
2
8
4
3
7 6
5
4
PL
E
4
6:54
4:28
10:44
Write three digital times that come between the times shown.
Draw the hands on the analogue clock to match the digital time.
a
M
6
11 12 1
10
2
3
SA
9
8
c
7 6
5
9
3
7 6
5
4
11 12 1
10
2
9
4
11 12 1
10
2
8
b
8
d
3
7 6
5
4
11 12 1
10
2
9
8
3
7 6
5
4
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8 Time
Challenge
8
Complete these sentences.
a
3:45 is the same as quarter to
b
A quarter to two can be written as
c
A quarter to eleven can be written as
d
10:15 can be written as
e
1:45 is the same as quarter to
PL
E
7
Dembe looks at her digital watch and sees that each number
is one higher than the number to its left.
Find three different times that she might see.
M
Write the times underneath, using words for analogue times.
Write any time that comes between the two times shown.
SA
9
a
11 12 1
10
2
9
3
8
7 6 5
1:11
4
11 12 1
10
2
9
3
8
7 6 5
11:37
4
b
11 12 1
10
2
9
3
8
7 6 5
2:00
4
11 12 1
10
2
9
3
8
7 6 5
4
2:30
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8.1 Time
c
11 12 1
10
2
9
3
8
7 6 5
10 a
8
7 6 5
4
d
11 12 1
10
2
9
3
8
7 6 5
7:32
11 12 1
10
2
9
3
4
8
9:30
7 6 5
4
10:00
PL
E
7:01
4
11 12 1
10
2
9
3
Draw hands on the analogue clock and write on the digital clock
the time that you get up in the morning. Is this a.m. or p.m.?
11 12 1
10
2
3
8
7 6
5
4
Draw hands on the analogue clock and write on the digital clock
the time that you go to bed. Is this a.m. or p.m.?
SA
b
M
9
11 12 1
10
2
9
8
3
7 6
5
4
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9
More addition
and subtraction
Exercise 9.1
Focus
1
PL
E
9.1 Addition: regrouping tens
and reordering
associative
column addition
commutative
Estimate the total. Find the total and represent it in the
place value grid. Complete the number sentence.
10s
SA
M
100s
1s
estimate:
100s
+
10s
1s
=
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9.1 Addition: regrouping tens and reordering
Estimate and then solve these 2-digit number additions.
Show your method.
a
53 + 76 =
c
Estimate:
46 + 81 =
3
b
Estimate:
65 + 54 =
d
Estimate:
66 + 42 =
Estimate then solve these additions. Show your method.
a
Estimate:
Estimate:
SA
c
b
Estimate:
187 + 50 =
M
129 + 60 =
164 + 71 =
4
Estimate:
PL
E
2
d
Estimate:
245 + 172 =
Write one thousand in numbers.
How many hundreds are there in one thousand?
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9 More addition and subtraction
Add these single-digit numbers together in two different ways.
Is there a complement to 10 that you can use to help you?
4
5
Practice
6
6
PL
E
5
Sort these additions into the table.
25 + 57 75 + 63 34 + 52 28 + 61
54 + 82 96 + 21 34 + 38 69 + 27
43 + 55 36 + 46 46 + 31 67 + 52
Regrouping ones
Regrouping tens
SA
M
No regrouping
7
How do you know if you need to regroup ones when adding?
8
Tick the true statements.
When I add a 3-digit number and some tens:
a
the ones digit does not change
b
the tens digit always changes
c
the hundreds digit always changes
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9.1 Addition: regrouping tens and reordering
9
Estimate then solve these additions. Show your method.
a
b
Estimate:
135 + 73 =
Estimate:
d
245 + 272 =
Estimate:
PL
E
c
Estimate:
571 + 243 =
352 + 153 =
M
10 Sofia says that the only new number word that she learned
in Stage 3 was thousand. Is she correct? Explain why.
11 Nawaf adds three different single-digit numbers. His total is 18.
SA
Find three different sets of three numbers with a total of 18.
Which complements to 10 did you use?
12 Estimate and then add 375, 321 and 283. Show your method.
Estimate:
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9 More addition and subtraction
Challenge
b
PL
E
13 aOditi adds a 3-digit number and some tens. Her total is 364.
What could her numbers be?
Usman finds six possible solutions.
Can you find more than six solutions?
14 Add the numbers in each set together. Show your method.
3
8
2
7
4
5
9
8
6
9
2
4
1
5
8
SA
M
4
7
Compare your method with your partner’s method.
How are they the same? How are they different?
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9.1 Addition: regrouping tens and reordering
15 Here are Afua’s column additions.
227
151
213
+ 243
+ 334
8
14
140
60
+ 400
548
PL
E
154
+ 700
774
SA
M
Why do you think that Afua added her numbers in the
order shown?
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9 More addition and subtraction
9.2 Subtraction: regrouping tens
Exercise 9.2
Focus
Estimate the answer.
Find and represent your answer in the place
value grid. Complete the number sentence.
trial and improvement
PL
E
1
Estimate:
158 – 73 =
10s
M
100s
10s
1s
1s
SA
100s
unknown
+
=
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9.2 Subtraction: regrouping tens
2
Estimate and then solve these subtractions. Show your method.
a
b
Estimate:
178 − 53 =
Estimate:
154 − 72 =
d
Estimate:
236 − 84 =
Mum buys two packets of sweets.
There are 42 sweets all together.
If both packets have the same number of sweets,
how many sweets are in each packet?
Use trial and improvement to help you find your answer.
SA
M
3
267 − 64 =
PL
E
c
Estimate:
+
= 42
So
=
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9 More addition and subtraction
Practice
Sort these subtractions into the table.
188 – 54
337 – 119
345 – 213
247 – 163
269 – 182
276 – 163
437 – 264
257 – 125
143 – 28
736 – 283
296 – 158
172 – 127
No regrouping
PL
E
4
Regrouping ones
Regrouping tens
How do you know if you need to regroup tens when subtracting?
6
Estimate and then solve the subtractions that you sorted
into the regrouping tens part of the table in question 4.
Show your method.
SA
M
5
Share and discuss your methods with your partner.
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9.2 Subtraction: regrouping tens
7
Here is Danh’s calculation of 419 – 187.
What mistakes has Danh made?
Estimate: 410 – 180 = 230
419 = 400 + 10 + 9
– 187 = 100 + 80 + 7
PL
E
300 + 70 + 2 = 372
Check: 372 + 187 = 559
8
A newspaper shop has 364 newspapers delivered
early in the morning. By lunchtime there are only 83 left.
How many newspapers have been sold?
Use trial and improvement to help you find out.
364 –
So
=
SA
M
= 83
Challenge
9
When you subtract 90 from a 3-digit number, you will
need to exchange 1 hundred for 10 tens.
Is this always true, sometimes true, or never true?
Explain your answer.
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9 More addition and subtraction
10 There are 764 children in the school.
392 of them are girls.
How many boys are there?
PL
E
Write your number sentence and show your method.
Remember to estimate before you calculate!
11 Kwanza buys two footballs.
Kwanza pays Rs38 for the footballs.
What is the price of each football?
Use trial and improvement to help you find out.
= Rs38
So
=
M
+
SA
Explain to your partner what you did to find your answer.
12 Aarvi and her family are travelling 354 kilometres
to visit her grandparents.
When the family stops for lunch, they have 171 kilometres to go.
How far have they travelled when they stop for lunch?
Use trial and improvement to help you find out.
354 –
= 171
So
=
100
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9.3 Complements
9.3 Complements
Exercise 9.3
blank
Focus
mentally
Which complements for 100 are shown on the blank 100 squares?
Write the matching number sentences.
PL
E
1
complement
SA
M
a
+
= 100
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9 More addition and subtraction
What are the six complements for 1000, using multiples of 100?
SA
2
= 100
M
+
PL
E
b
Practice
3
Find the complement of 100 for each number.
Write your answer in the matching square of the grid.
19
82
93
46
78
37
3
51
64
complement
of 100
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9.3 Complements
Use the complements that you found in question 3 to
write nine number sentences that have a total of 100.
+
= 100
+
= 100
+
= 100
+
= 100
+
= 100
+
= 100
+
= 100
PL
E
4
+
= 100
5
Find all the pairs of numbers with 5 tens that are
complements for 1000.
6
Complete Ibrahim’s estimates. Remember to calculate
to find the estimates.
410 + 240 =
c
940 – 340 =
M
a
b
720 + 180 =
d
530 – 270 =
+
= 100
SA
Challenge
7
Use complements of 100 to help you solve these problems.
a
There are 100 books on the bookshelf.
23 are borrowed.
How many books are left on the shelf?
b
Liling has 100 marbles.
She lost 17 of them.
How many marbles does she have left?
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9 More addition and subtraction
Ajmal has Rs100.
He spends Rs38.
How much money does he have left?
d
43 cm was cut off a 1 metre length of string.
How long is the remaining piece?
e
There are 100 pencils in a pack.
32 children are given a new pencil.
How many pencils are left?
PL
E
8
c
Complete the complements for the 100 cross-number puzzle.
The answer to each clue is the complement for 100 for that number.
3
2
Tip
M
1
4
6
SA
5
7
9
Across
7 26
1 73
8 81
2 25
9 49
3 59
4 68 10 43
5 53
8
Think about where each
number is, on a 100
square. The number of
squares that will take
you to 100 is the
complement to 100
of that number.
10
Down
1 79
2 28
3 52
4 63
5
6
7
8
56
11
29
83
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9.3 Complements
9
1
2
3
4
5
6
7
8
9
Use each digit only once to make complements of multiples
of 10 to 1000. Which digit is not used?
+
0
+
Unused digit is
0
= 1000
PL
E
0
0
= 1000
.
10 Complete Hasan’s estimates.
Remember to calculate mentally to find the answers.
170 + 390 =
c
960 – 570 =
e
840 – 490 =
M
a
b
420 – 280 =
d
430 + 490 =
f
750 – 670 =
SA
11 I am a 3-digit complement to a multiple of 10 less than 1000.
My digits add up to 16.
The digits of the 3-digit number that my complement and
I add to has digits that total to 17.
What number could I be?
What number could my 3-digit multiple of 10 complement be?
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10 More multiplication
and division
Exercise 10.1
diagonal
extend
product
Focus
Complete these rows from the multiplication square.
Think about how you can use one row to help you
complete another row.
×
2
1
2
3
4
5
6
7
8
9
10
SA
4
M
1
PL
E
10.1 Revisiting multiplication
and division
8
2
Use the multiplication grid in question 1 to help you find
the numbers in the fact family for 32. Write the fact family.
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10.1 Revisiting multiplication and division
3
Extend each sequence. What is the term-to-term rule for each sequence?
How could you describe the numbers in this sequence?
a
,
8, 12, 16, 20,
,
.
The term-to-term rule is
b
.
,
,
.
PL
E
26, 31, 36, 41,
The term-to-term rule is
d
.
,
27, 24, 21, 18,
,
.
The term-to-term rule is
Complete these rows from the multiplication square.
Think about how you can use one row to help you
complete another row.
SA
4
M
Practice
.
×
1
2
3
4
5
6
7
8
9
10
3
6
9
5
Which eight numbers are included four times in the
multiplication grid?
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10 More multiplication and division
6
Choose a number that is included in the multiplication
grid twice. Write its fact family.
PL
E
Challenge
Which numbers are included three times in the multiplication grid?
Explain why.
8
Sanjay wonders why there is no zero row or column on
the multiplication square. Explain why to Sanjay.
9
Jinghua wants to write a sequence with the term-to-term
rule – 9. Where could she look on the multiplication square
to get started?
SA
M
7
10 17 and 29 are two of the numbers in a sequence.
What could the sequence be? What is the term-to-term rule?
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10.2 Playing with multiplication and division
10.2 Playing with multiplication
and division
Exercise 10.2
Focus
2
quotient
PL
E
1
distributive
a
2×3×5
c
5×5×4
b
4×5×6
d
9×3×2
Complete these simplified multiplications.
×3=
10 × 5 =
+
18 × 3 =
M
14 × 5 =
SA
+
×3=
4×5=
3
simplify
Multiply each set of three numbers in any order
to simplify the calculation and find the product.
Complete each division.You could use counters to help you.
a
20 ÷ 2 =
b
21 ÷ 3 =
c
20 ÷ 4 =
d
20 ÷ 5 =
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10 More multiplication and division
Practice
aChoose three 1-digit numbers to multiply together
to make an easy calculation. Find the product.
×
b
×
=
Choose three 1-digit numbers to multiply together
to make a difficult calculation. Find the product.
×
PL
E
4
×
=
What makes this calculation difficult?
Find each product.
Simplify the calculation or use a different method.
11 × 5 =
SA
a
M
5
c
6
13 × 3 =
b
19 × 2 =
d
15 × 4 =
Find at least three different solutions to this
division calculation.
30 ÷
=
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10.2 Playing with multiplication and division
Six children share a bag of 48 sweets between them
equally. How many sweets does each child get?
PL
E
7
Write the division calculation that shows the result.
Challenge
Three different numbers from 2 to 10 are multiplied together.
The product is 120. What could the numbers be?
M
8
SA
Find two different solutions.
9
Complete the multiplication grid using any method that you choose.
×
13
16
19
3
4
5
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10 More multiplication and division
10 A school orders 60 glue sticks to be shared
equally between five classes. When the glue
sticks arrive, five extra free glue sticks have
been added to the box.
PL
E
Write the division calculation to show how
the school shares the glue sticks.
11 Complete each division calculation.
a
M
÷4=7
SA
c
÷2=7
e
÷ 10 = 7
b
÷3=4
d
÷3=9
f
÷9=4
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10.3 Extending multiplication and division
10.3 Extending multiplication
and division
approach
Focus
interpret
1
Estimate the product of 27 × 5. Record the multiplication
calculation in a grid and find the product.
Estimate:
×
Complete this division calculation.
M
2
PL
E
Exercise 10.3
92 ÷ 4 =
Estimate of 80 ÷ 4 = 20, so 92 ÷ 4 is a bit more than 20.
SA
92
– 40
10 groups of 4
52
3
The bicycle maker has 18 wheels.
How many bicycles can she make?
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10 More multiplication and division
Three children can sit at a small table.
How many small tables are needed for 39 children?
5
M
Practice
PL
E
4
Estimate then find the product for each multiplication.
a
b
Estimate:
SA
46 × 5 =
c
Estimate:
67 × 3 =
d
Estimate:
89 × 2 =
Estimate:
78 × 4 =
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10.3 Extending multiplication and division
Estimate and then find the answer for each division.
a
54 ÷ 2 =
c
Estimate:
96 ÷ 3 =
d
Estimate:
96 ÷ 4 =
Estimate:
75 ÷ 5 =
The timber store is making three-legged stools.
The store has 42 stool legs.
How many stools can they make?
SA
M
7
b
Estimate:
PL
E
6
8
A taxi can carry four people.
Twelve people want to go to a show.
How many taxis do they need?
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10 More multiplication and division
Challenge
Choose which numbers to multiply by 2, 3, 4 or 5 to find
the smallest and greatest product.
Remember to estimate the product before you multiply.
68
37
86
93
45
69
74
96
39
Smallest product:
Estimate:
Greatest product:
M
Estimate:
PL
E
9
SA
10 Using the numbers in question 9, choose a number to divide
by 2, 3, 4 and 5. If you cannot divide your chosen number exactly by 2, 3,
4 or 5, either choose a different number or a different number to divide
by. Remember to estimate before dividing.
Estimate:
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10.3 Extending multiplication and division
PL
E
11 I have Rs25. Computer games cost Rs4.
How many computer games can I buy?
How much change will I get?
SA
M
12 How many 3 cm lengths of ribbon can be cut from 1 metre of ribbon?
How long is the piece left over?
13 I am thinking of a number. I multiply it by 3 and add 2 to
get the answer 83. What is my number?
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11
More fractions
Exercise 11.1
Focus
a
Where should she mark
b
Where should she mark
c
Where should she mark
a
Draw a ring around
1
4
2
4
3
? At
cm.
? At
cm.
1
3
4
? At
cm.
diagram
dividing line
non-unit fraction
unit fraction
of the cubes.
SA
2
A fraction strip is 20 cm long.
Wunmi is marking quarters on the strip.
M
1
PL
E
11.1 Fractions of numbers
b
What fraction of the cubes are not ringed?
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11.1 Fractions of numbers
3
Find these fractions of 12.
1
1
1
1
1
3
2
3
4
5
10
4
X
X
Find each fraction and complete the matching
division calculation.
a
b
c
2
1
5
1
4
1
of 6 =
of 15 =
,6÷
, 15 ÷
=
=
of 16 =
10
of 40 =
, 16 ÷
, 40 ÷
=
=
SA
d
1
M
4
PL
E
12
5
A new chocolate bar has three separate fingers.
Four children want an equal share. How much does
each child get? Draw a diagram to help you.
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11 More fractions
Practice
A fraction strip is 1 metre long.
Where should you mark the quarters on the strip?
a
b
cm.
2
4
at
cm.
a
What fraction of the cubes are ringed?
b
What fraction of the cubes are not ringed?
c
3
4
at
cm.
What is the whole in the table below?
Complete the rest of the table.
1
1
1
1
1
3
2
3
4
5
10
4
SA
8
4
at
PL
E
7
1
M
6
21
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11.1 Fractions of numbers
9
Complete each fraction statement and write the
matching division calculation.
a
c
1
4
1
5
of
= 12
b
of
=7
d
1
3
of
1
10
of
= 27
=5
PL
E
10 There are four tomatoes in a pack. Kai uses two tomatoes.
What fraction of the tomatoes does he use?
Challenge
11 a
A fraction strip has
1
5
marked at 9 cm.
Where should
1
3
be marked on this fraction strip?
SA
b
M
How long is the fraction strip?
12 Zara and Sofia both made a fraction strip, but both strips
are torn. Zara’s strip is grey, Sofia’s strip is white.
Whose strip is shorter? How do you know?
Zara
1
3
Sofia
1
3
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11 More fractions
13 There are 24 marbles in
3
4
of a bag of marbles.
How many marbles are in a full bag?
PL
E
24 marbles
14 Fatima buys a bunch of grapes.
She eats
1
3
of the bunch.
M
There are 18 grapes left.
How many grapes were in the bunch that Fatima bought?
SA
15 There are 12 nails in a pack.
Feng uses nine nails.
What fraction of the pack does he use?
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11.2 Ordering and comparing fractions
11.2 Ordering and comparing
fractions
Focus
1
Mark
1 2
,
4 4
and
3
4
PL
E
Exercise 11.2
on this number line.
0
2
1
Which fractions would be marked on a number line
3
1
4
?
M
between 0 and
Use the fraction strips to help you complete the inequalities.
1
4
1
4
SA
1
4
1
3
1
3
1
4
1
3
is less than
<
is greater than
>
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11 More fractions
4
Use the fraction wall to help you find three pairs of
equivalent fractions.
1
1
2
1
4
1
5
1
10
1
5
1
10
b
1
10
1
10
=
1
5
1
10
c
1
10
1
10
=
M
=
1
10
1
4
Which row on this fraction wall does not have
any equivalent fractions within 1?
SA
d
1
4
1
5
1
10
a
1
3
1
4
1
5
1
10
1
3
PL
E
1
3
1
2
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11.2 Ordering and comparing fractions
Practice
Mark
5
,
3
,
7
,
4
10 5 10 5
and
0
6
10
on this number line.
1
Which fractions would be marked on a number line
between
7
9
PL
E
5
1
4
and
Zara marks
Sofia marks
1
4
1
3
1
2
?
on her number line.
on her number line.
0
1
4
SA
Zara
M
Whose 0 to 1 number line is shorter?
How do you know?
Sofia
0
1
3
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11 More fractions
Which fraction will give you the biggest amount?
a
c
9
1
or
3
6
10
3
10
or
2
5
b
of a cake?
1
2
of Rs3 or
3
4
of Rs2?
of a pizza?
PL
E
8
Use the fraction strips to help you complete the inequalities.
1
4
1
4
1
5
1
5
1
4
1
5
1
4
1
5
1
5
M
is less than
is greater than
<
>
SA
10 Is each statement true or false?
Draw a ring around the correct answer.
If the statement is false, change the sign to make it
correct and rewrite the statement.
a
b
c
d
1
5
2
3
2
4
1
2
=
2
true false
= true false
10
3
4
=
=
4
10
5
10
true false
true false
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11.2 Ordering and comparing fractions
Challenge
11 Which fraction lies between
3
5
and
7
10
on a number line?
12 Use the fraction strips to help you compare some fractions.
1
4
1
5
1
5
4
a
>
3
1
4
1
4
PL
E
1
4
1
5
1
5
1
5
4
b
<
4
13 Use <, > or = to complete each statement.
2
1
c
of 18
1
4
of 32
M
1
a
5
of 25
SA
10
1
of 40
b
d
14 Find three fractions that are equivalent to
1
3
=
=
1
3
of 60
6
10
1
3
of 60
2
3
of 30
3
5
of 60
.
=
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11 More fractions
11.3 Calculating with fractions
Exercise 11.3
decrease
Focus
original
1
10
1
10
1
10
1
10
1
10
Complete the numerators to make this calculation correct.
Find three different solutions.
M
2
reduce
What addition is shown on this diagram?
PL
E
1
a
+
5
=
5
b
5
+
5
=
5
SA
5
c
3
5
+
5
=
5
What subtraction is shown on this diagram?
8
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
3
10
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11.3 Calculating with fractions
4
A television programme
goes for
1
5
of an hour.
PL
E
How many minutes is that?
Practice
Use diagrams or fraction strips to help you complete each calculation.
Estimate before you calculate.
Draw a ring around your estimate.
a
2
3
M
5
+
1
3
=
b
1
2
,=
1
2
1
, > 2
SA
Estimate: <
c
1
10
+
10
=
Estimate: <
1
2
10
,=
1
2
1
d
, > 2
1–
5
5
=
Estimate: <
1
2
−
1
4
1
2
,=
1
2
,>
1
2
=
Estimate: <
1
2
,=
1
2
,>
1
2
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11 More fractions
6
Find all the possible solutions for this calculation.
1−
=
3
PL
E
7
3
Mariposa buys a shirt in the sale.
Its price was Rs30 originally,
but then reduced by
1
5
.
Rs30
M
How much does Mariposa pay for the shirt?
SA
Challenge
8
Hien mixes 200 millilitres of orange juice,
200 millilitres of pineapple juice and
200 millilitres of lemonade.
What fraction of a litre is the drink
that he makes?
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11.3 Calculating with fractions
Use diagrams or fraction strips to help you
check each calculation.
Tick the correct answers.
If the calculation is incorrect, correct it.
a
c
e
5
10
3
4
1
2
+
−
−
4
10
1
4
=
3
10
=
9
10
1
d
2
=
b
1
10
5
5
3
−
1
5
0
=
3
5
0
PL
E
9
3
−
3
=
3
10 Inaya buys 20 metres of fabric to make some curtains.
7
10
of the fabric. How much fabric is left over?
SA
M
She uses
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12
Measures
12.1 Mass
Worked example 1
kilogram (kg)
PL
E
Exercise 12.1
mass
If the apple has a mass of 70 g,
what is the mass
of the pear?
160 g
160 g – 70 g = 90 g
SA
Focus
M
The pear has a mass of 90 g.
The total mass of the
apple and the pear is 160 g.
To find the mass of the pear,
take away the mass of the apple.
1
If the skin has a mass of 850 g, how much watermelon can be eaten?
3 kg
Tip
Change 1 kg
to grams.
Show how you worked out the answer.
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12.1 Mass
2
Write the mass that is showing on each scale.
Round each reading up or down, to the nearest whole number.
a
b
900 0 100
PL
E
900 0 100
200
800
700 grams 300
600
500
700 grams 300
400
600
500
400
M
c
200
800
900 0 100
200
800
700 grams 300
400
SA
600
3
500
Estimate and ring the mass of each object.
a
carrot
8 kg
4 kg
18 g
b
sheep
9 kg
90 kg
900 g
c
feather
1g
50 g 1 kg
d
frog
3g
300 g
3 kg
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12 Measures
Practice
4
Zara, Arun and Sofia are finding out the mass of
the potatoes and the flour.
900 0 100
PL
E
flour
9
10 0
1
200
8
2
300
grams
400
600
500
7
3
kilograms
4
6
5
800
M
700
SA
The potatoes have more
mass because the arrow
is further around the
scale than the flour.
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12.1 Mass
PL
E
The flour has less
mass because 2 kg is
less than 700 g.
SA
M
The flour has more
mass because 2 kg is
more than 700 g.
Who is correct? Explain your answer.
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12 Measures
a
What is the mass of this parcel?
0
700
600
500
100
200
grams
400
b
300
PL
E
5
What is the mass of the chick?
M
grams
50
100
150
SA
0
6
200
250
Estimate and then ring the mass.
a
A squirrel has a mass of about
10 g
100 g
1 kg.
b
A watermelon has a mass of about
700 g
3 kg
13 kg.
c
A cell phone has a mass of about
2 kg
1g
140 g.
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12.1 Mass
Challenge
a
If one parcel has a mass of 900 g, what is the mass
of the other parcel?
3 kg
PL
E
7
b
Draw scales that show more than 1 kg.
c
Draw three parcels. One has a mass of less than
500 g, one has a mass of between 600 g and 950 g
and the last one can be your choice.
M
Label the parcels.
SA
Write a question of your own and its answer.
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12 Measures
8
Round up or down the readings, to the nearest
whole number.
a
b
c
0
2
1
1
3
kilograms
2
kilograms
3
2
Estimate the weight of the potatoes.
M
9
kilograms
4
4
PL
E
1
3
0
0
4
SA
POTATOES
10 0
The potatoes
weigh 13 kg.
kilograms
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12.2 Capacity
I don’t know
because there is
no number.
PL
E
The potatoes
weigh more than
half of 10 kg.
a
Who is correct? Explain your thinking.
b
How much do the potatoes weigh?
M
12.2 Capacity
Exercise 12.2
Worked example 2
capacity
litre (L)
millilitre (ml)
SA
The sheep farmer has a full 5 litre bucket of water.
Each lamb needs 500 ml of water.
Does the farmer have enough water?
Yes, she does.
One lamb will have half a litre. Two lambs will have 1 litre.
So four lambs will have 2 litres and six lambs will have 3 litres.
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12 Measures
Focus
1
Three friends want a drink of water. Each cup has the
capacity to hold 500 ml of water.
2
PL
E
Can they all have a drink from a bottle that holds 2 litres?
Explain how you know.
Each container has a different capacity.
Write the amount held in each container.
a
b
500 ml
400 ml
300 ml
200 ml
M
300 ml
c
200 ml
100 ml
250ml
200 ml
150 ml
SA
100 ml
100 ml
50 ml
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12.2 Capacity
d
This jug has the capacity to hold 3 litres of liquid.
Fill this jug to two and a half litres.
3L
1L
3
PL
E
2L
The capacity of the jug is 2 litres.
Nadine estimates that if
she pours 500 ml of water away,
she will have 1 litre left.
2L
SA
M
1L
What do you think? Explain your answer.
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12 Measures
Practice
5
My flask has the full capacity of 400 ml of water.
Show how you worked out your answers.
a
I pour out half. How many millilitres did I pour out?
b
I pour out a quarter of 400 ml. How much is left in my flask?
c
I pour out three-quarters of 400 ml. How much is left in my flask?
PL
E
4
Each of these containers has a capacity of 1 litre. They are not all full.
Use the clues to find out who has which container.
1L
1L
M
1L
500 ml
SA
500 ml
A
I have exactly
half a litre.
B
500 ml
C
I have more
than 300 ml but less
than 400 ml.
I have 1000 ml.
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12.2 Capacity
Write what you have found out.
b
How much does Zara have?
PL
E
6
a
Kaleem has put juice in each of these jugs.
Each jug has a capacity of 1 litre.
Kaleem estimates that if he pours three more drinks using
jug 2, both jugs will have the same amount of juice in them.
Each drink is 125 ml.
1L
M
900 ml
800 ml
700 ml
600 ml
500 ml
400 ml
300 ml
200 ml
100 ml
750 ml
500 ml
SA
jug 1
1L
250 ml
jug 2
Is he right?
How much juice will be left in jug 2?
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12 Measures
Challenge
7
True or false:
The tallest container always has the largest capacity.
Is that statement correct?
I bought a full bottle of water with a capacity of 1 litre.
I poured one-quarter of a 1 litre bottle of water into a glass.
SA
8
M
PL
E
Explain your reasons and draw examples.
a
How many millilitres are left in the bottle?
b
What fraction is left in the bottle?
c
If I had poured out three-quarters of a full bottle,
how many millilitres is that?
d
How many millilitres would have been left in the bottle?
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12.2 Capacity
The area of this wall is 4 square metres.
PL
E
9
Each two and a half litre tin of paint covers an
area of 2 square metres.
Estimate and then work out how many litres of paint
will cover the wall.
M
a
.
I think
.
SA
I know
b
Estimate and work out how many litres of paint are
needed to cover a wall that is a quarter of the area.
I think
I know
.
.
Show how you worked out the answer.
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12 Measures
12.3 Temperature
Celsius (C)
Exercise 12.3
degree (°)
Worked example 3
PL
E
This water is boiling. Look at the thermometer.
What temperature is boiling water?
M
115
110
105
100
The black line shows 100 °C. The boiling point is 100 °C.
SA
Temperature is measured in degrees Celsius.
Focus
1
The thermometer is in ice.
a
What temperature does it show?
b
What is the difference between the
temperature of the ice and the temperature
of boiling water?
115
110
105
100
0
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12.3 Temperature
a
Which thermometer below shows the coldest temperature?
b
Which thermometer shows the warmest temperature?
c
What is the temperature on thermometer D?
d
Which two thermometers are above 20 °C?
A
°C
40
35
30
25
20
15
10
e
B
°C
40
C
°C
D
40
°C
40
35
35
35
30
30
30
25
25
25
20
20
20
15
15
15
10
10
10
5
0
5
0
5
0
M
5
0
PL
E
2
Use this thermometer to show the temperature that
you like best. Do you like to be hot, warm or cold?
because
SA
I like to be
°C
.
40
35
30
25
20
15
10
5
0
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12 Measures
3
a
ound the temperature up or down, to the nearest
R
number on the scale.
A
°C
B
°C
PL
E
0 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
0 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
C
Draw on the thermometers the temperatures to
show just over 27 °C and just under 14 °C.
M
b
SA
°C
0 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
D
°C
0 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
c
For each reading, round up or down to the nearest number.
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12.3 Temperature
Practice
a
hat is the difference between the temperature in
W
ice and the temperature of the air?
115
110
105
100
0
PL
E
4
°C
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30
M
Look at the temperatures shown in the table. This table
shows the temperature on the same day but in two
different countries.
Country A
SA
Month
b
April
9 °C
31 °C
May
12 °C
31 °C
June
17 °C
32 °C
July
18 °C
33 °C
Write the difference between the temperatures in the
two countries in:
June
c
Country B
April
July
May
Which month has the biggest temperature difference?
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12 Measures
a
ouse plants like a temperature that is over 18 °C.
H
Which thermometer shows the best temperature for the plants?
A
°C
40
0
B
°C
40
C
°C
40
D
°C
PL
E
5
0
0
What temperature does it show?
c
In school, temperatures should not fall below 18 °C.
Show and write a temperature that would close schools.
M
b
SA
°C
40
0
40
0
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12.3 Temperature
6
This thermometer is labelled to show each 10 °C.
a
Write all of the missing labels.
40
PL
E
°C
0
b
Show a temperature of more than 15 °C but less
than 23 °C. What temperature have you shown?
a
Look at these two thermometers. Then fill in the gaps.
SA
7
M
Challenge
115
110
105
100
0
°C
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30
Day temperature of the room
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12 Measures
The temperature of the
is higher than
the temperature of the
b
.
The night air temperature is 15 °C lower than
.
the day temperature. The temperature at night is
8
PL
E
Boiling water is left to cool. The thermometer
shows 28 °C lower. Show the new temperature
on the thermometer.
°C
100
90
80
70
60
50
40
30
20
10
0
M
c
Compare the thermometers.
Choose the correct answer.
SA
a
A
°C
38
36
34
32
30
28
26
24
22
20
B
C
°C
38
36
34
32
30
28
26
24
22
20
°C
99
96
93
90
87
84
81
78
75
72
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12.3 Temperature
D
E
°C
°C
48
48
44
44
40
40
36
36
32
32
28
28
24
24
20
20
16
16
PL
E
99
96
93
90
87
84
81
78
75
72
F
°C
Thermometer A shows a higher/lower temperature
than thermometer B.
M
Thermometer C shows a higher/lower temperature
than thermometer D.
Thermometer E shows a higher/lower temperature
than thermometer F.
Write the temperatures that each thermometer shows.
SA
b
A
c
B
C
D
E
F
Write the temperature differences between A and E,
D and B, and F and C.
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12 Measures
Read the thermometers.
a
Write the temperatures in the boxes.
°C
°C
50
°C
50
°C
50
50
40
40
40
40
40
30
30
30
30
30
20
10
0
°C
20
20
20
20
10
10
10
10
0
0
0
0
°C
°C
°C
°C
Write the temperatures from the warmest to the coldest.
SA
M
b
°C
50
PL
E
9
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13
Time (2)
13.1 Time
Focus
1
a
How many times can you clap your hands in 1 minute?
estimate =
b
measure =
How many times can you stamp your feet in 1 minute?
estimate =
measure =
Write three things that would take more than a minute to do.
1
2
SA
3
M
c
time interval
PL
E
Exercise 13.1
time
2
a
If you sleep eight hours a night, how many hours
do you sleep in a week?
b
Write two questions and their answers about things
that that take you hours to do.
1
2
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13 Time (2)
3
Use the calendar to find the answers.
May
April
M
T
W
T
F
S
S
1
2
3
4
5
M
T
W
T
F
S
S
1
2
3
7
8
9
10
11
12
4
5
6
7
8
9
10
13
14
15
16
17
18
19
11
12
13
14
15
16
17
20
21
22
23
24
25
26
18
19
20
21
22
23
24
27
28
29
30
25
26
27
28
29
30
31
June
T
W
T
1
2
3
4
8
9
10
11
15
22
29
F
S
S
5
6
7
12
13
14
M
M
PL
E
6
16
17
18
19
20
21
23
24
25
26
27
28
30
Rayan planned a holiday to last two weeks.
He left on 15th May. When did he arrive home?
b
Schools will close for a holiday on 14th April.
Learners will go back to school 20 days later.
What date do they go back to school?
SA
a
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13.1 Time
Four weeks after 3rd May is my birthday.
What date is that?
d
My dentist appointment was on 24th June.
I was asked to go two weeks earlier.
When did I go to my appointment?
PL
E
c
Practice
4
aChoose from the choices in the box to estimate the length
of time each of these activities would take.
1 hour
1 minute
more than 1 min
ute
M
one clap
te
less than 1 minu
walk around your classroom
stamp your foot
SA
blink your eyes
math lesson
travel to school
get dressed
eat your breakfast
b
What would take you more than an hour to do?
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13 Time (2)
5
I was born in April 1999. My sister was born in
March 1996. My brother was born in 2007.
April
March
M
T
W
T
F
S
M
S
T
1
3
4
5
9
10
11
12
16
17
18
19
23
24
25
26
30
31
T
F
S
S
1
2
3
4
5
6
7
8
6
7
8
9
10
11
12
13
14
15
13
14
15
16
17
18
19
20
21
22
20
21
22
23
24
25
26
27
28
29
27
28
29
30
PL
E
2
W
All of our birth dates are the 26th.
How many days and months apart are they?
b
My brother was born nine days after me.
When was he born?
SA
M
a
c
How many years’ difference is there between my
brother and my sister?
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13.1 Time
6
Use the calendar to help you solve these problems.
June
T
W
T
F
S
S
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
PL
E
M
a
A bag of bird food lasts six days.
You opened the packet on Thursday 4th.
When will you open the next bag?
b
I planned to visit the zoo on the 30th but went
two weeks earlier. When did I go?
M
Challenge
minutes
7
days
weeks
Choose from the choices in the box to estimate how long it takes:
SA
a
hours
to shake hands with a friend
to eat your breakfast
to walk around the outside of your school building
for the grass to grow 5 cm
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13 Time (2)
b
Write one more thing for each of these time units.
minutes:
hours:
weeks:
8
PL
E
days:
November
M
T
W
T
F
S
S
December
M
1
3
4
5
9
10
11
12
16
17
18
19
23
24
25
26
30
W
T
F
S
S
1
2
3
4
5
6
6
7
8
7
8
9
10
11
12
13
13
14
15
14
15
16
17
18
19
20
20
21
22
21
22
23
24
25
26
27
27
28
29
28
29
30
31
M
2
T
January
T
W
T
F
S
S
1
2
3
4
SA
M
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
a
Find two days and dates that are 17 days apart.
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13.1 Time
b
Marsile, Mustafa and Majak went camping.
Marsile left on 9th November, Mustafa left on
12th November and Majak left on 27th November.
They all came home on 6th December.
How long was each boy away camping?
c
Mustafa went camping again six weeks after he came
home on 6th December and he stayed 11 days.
Which day did he go and when did he come home?
aAnna was away for 13 days. Write two possible
pairs of dates for when she left and came back.
M
9
PL
E
Marsile: Mustafa: Majak:
August
T
W
T
F
SA
M
S
S
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
1
2
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13 Time (2)
b
Javed was away for 17 days. Write two possible
pairs of dates for when he left and came back.
May
T
W
4
5
6
11
12
13
18
19
20
25
26
27
1
2
T
F
S
S
1
2
3
7
8
9
10
14
15
16
17
21
22
23
24
28
29
30
31
PL
E
M
M
13.2 Timetables
timetable
Exercise 13.2
SA
Worked example 1
This timetable shows a day at the seaside.
Play games
10.30 a.m – 12 p.m.
Eat lunch
Walk
Swim
12 – 1.15 p.m. 1.30 – 2.30 p.m. 2.45 – 3.30 p.m.
a Which activity lasts the longest time?
b Which activity lasts the shortest time?
c Work out the length of time for each activity.
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13.2 Timetables
Continued
Play games: 1 hour 30 minutes, eat lunch: 1 hour 15 minutes,
walk: 1 hour, swim: 45 minutes
Playing games lasts the longest time: 1 hour 30 minutes.
Focus
This timetable shows a day on holiday for Iqra.
Use it to find the length of each activity.
Arrive
Play games
10.15 a.m.
10.45 a.m. –
12.15 p.m.
a
Eat lunch
12.15 –
1.15 p.m.
Walk
1.30 –
2.15 p.m.
Swim
2.15 –
3 p.m.
Leave
3.15 p.m.
What time did Iqra arrive? What time did she leave?
M
1
PL
E
Swimming is the shortest time: 45 minutes.
SA
How long did she stay at the seaside?
b
Which activity lasted for one hour?
c
Name an activity that lasted more than an hour.
d
Name an activity that lasted less than an hour.
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13 Time (2)
e
2
For how long did Iqra walk?
This table shows the journeys of five short flights.
Take-off
Landing
11:05 a.m. 11:55 a.m.
flight B
9:20 a.m.
9:58 a.m.
flight C
2:06 p.m.
2:42 p.m.
flight D
1:03 p.m.
1:47 p.m.
flight E
6:12 p.m.
6:52 p.m.
PL
E
flight A
Time
Calculate the time from the first flight taking off to the
last flight landing.
b
Which flight has the shortest journey?
c
Which flight has the longest journey?
SA
M
a
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13.2 Timetables
3
Use the school timetable to answer the questions.
9:00 a.m. – 9:15 a.m.
spelling
9:15 a.m. – 10:15 a.m.
writing
10:15 a.m. – 11:00 a.m. maths
PL
E
11:00 a.m. – 11:20 a.m. morning break
11:20 a.m. – 11:45 a.m. reading
11:45 a.m. – 12:45 p.m. science
12:45 p.m. – 1:00 p.m.
break
1:00 p.m. – 1.30 p.m.
lunch
1:30 p.m. – 2:00 p.m.
2:00 p.m. – 3:00 p.m.
music
art
How long is the school day?
b
At what time does the music lesson start?
At what time does it finish?
SA
M
a
c
At what time does maths start?
How long does the lesson last?
d
By what time do you need to get to school in
the morning?
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13 Time (2)
Practice
This timetable shows the buses that go from the train
station to the bus station each morning.
train station
9:06 a.m.
10:05 a.m. 12:00 p.m.
shopping centre 9:21 a.m.
10:23 a.m. 12:18 p.m.
school
park
bus station
PL
E
4
9:35 a.m.
–
9:48 a.m.
10:40 a.m. –
10:00 a.m. 9:59 a.m.
12:32 p.m.
12:50 p.m.
Kalpana missed the 9:21 a.m. bus from the shopping
centre to school. What time is the next bus that
she could catch?
b
What time is the last bus from the train station to
the park? How long is the journey? What time does
the bus arrive?
SA
M
a
c
Use the information in this timetable to write a
question and its answer.
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13.2 Timetables
5
The timetable shows the times that it takes to travel between
Elmswell and Norton, using different types of transport.
Elmswell
Daisy Green
Norton
8:00 a.m.
8:14 a.m.
8:25 a.m.
8:37 a.m.
taxi
8:00 a.m.
8:12 a.m.
8:21 a.m.
8:30 a.m.
train
8:07 a.m.
PL
E
bus
–
8:19 a.m.
8:28 a.m.
You need to be at Norton before 8:30 a.m. Which transport
would you use? What time would you arrive?
b
You miss the 8:12 a.m. taxi to Daisy Green.
What else could you use? What time would you arrive?
c
Work out how long each journey from Elmswell to
Norton will take. Which journey has the shortest length
of time?
M
a
This timetable shows the A14 bus route from the bus
station to the train station.
SA
6
Nacton
bus station
6:05 a.m. 7.10 a.m. 9:00 a.m. 10:10 a.m. 12:05 p.m. 1:05 p.m.
High Road
6:15 a.m. 7:18 a.m. 9:15 a.m. 10:30 a.m. 12:20 p.m. 1:20 p.m.
shopping centre 6:34 a.m. 7:36 a.m. 9:30 a.m. 10:45 a.m. 12:34 p.m. 1:34 p.m.
village hall
6:48 a.m. 7:50 a.m. 9:40 a.m.
–
train station
7:00 a.m. 8:00 a.m. 9:59 a.m.
–
12:50 p.m. 1:50 p.m.
–
2:00 p.m.
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13 Time (2)
What time does the first bus leave from the bus station?
b
When does it arrive at the village hall?
How long is the journey?
c
If I want to get to the village hall before 8:00 a.m., which two
buses can I catch from High Road?
d
How many A14 buses stop at the village hall?
Challenge
7
PL
E
a
This timetable shows the B26 bus route from the bus station
to the train station. Some rain has dropped onto the timetable
and washed out some times.
9:00 a.m. X
M
bus station
High Road
11:15 a.m.
shopping centre 9:25 a.m. X
train station
a
X
2:10 p.m. 4:55 p.m. 6:25 p.m.
X
X
9:55 a.m. X
X
SA
village hall
2:00 p.m. 4:30 p.m.
Fill in the spaces from these clues.
•It takes 10 minutes to get from the bus station to
High Road.
• The village hall is 5 minutes before the train station.
•The 2:00 p.m. bus from the bus station takes 5 minutes
longer at each stop.
•The 6:25 p.m. from the shopping centre takes 10 minutes
from and to each stop.
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13.2 Timetables
b
Use the timetable to answer the questions. All of the times shown are a.m.
PL
E
8
Which is the longer journey to the train station: the one
that leaves the bus station at 9:00 a.m. or the one that leaves
at 6:05 p.m.? How long are both journeys?
Bus timetable
Baldia Town
Kiamari Town
Jamshed Town
Korangi Town
Gadap Town
7:13
8:12
6:10
6:40
7:29
8:28
6:14
6:44
7:18
7:34
8:31
6:23
6:50
7:23
6:28
6:55
7:28
7:51
8:45
6:35
7:00
7:43
7:59
9:00
7:10
On the 6:30 bus from Baldia Town, how long does it
take to get from Kiamari Town to Gulberg Town?
SA
a
6:30
M
Gulberg Town
6:00
b
Can you travel from Baldia Town to Korangi Town on the 7:13 bus?
c
If you had to travel from Baldia Town to Gadap Town and had to
arrive by 8:30, which would be the best bus to catch?
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13 Time (2)
9
The teacher from class 3 has made a timetable of
school activities. All of these times are p.m.
Monday
Tuesday
Wednesday
Thursday
cycling
2:00–3:00
Jujitsu
2:00–3:00
gardening
3:00–4:00
cooking
3:00–4:15
gardening
3:00–4:00
drama
3:00–4:00
football
3:00–3:45
French
computer
studies
3:00–4:00
arts &
crafts
4:00–5:00
dodgeball
PL
E
3:00–4:00
3:00–4:00
singing
4:00–5:15
arts &
crafts
4:00–5:00
SA
M
Li-Ming wishes to go to arts and crafts, cooking,
gardening and cycling. Make a list for Li-Ming of the
days and times that she can do her activities.
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14 Angles and
movement
Exercise 14.1
Worked example 1
PL
E
14.1 Angles, direction, position and
movement
cardinal point
compass
point
right angle
Draw a ring around all the angles that are
not right angles.
M
Use your angle measure to help you.
SA
How do you know the other angles are not
right angles?
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14 Angles and movement
Continued
PL
E
They are not right angles because a right angle is made
when a horizontal line and a vertical line meet.
SA
M
right
angle
Focus
1
a
Put a ring around all the right angles inside the shape.
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14.1 Angles, direction, position and movement
b
Draw two shapes of your own that have right angles.
Write the missing compass points.
M
2
PL
E
Mark the angles.
SA
West
•
Starting at the star, draw a
•
green circle four spaces north
•
blue circle three spaces south
•
yellow circle two spaces west
•
red circle one space east.
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14 Angles and movement
3
On the side of the grid, write the missing cardinal points.
Complete the sentences.
Castle
School
PL
E
Tree
Tent
Bridge
Park
Fire station
House
M
Pond
a
The tree is
b
The school is
c
The park is
of the pond and
of the fire station.
d
The tent is
of the castle and
of the fire station and
SA
of the castle and
of the castle and
of the pond and
e
of the pond.
of the bridge.
of the bridge.
Where is the house?
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14.1 Angles, direction, position and movement
Practice
4
Some of these shapes have right angles, some are greater
than a right angle and some are less than a right angle.
Join one of the angles from each shape to the correct word.
ght angle
greater than a ri
PL
E
smaller than a right angle
M
right angle
SA
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14 Angles and movement
5
Book shop
Mosque
Hospital
PL
E
Church
Newsagent
Letterbox
Taxi rank
NEWS
Fire
station
Petrol
station
Coffee shop
M
School
SA
N
W
E
S
Write two different ways to get from the school to the hospital.
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14.1 Angles, direction, position and movement
PL
E
Fill the map to show these objects: a tree, a pond, a pot
of gold, some bushes, a river with a bridge and a person.
a
Write the four cardinal points.
b
Write two sentences to describe the position of the objects
on your map. Use two cardinal points for each sentence.
M
6
SA
For example: The tree is west of the bridge and south
of the pot of gold.
1
2
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14 Angles and movement
Challenge
aDraw a ring around the angles that are greater than
a right angle.
Cross through the angles that are less than a right angle.
c
Explain what this angle is and how it is made.
PL
E
b
SA
M
7
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14.1 Angles, direction, position and movement
M
PL
E
8
SA
Using the cardinal points north, south, east and west,
write the position of six things on the map.
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14 Angles and movement
PL
E
9
N
W
E
a
M
S
Write the missing words.
is west of the treasure box.
The
SA
The hut is
of the treasure box.
b
Where are the mountains?
c
Where is the ship?
d
Walk from the tree towards the ship. In which direction
will you walk?
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14.1 Angles, direction, position and movement
e
Add two more objects to the map. Write instructions
to get to the two objects, starting from the tree.
SA
M
PL
E
Use all four cardinal points for each object.
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15
Graphs
15.1 Pictograms and bar charts
Worked example 1
axes
PL
E
Exercise 15.1
axis
On which day did the bookshop sell most books?
Monday
Tuesday
Wednesday
Key:
= 2 books
M
Thursday
discrete data
The bookshop sold most books on Tuesday.
SA
The key shows that each book represents two books, so ten
books were sold on Tuesday.
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15.1 Pictograms and bar charts
Focus
1
Look at this pictogram from a phone shop.
Key
Tuesday
=2
Thursday
Friday
PL
E
Wednesday
How many phones were sold on Friday?
b
How many phones were sold on Wednesday?
c
How many phones were sold all together?
d
On which day were the most number of phones sold?
e
On which day were the least number of phones sold?
f
Make your own phone pictogram.
Ask two questions about it. Complete the key.
SA
M
a
Key
=
1
2
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15 Graphs
2
Correct the data on the bar chart.
Six people like cricket.
Three people like golf.
Five people like tennis.
Seven people like football.
PL
E
My favourite sport
7
6
Total amount
5
4
3
2
0
M
1
cricket
golf
tennis
football
Type of sport
How many people were asked all together?
b
Which sport is liked the most?
c
Which sport is liked the least?
d
Write the sports in order, starting with the least liked.
SA
a
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15.1 Pictograms and bar charts
3
This pictogram shows how many families visited the park
on different days of the week.
Key
PL
E
= 2 families
M
= 1 family
Tuesday
Wednesday Thursday
Friday
Saturday
Sunday
SA
Monday
a
Which day had the most visitors?
b
Which day had the least visitors?
c
How many families went on Tuesday?
d
How many families went on Wednesday?
e
Write a question of your own and give the answer.
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15 Graphs
Practice
4
This is a pictogram to show how many goals were
scored this season. Look at the key.
Key:
team A
= 2 goals
team C
team D
PL
E
team B
Which team scored the most goals?
b
How many did they score?
c
Which team scored the fewest goals?
How many did they score?
d
How many goals were scored by team A and
team B all together?
e
Write two questions with answers of your own.
SA
1
M
a
2
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15.1 Pictograms and bar charts
5
This is the bar chart.
Make up your own title for it.
M
PL
E
Write your own labels and numbers on the axes.
Write two questions for someone else to answer.
SA
1
2
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15 Graphs
6
a
Show this pictogram as a bar chart.
Key
week 1
= 2 trees
week 2
week 4
week 5
PL
E
week 3
Planting trees each week
14
10
8
6
M
Number of trees
12
4
2
week 2
SA
week 1
b
week 3
week 4
week 5
Weeks
Write two questions about the data in the graphs.
1
2
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15.1 Pictograms and bar charts
Challenge
Use the data about the vehicles to complete the pictogram.
SA
M
PL
E
7
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15 Graphs
How many vehicles are there all together?
There are
cars.
There are
tractors.
There are
trucks.
PL
E
a
bikes.
There are
trikes.
There are
b
Is the number of cars greater than the number
of trucks?
What is the difference between them?
c
M
The ice cream seller does a survey to find the most
popular ice cream flavour.
•
12 like vanilla.
•
Three more than that like chocolate.
•
Six like strawberry
•
11 like lemon.
•
The favourite flavour is mint. It has the same
number as strawberry and lemon together.
SA
8
What is the difference between the number of
trikes and the number of tractors?
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15.1 Pictograms and bar charts
Write a title and a key for this pictogram.
M
9
PL
E
Make a bar chart to show the data. Count up in twos.
Title:
Key:
SA
9
8
7
6
5
4
3
2
1
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15 Graphs
10 Write a title for this bar chart.
Use the data from question 9 to complete the bar chart.
Write two questions and the answers about the data.
2
Title:
8
6
M
Number of insects
10
PL
E
1
4
2
SA
0
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15.2 Carroll diagrams
15.2 Carroll diagrams
Exercise 15.2
Carroll diagram
Worked example 2
19
13
22
11
12
PL
E
Write each number in the correct place in the Carroll diagram.
9
28
15
17
Multiple of 3
Even numbers
Not even numbers
14
26
24
Not a multiple of 3
First, sort the numbers that are multiples of 3. Write the number in the first
column and first row if it is a multiple of 3 and an even number, and in the
first column, second row if it is a multiple of 3 and an odd number.
M
The remaining numbers are not multiples of 3. They belong in the second
column. Even numbers less belong in the second column, first row. Odd
numbers belong in the second column, second row.
Not a multiple of 3
12, 24
22, 28, 14, 26
SA
Even numbers
Multiple of 3
Not even numbers 9, 15
19, 11, 17
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15 Graphs
Focus
1
Put the following numbers into the correct place on
the Carroll diagram.
Cross out the numbers as you use them.
PL
E
1, 2, 5, 10, 14, 15, 21, 27, 35, 47, 55, 62, 76, 83, 91, 108
one-digit numbers
even numbers
not even numbers
2
not one-digit numbers
This bar chart shows the number of hours of cloud
last week. Each space is one hour.
M
Days with cloud
Monday
Tuesday
Wednesday
Thursday
SA
Days
Friday
Saturday
Sunday
1
2
3
4
5
Number of hours with clouds
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15.2 Carroll diagrams
a
Complete the pictogram to show the same data.
Monday
Key:
Tuesday
= 1 hour
Wednesday
Friday
Saturday
Sunday
b
Write two questions about the data and the answers.
1
M
2
3
PL
E
Thursday
Look at the numbers.
13 17
245
555
4
18
56
106
912
Put them in the correct box in the Carroll diagram.
SA
a
45 71
less than 50
not less than 50
odd
not odd
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15 Graphs
b
Choose a number and write it in the Carroll diagram.
More than 50 and odd:
Less than 50 and even:
PL
E
Less than 50 and odd:
More than 50 and even:
4
Which numbers are multiples of 3 and multiples of 5?
Complete the Carroll diagram.
45 69
125 51 60
59
120
68
multiple of 3
not a multiple of 3
M
multiple of 5
35
not a multiple of 5
aPut numbers 10 to 40 in the correct place in this
Carroll diagram.
SA
5
Between 10 and 20
Not between 10 and 20
Digits add to
an even number
Digits do not add
to an even number
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15.2 Carroll diagrams
c
If you saw a pattern, describe what you saw.
a
Write labels in the Carroll diagram.
PL
E
Explain how you knew where to place the numbers.
107, 156, 235
140, 490
18, 24, 51, 6
30, 50, 20
SA
M
6
b
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16 Pattern and
symmetry
Exercise 16.1
Worked example 1
PL
E
16.1 Shape and symmetry
horizontal
line of symmetry
reflection
Each flag has zero, one or two lines of symmetry.
symmetry
Draw the vertical and horizontal lines of symmetry
on each flag. Write how many lines you found.
M
vertical
Lines of symmetry
Lines of symmetry
SA
Lines of symmetry
If a shape has symmetry, it must match exactly both sides. Flag 1 does
not have horizontal or vertical symmetry. Flag 2 has one vertical and one
horizontal line of symmetry. Flag 3 has no lines of symmetry.
0
Lines of symmetry
2
Lines of symmetry
0
Lines of symmetry
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16.1 Shape and symmetry
Focus
Each flag has zero, one or two lines of symmetry.
PL
E
1
Lines of symmetry
Lines of symmetry
Draw the vertical and horizontal lines of symmetry
on each flag.
b
Write how many lines you found.
c
Draw two flags: one has one line of symmetry and
one has two lines of symmetry.
SA
M
a
Lines of symmetry
2
a
Draw the reflection of each of these shapes.
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16 Pattern and symmetry
Draw two shapes of your own. Draw the line of symmetry.
a
Draw the lines of symmetry in these shapes. Use a ruler.
PL
E
3
b
M
Draw two lines of symmetry in these patterns.
SA
b
c
Draw your own symmetrical pattern.
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16.1 Shape and symmetry
Practice
Each flag has zero, one or two lines of symmetry.
PL
E
4
Lines of symmetry
Lines of symmetry
Lines of symmetry
Draw the vertical and horizontal lines of symmetry
on each flag.
5
a
Where a flag has zero lines of symmetry, add to the flag
the shapes that will give it one or two lines of symmetry.
b
Draw the new vertical or horizontal lines on those flags.
aThese shapes were made by folding and cutting squares.
B
SA
A
M
Draw the lines of symmetry where you can.
D
C
E
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16 Pattern and symmetry
Draw the vertical or horizontal line of symmetry on this
pattern. Use a ruler.
SA
M
6
Draw three cut-out shapes of your own.
They must show symmetry.
PL
E
b
Use colours to make the pattern symmetrical.
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16.1 Shape and symmetry
Challenge
Choose the shape for your flag.
PL
E
7
Choose a design.
Create a symmetrical flag that has one or two lines of symmetry.
Use three different colours that are symmetrical too.
Draw the lines of symmetry on your flag.
a
Complete the missing half of each shape.
SA
8
M
Explain why they show symmetry.
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16 Pattern and symmetry
This pattern has two lines of symmetry.
SA
M
9
Draw two symmetrical shapes of your own that have
two lines of symmetry. Mark the lines of symmetry.
PL
E
b
a
Label the vertical line. Label the horizontal line.
b
Using shapes, make your own pattern with two
lines of symmetry. Colour it so that the colours
are symmetrical.
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16.2 Patterns and symmetry
16.2 Patterns and symmetry
Exercise 16.2
a constant
Worked example 2
M
PL
E
Extend this pattern using a constant.
SA
10
15
20
To extend the pattern by adding the constant ‘5’, we add five
circles each time.
This pattern goes up in fives.
5, 10, 15
The next pattern will have 20.
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16 Pattern and symmetry
Focus
2
a
Extend this pattern.
b
The pattern goes up in
c
Draw the next two patterns.
PL
E
1
.
This is the constant.
Reduce this pattern by subtracting one constant at a time.
M
a
SA
4
b
3
The pattern goes down in
1
.
This pattern has one line of vertical symmetry.
Use colours to show colour symmetry.
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16.2 Patterns and symmetry
Practice
4
This is the constant.
a
Extend the pattern by one. Do this twice.
b
Complete the number sentences.
3
3+1=
4+1=
Write one thing that you notice.
M
c
5
PL
E
This is the starting pattern.
Make an extending pattern of your choice.
SA
This is my starting pattern:
This is my constant:
This is my extended pattern:
Write one thing about your pattern to share with someone else.
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16 Pattern and symmetry
aDraw a picture or pattern with a horizontal line of
symmetry to show reflection.
b
How do you know that it is symmetrical?
Challenge
7
PL
E
6
Make an extending pattern using a constant of three different shapes.
M
This is my starting pattern:
This is my constant:
SA
This is my extended pattern:
Write the total number of shapes below each extended pattern.
Write one thing about your pattern to share with someone else.
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16.2 Patterns and symmetry
8
Make a pattern that reduces by one constant each time.
This is my starting pattern:
PL
E
This is my constant:
This is my extended pattern:
Write the total number of shapes below each pattern.
a
Draw a picture or pattern to show vertical and horizontal symmetry.
SA
9
M
Write one thing about your pattern to share with someone else.
b
Where did you start?
c
Explain what you did.
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17 Looking forward:
4-digit numbers
Exercise 17.1
Focus
1
2000
5000
7000
10,000
Complete the place value grid or the abacus to show the same number
in two different ways.
M
2
0 1000
PL
E
17.1 Numbers up to 10,000
1s
1000s 100s 10s
1s
1000s 100s 10s
1s
1000s 100s 10s
1s
1000s 100s 10s
1s
1000s 100s 10s
1s
SA
1000s 100s 10s
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17.1 Numbers up to 10,000
aWhat is the value of the ringed digit in each 4-digit number? You
could use the place value grid to help you.
1837
3614
7526
4352
1000s
4
10s
1s
Use the values you have found to make a 4-digit number. Write the
number in words and numbers.
0
10
ten
20
twenty
one
11
eleven
30
thirty
two
12
twelve
40
forty
three
13
thirteen
50
fifty
4
four
14
fourteen
60
sixty
5
five
15
fifteen
70
seventy
6
six
16
sixteen
80
eighty
7
seven
17
seventeen
90
ninety
8
eight
18
eighteen
100
one hundred
9
nine
19
nineteen
1000 one thousand
1
2
SA
3
zero
M
b
100s
PL
E
3
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17 Looking forward: 4-digit numbers
a
Read these numbers in words, then write them as numbers.
two thousand four hundred and thirty-six
eight thousand six hundred and fifteen
six thousand seven hundred and ninety-eight
b
Read these numbers, then write them in words.
PL
E
5271
3153
9087
Practice
Draw beads on each abacus to represent the 4-digit number.
M
5
1000s 100s 10s
1s
1000s 100s 10s
1000s 100s 10s
7214
1s
5672
SA
2431
1s
6
Arun has these digit cards to make 4-digit numbers with.
3
7
1
9
What is the greatest 4-digit number Arun can make?
What is the smallest 4-digit number he can make?
What is the closest number to 3000 he can make?
What is the closest number to 5000 he can make?
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17.1 Numbers up to 10,000
7
Round each measurement to the nearest 10 and the nearest 100.
Remember to write the units of measure.
Number
Nearest 10
Nearest 100
Rs2467
3148 L
1932 kg
Challenge
8
PL
E
1392 km
What is my number? Write my number in words and numbers.
My number has no tens.
It has four ones.
M
It has two more thousands than it has ones.
It has 1 fewer hundreds than it has thousands.
SA
My number is:
9
Use these number words to make 4-digit numbers in words.
There are 12 possible numbers. Can you find them all?
seventy
nine
six
hundred
thousand
two
forty
and
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17 Looking forward: 4-digit numbers
10 Match each clue to one of these numbers. Use each number once only.
2113
2648
3964
5842
7359
PL
E
8364
3433
2321
7409
9236
All the digits are even.
b
All the digits are odd.
c
The tens digit is 0.
d
The total of the digits is 7.
e
The total of the digits is 8.
f
Three of the digits are the same.
g
The thousands digit is double the ones digit.
h
The thousands digit is three times the tens digit.
i
The hundreds digit is double the tens digit.
j
The thousands digit is half the tens digit.
SA
M
a
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17.2 Addition and subtraction with up to 4-digit numbers
17.2 Addition and subtraction
with up to 4-digit numbers
borrow
carry
1
Find the totals. Estimate then calculate.
Choose which method to use. Show your method.
1232 + 457 =
estimate:
1414 + 1327 =
1576 + 1282 =
Find the answers. Estimate then calculate. Choose which method to use.
Show your method.
M
2
expanded column
method
PL
E
Focus
2467 – 1123 =
2877 – 1359 =
3628 – 1273 =
SA
estimate:
3
Umaimia wants to save Rs5000 in 2 months. She saved Rs2345 last
month and Rs2642 this month. How much has she saved altogether?
Has she reached her target?
Estimate then calculate. Choose which method to use. Show your method.
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17 Looking forward: 4-digit numbers
4
3782 people are at the village festival. 1638 of them are children. The
rest are adults. How many adults are at the festival?
Practice
5
PL
E
Estimate then calculate. Choose which method to use. Show your method.
Find the answers. Estimate then calculate. Choose which method to use.
Show your method.
a
1683 + 1104 = 2987 – 1575 = 1768 + 1123 =
b
M
estimate:
3624 – 2418 = 2381 + 1265 = 4348 – 2197 =
SA
estimate:
6
Hassam wants to drive along the full 2461 km of the Western Alignment
roads. He has already travelled 1248 km. How much further does he
have to travel to complete the route?
Estimate then calculate. Choose which method to use. Show your method.
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17.2 Addition and subtraction with up to 4-digit numbers
7
A chef mixes a large batch of spices. He needs 1242g for one recipe and
1626g for another recipe. What mass of spices does he need altogether?
8
PL
E
Estimate then calculate. Choose which method to use. Show your method.
Here is Sofia’s number line. What calculation is Sofia doing? Has she
found the correct answer? How do you know?
Check her answer using a different method.
– 6 – 70 – 300 – 1000
2837 tickets are sold in one week for a new children’s film. 2129 of the
tickets are for children. The rest are for adults. How many adult tickets
have been sold?
SA
9
M
2272 2278 2348 2648 3648
Estimate then calculate. Choose which method to use. Show your method.
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17 Looking forward: 4-digit numbers
Challenge
10 A farmer harvests a total of 8798 kg of chickpeas and lentils. 7246 kg
of the harvest is chickpeas. The rest is lentils. What is the mass of lentils
harvested?
PL
E
Estimate then calculate. Choose which method to use. Show your
method.
11 Find the missing digits
3
3
4
+1
5
9
8
–
8
5
2
6
9
8
5
4
–2
3
4
7
1
7
6
3
SA
M
8
1
4
12 Husnain recorded these calculations:
Estimate 4330 – 2160 = 2170, 4327 – 2155 = 2172.
What word problem could Husnain be solving?
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E
M
SA
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E
M
SA
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E
M
SA
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E
M
SA
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E
M
SA
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SA
M
PL
E
Acknowledgements
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