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PL
E
1
Numbers and the
number system
1.1 Counting and sequences
Worked example 1
The numbers in this sequence increase by 30 each time.
10, 40, 70, . . .
The sequence continues in the same way.
Which number in the sequence is closest to 200?
M
List the terms in the sequence.
The next terms in the sequence are:
10
+30
40
+30
70
+30
100
+30
130
+30
160
+30
190
+30
220
SA
200
190
220
Work out which term is
closest to 200.
Answer: 190 is closest to 200.
difference
linear sequence negative number non-linear sequence rule
sequence
spatial pattern
square number term
term-to-term rule
8
Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.
We are working with Cambridge Assessment International Education towards endorsement of this title.
1.1 Counting and sequences
Exercise 1.1
Focus
Hassan shaded in grey these numbers on a hundred square.
The numbers form a pattern.
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
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2
What is Hassan’s rule for finding the next number?
SA
a
1
M
1
b
2
What is the next number in his pattern?
The sequence 10, 16, 22, . . . continues in the same way.
Write the next two numbers in the sequence.
,
9
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1 Numbers and the number system
3
The rule for a sequence of numbers is ‘add 3’ each time.
1, 4, 7, 10, 13, . . .
The sequence continues in the same way.
Circle the numbers that are not in the sequence.
22 28 33 40
A sequence has the first term 2020 and the term-to-term rule is ‘add 11’.
Write the first five terms of the sequence.
,
5
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4
,
,
,
Write the next four terms in these linear sequences.
a
10, 7, 4,
b
−9, −7, −5,
c
1095, 1060, 1025,
,
,
,
,
,
,
,
,
M
Tip
,
Remember that −9 is less than −7.
0
SA
–10
–9
–7
Practice
6
Here is part of a number sequence.
The numbers increase by 25 each time.
25, 50, 75, 100, 125, . . .
Circle all the numbers below that will be in the sequence.
355 750 835 900 995
10
Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.
We are working with Cambridge Assessment International Education towards endorsement of this title.
1.1 Counting and sequences
Amy makes a number sequence.
The first term of her sequence is 1.
Her term-to-term rule is ‘add 7’.
Amy says, ‘If I keep adding 7, I will reach 77.’
Is Amy correct? Explain your answer.
8
Here is part of a number sequence.
The first number is missing.
–5
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7
297
–5
Tip
292
–5
287
Remember to
work backwards.
Write the missing number.
A sequence has first term 1001 and last term 1041.
The term-to-term rule is ‘add 5’.
Write down all the terms in the sequence.
M
9
SA
10 Each number in this sequence is double the previous number.
Write the missing numbers.
, 3, 6, 12, 24, 48,
Challenge
11 Write the missing number in this sequence.
1, 3, 6, 10,
Explain how you worked it out.
11
Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.
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1 Numbers and the number system
12 The numbers in this sequence increase by 10 each time.
4, 14, 24, . . .
The sequence continues in the same way.
Write two numbers from the sequence that make a total of 68.
and
Tip
You might find
it useful to
continue writing
the terms of
the sequence.
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13 Describe each of the sequences below.
• Is the sequence linear or non-linear?
• What is the first term?
• What is the term-to-term rule?
• What are the next two terms in the sequence?
5, 9, 13, 17, . . .
b
3, 11, 18, 24, . . .
SA
M
a
c
3, 6, 12, 24, . . .
12
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1.1 Counting and sequences
1 and 10
b
6 and 20
c
3 and 15
You could
choose a linear
or a non-linear
sequence.
SA
M
a
Tip
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14 Write a sequence containing these numbers.
Your sequence must have at least one number between
the two given numbers.
Describe the rule you use.
There could be different answers.
d
1 and 100
13
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1 Numbers and the number system
1.2 More on negative numbers
Worked example 2
temperature zero
Here is a temperature scale.
0
10
°C
20
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–10
The temperature is 1° below freezing on a cold day.
Mark the position of this temperature on the scale with an arrow.
Each division on the number line represents 2 units.
1° below freezing is –1° and it is half way between −2 and 0.
Answer:
0
10
°C
20
M
–10
Exercise 1.2
Focus
Here is a thermometer. The arrow is pointing to 10 °C.
SA
1
−10
0
10°
10
20
30
40
Draw an arrow on the thermometer pointing to −5 °C.
14
Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.
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1.2 More on negative numbers
2
Here are some temperatures.
4 °C −3 °C 5 °C 0 °C −2 °C
Which is the warmest temperature?
b
Which is the coldest temperature?
Look at the number line.
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a
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
8
9 10
Write where you would land on the number line after these moves.
start
count on
–4
1
start
count on
–5
3
c
end
count back
6
6
start
count back
0
9
d
end
end
Circle the larger number in each pair.
Find the difference between the two numbers.
Use the number line to help you.
SA
4
start
b
M
a
end
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0
a
−6
−2
Difference:
b
−3
−1
Difference:
c
4
−4
Difference:
1
2
3
4
5
6
7
8
9 10
15
Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.
We are working with Cambridge Assessment International Education towards endorsement of this title.
1 Numbers and the number system
Practice
5
Here is part of a number line.
Write the missing numbers in the boxes.
6
0
10
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–10
The thermometer shows a temperature of –8 °C.
−10
0
10
20
30
40 °C
Draw arrows on the thermometer to point to these temperatures.
−4 °C 14 °C −1 °C
a
−12, −8,
b
−15,
, 0, 4, 8,
, −5, 0, 5,
,
The temperature outside when Soraya arrived at school was −1 °C.
By lunchtime the temperature had risen by 8 °C.
What was the temperature at lunch time?
SA
8
Write the missing numbers in these sequences.
M
7
Challenge
9
Put these numbers in order on the number line.
−1 1 −2 −3 −5
0
16
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We are working with Cambridge Assessment International Education towards endorsement of this title.
1.2 More on negative numbers
10 The temperature in Amsterdam is 2 °C.
The temperature in Helsinki is −7 °C.
How many degrees warmer is it in Amsterdam than in Helsinki?
11 Here is a fridge freezer.
PL
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The temperature in
the freezer is –15 °C
The temperature in
the fridge is 4 °C
What is the difference in temperature between the fridge and the freezer?
M
12 Here is part of a number line.
Write the missing numbers in the boxes.
100
SA
0
13 Mira counts on in threes starting at −13.
She says, ‘If I start at −13 and keep adding 3, I will reach 0.’
Is Mira correct?
Explain your answer.
17
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We are working with Cambridge Assessment International Education towards endorsement of this title.
1 Numbers and the number system
1.3 Understanding place value
Worked example 3
Which number is 10 times smaller than seven thousand and seventy?
1000s 100s
7
0
7
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7700 707 7007 770 7070
10s
1s
7
0
0
7
When you divide by 10,
all the digits move one place
to the right.
Answer: 7070 ÷ 10 = 707
compose
decompose
regroup ten thousand
million
thousand
M
place holder
equivalent hundred thousand
SA
Exercise 1.3
Focus
1
The distance from London in England to Budapest in Hungary is 1450 km.
Write the number 1450 in words.
2
Circle the number that is five thousand and five.
50 005 5050 5005 50 050 5550
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We are working with Cambridge Assessment International Education towards endorsement of this title.
1.3 Understanding place value
The table shows the number of visitors to a sports centre during four months.
Month
Number of visitors
January
6055
February
6505
March
6500
April
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3
6550
Which month had the most visitors?
4
Complete this decomposition.
305 469 =
+
+9
Heidi’s password is a 5-digit number.
is in the ten thousands place
2
is in the ones place
3
is in the hundreds place
4
is in the thousands place
5
is in the tens place
M
1
SA
5
+ 5000 +
What is Heidi’s password?
Write your answer in words and in figures.
19
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1 Numbers and the number system
6
Fill in the missing numbers.
6
1400
×10
×100
÷100
32
÷10
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×10
×100
8000
×10
÷10
Tick the largest number that can be made using these four digit cards.
M
7
÷10
÷100
×10
Practice
÷10
3
9
0
9
Nine thousand nine hundred and three
SA
Nine thousand and thirty-nine
Nine thousand nine hundred and thirty
Nine thousand and ninety-three
8
Write in digits the number that is equivalent to 130 thousand + 3 tens.
20
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We are working with Cambridge Assessment International Education towards endorsement of this title.
1.3 Understanding place value
9
Here are four number cards.
A
eight hundred and fifty
B
five hundred and eight
C
five hundred and eighty
D
fifty eight
PL
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Write the letter of the card that is the answer to:
a
85 × 10
b
5800 ÷ 10
c
5800 ÷ 100
d
58 × 10
e
580 ÷ 10
f
50 800 ÷ 100
10 Four students decompose the number 29 292.
Here are the results. One answer is incorrect.
9000 + 90 + 20 000 + 200 + 2
B
20 000 + 9000 + 200 + 90 + 2
C
2 + 200 + 20 000 + 90 + 9000
M
A
D
2 + 200 + 20 000 + 90 + 900
Which answer is incorrect?
SA
Challenge
11 Write in words the largest number that can be made using all the digits
3, 1, 0, 9, 7 and 5.
21
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1 Numbers and the number system
12 Use the clues to solve the crossword.
1
3
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2
4
5
6
Across
2. The digit in the ones place in the number 742 793.
M
5. Seven groups of ten.
6. The digit in the ten thousands place in 842 793.
Down
1. The name for 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
SA
3. The digit in the hundred thousands place in the number 814 682.
4. This digit is used to hold an empty place in a number.
13 Fill in the missing numbers.
a
358 × 100 =
c
29 ×
e
= 2900
b
3000 ÷ 100 =
d
2700 ÷
= 27
÷ 100 = 3040
22
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We are working with Cambridge Assessment International Education towards endorsement of this title.
1.3 Understanding place value
14 Here are six number cards.
10
100
1000
35
305
350
Use two cards to complete each calculation. You can use a card more than once.
= 35
×
= 350
SA
M
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÷
23
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