Cambridge University Press
978-1-316-50925-8 — Cambridge Primary Mathematics Challenge 6
Emma Low
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The number system
Remember
To solve these problems you need to understand that the
position of a digit in a number is important to its value.
Some of the positions are millions, hundred thousands,
ten thousands, thousands, hundreds, tens, ones,
tenths, hundredths, thousandths.
You will need:
resource 1,
page 78
Vocabulary
million
<, > and = are signs used to compare two values. < means
‘less than’, > means ‘greater than’, and = means ‘equal to’.
1
Expand each of these numbers and shade the corresponding sections of the
place-value chart. You will reveal a hidden number.
37005.92, 790 083.19, 251 030.75, 979 209.3, 10 857.57
100 000
200 000
300 000
400 000
500 000
600 000
700 000
800 000
900 000
10 000
20 000
30 000
40 000
50 000
60 000
70 000
80 000
90 000
1000
2000
3000
4000
5000
6000
7000
8000
9000
100
200
300
400
500
600
700
800
900
10
20
30
40
50
60
70
80
90
1
2
3
4
5
6
7
8
9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Use the place value chart below and/or resource 1 to make your own hidden word.
Use numbers up to 1 million, with up to two decimal places.
100 000
200 000
300 000
400 000
500 000
600 000
700 000
800 000
900 000
10 000
20 000
30 000
40 000
50 000
60 000
70 000
80 000
90 000
1000
2000
3000
4000
5000
6000
7000
8000
9000
100
200
300
400
500
600
700
800
900
10
20
30
40
50
60
70
80
90
1
2
3
4
5
6
7
8
9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Give your numbers to a partner to expand and shade, to find your hidden word.
4
Unit 1A: Number and problem solving
CPM framework 6Nn2, 6Nn3, 6Nn8, 6Nn10, 6Nn12, 6Nn13, 6Pt5; Teacher’s Resource 1.1, 1.2
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Cambridge University Press
978-1-316-50925-8 — Cambridge Primary Mathematics Challenge 6
Emma Low
Excerpt
More Information
2
Mark these numbers as accurately as you can on the number line.
2458
5230
9103
7312
1085
0
9862
10 000
Hint: Mark ‘landmark’ numbers such as 5000, on the line first.
Round each number to the nearest 1000 or 100 to help position them on the number line.
3
Complete each number sentence with <, > or =.
986 577
4
985 677
5 × 210
9.23 + 8.69
27.74 – 9.95
8.45 × 100
845 000 ÷ 100
8.29
150 × 7
8.3
Maria has carefully measured
the amount of water she can
store in one container.
12476 ml
Approximately how much can she store in 16 containers?
Explain how you worked out your approximation, and why you think it is a good
approximation.
Hint: Try rounding the number. Try partitioning to multiply.
Unit 1A: Number and problem solving
CPM framework 6Nn2, 6Nn3, 6Nn8, 6Nn10, 6Nn12, 6Nn13, 6Pt5; Teacher’s Resource 1.1, 1.2
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Cambridge University Press
978-1-316-50925-8 — Cambridge Primary Mathematics Challenge 6
Emma Low
Excerpt
More Information
Multiples, factors
and primes
Remember
When a number is a multiple of two different numbers, it is
a common multiple of the numbers, for example, 30 is a
common multiple of 3 and 5.
calculator
You will need:
Vocabulary
A prime number has exactly two factors, itself and 1.
factor, multiple, prime
A general statement is a rule that always works.
1
How many common multiples are there of 5 and 7 between 1 and 200?
There are
common multiples of 5 and 7 between 1 and 200.
The multiples are:
Hint: Use known facts about recognising multiples of 5.
Which numbers between 1 and 200 have the same property as multiples of 5?
2
Identify the three prime numbers in
this grid.
Prime numbers:
,
,
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
Which numbers in this grid have the most factors?
Use this space to investigate.
Which numbers in this grid have an odd number of factors? Why?
Hint: Find pairs of factors systematically, for example, is the number a multiple of 2?
If it is what is 2 multiplied by to make the number? Is the number a multiple of 3?
If it is then what is 3 multiplied by to make the number?
6
Unit 2A: Number and problem solving
CPM framework 6Nn6, 6Nn7, 6Nn17, 6Nn18, 6Nn19, 6Ps5; Teacher’s Resource 12.1, 12.2, 13.1
© in this web service Cambridge University Press
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Cambridge University Press
978-1-316-50925-8 — Cambridge Primary Mathematics Challenge 6
Emma Low
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3
Go through the maze to find the correct exit.
DO NOT solve the calculations, but work out whether the solution would be odd or even.
If the solution is even, turn right, if the solution is odd, turn left.
A
B
C
D
618
– 470
544
+ 930
V
E
621
– 598
782
x 813
U
491
x 369
270
x 385
F
T
G
S
398
+ 674
241
x 78
386
+ 195
167
x 992
924
– 428
H
START
R
918
– 797
I
913
– 545
272
x 890
835
x 768
429
x 753
438
+ 91
493
+ 829
Q
565
x 856
P
O
647
– 288
J
790
– 283
N
M
L
K
The correct maze exit is:
Explain how you knew whether a solution would be even or odd.
For all of the calculations in the maze, write E next to it if the solution is even,
and O if it is odd.
Unit 2A: Number and problem solving
CPM framework 6Nn6, 6Nn7, 6Nn17, 6Nn18, 6Nn19, 6Ps5; Teacher’s Resource 12.1, 12.2, 13.1
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Cambridge University Press
978-1-316-50925-8 — Cambridge Primary Mathematics Challenge 6
Emma Low
Excerpt
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4
What numbers between 1 and 40 can be made by adding pairs of
consecutive prime numbers? Shade them on the grid.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
What do you notice about the sums of consecutive prime numbers?
Write a general statement to describe the total when two consecutive
prime numbers are added.
Hint: 7 and 11 are consecutive prime numbers. 11 is the next
prime number after 7.
8
Unit 2A: Number and problem solving
CPM framework 6Nn6, 6Nn7, 6Nn17, 6Nn18, 6Nn19, 6Ps5; Teacher’s Resource 12.1, 12.2, 13.1
© in this web service Cambridge University Press
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Cambridge University Press
978-1-316-50925-8 — Cambridge Primary Mathematics Challenge 6
Emma Low
Excerpt
More Information
5
Use the numbers 1 to 9 once in each grid.
Place the numbers so that the totals of each row and each column are all prime numbers.
How many different grids can you complete?
Hint: Use what you know about the sums of odd and even numbers to
identify which sets of three numbers might total a prime number.
Unit 1A: Number and problem solving
CPM framework 6Nn4, 6Nc8, 6Nc10, 6Nc14, 6Nc15, 6Nc16; Teacher’s Resource 3.1, 3.2, 4.2
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