Q1.
Children in Year 6 make number patterns.
This group uses the rule ‘2 less than’.
Write in the missing number.
1 mark
This group uses the rule ‘divide by 3’.
Write in the missing number.
1 mark
Page 1 of 20
Q2.
Here is a number sequence.
Write the missing number.
1
3
6
10
Explain how you worked it out.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
2 marks
Q3.
This series of patterns grows in a regular way.
How many dots would be in pattern 5?
How many crosses would be in pattern 5?
1 mark
Page 2 of 20
Q4.
Write the co-ordinates of the next triangle in the sequence.
1 mark
Q5.
Here is part of a number line.
Write the missing numbers in the boxes.
2 marks
Page 3 of 20
Q6.
Here is part of a number grid.
Here is another part of the same grid.
Write in the missing number.
1 mark
Q7.
In this sequence each number is double the previous number.
Write in the missing numbers.
3
6
12
24
48
2 marks
Page 4 of 20
Q8.
The first two numbers in this sequence are 2.1 and 2.2
The sequence then follows the rule
‘to get the next number, add the two previous numbers’
Write in the next two numbers in the sequence.
2.1
2.2
4.3
6.5
2 marks
Q9.
Here are four digit cards.
Choose two cards each time to make the following two-digit numbers.
The first one is done for you.
an even number
a multiple of 9
a square number
a factor of 96
2 marks
Page 5 of 20
Q10.
Here is a repeating pattern of shapes.
Each shape is numbered.
The pattern continues in the same way.
Write the numbers of the next two stars in the pattern.
and
1 mark
Complete this sentence.
Shape number 35 will be a circle because ...
..............................................................................................................................
...............................................................................................................................
...............................................................................................................................
1 mark
Q11.
Here is a sorting diagram for numbers.
Write a number less than 100 in each space.
even
not even
a square number
not a square number
2 marks
Page 6 of 20
Q12.
Write all the factors of 30 which are also factors of 20
.................................................................................................................................
2 marks
Q13.
Here is a sorting diagram with four sections, A, B, C and D.
multiple of 10
not a
multiple of 10
multiple of 20
A
B
not a
multiple of 20
C
D
Write a number that could go in section C.
1 mark
Section B can never have any numbers in it.
Explain why.
1 mark
Page 7 of 20
Q14.
The numbers in this sequence increase by the same amount each time.
Write in the missing numbers
I mark
Q15.
Write these numbers in the correct places on the diagram.
5
6
7
8
2 marks
Q16.
Here is a number chart.
Circle the smallest number on the chart that is a multiple of both 2 and 7
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
1 mark
Page 8 of 20
Here is the same number chart.
Circle the largest number that is not a multiple of 2 or 3 or 5
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
1 mark
Q17.
Amir says,
‘All numbers that end in a 4 are multiples of 4’.
Is he correct?
Circle Yes or No.
Yes / No
Explain how you know.
1 mark
Page 9 of 20
Q18.
Dev says,
‘When you halve any number that ends
in 8 the answer always ends in 4’.
Is he correct?
Circle Yes or No.
Yes / No
Explain how you know.
1 mark
Page 10 of 20
Q19.
The numbers in this sequence increase by 3 each time.
3
6
9
12
...
The numbers in this sequence increase by 5 each time.
5
10
15
20
...
Both sequences continue.
Write a number greater than 100 which will be in both sequences.
2 marks
Page 11 of 20
M1.
(a)
–2 (wherever written).
No mark is awarded for “2–”
1
(b)
162 (wherever written).
1
[2]
M2.
(a) 15 OR 19 OR any other number supported by acceptable explanation
in part (b)
Accept 15 OR 19 irrespective of explanation in part (b).
1
(b)
Explanation which is consistent with the sequence given in part (a)
If a correct answer to 11a appears and is justified by the
explanation, and the box in 11a was left blank, then award
the mark for part (a).
Do not accept vague or arbitrary explanations such as:
‘every time you add you go up’;
‘it does the same pattern’;
‘the numbers between keep going up’;
‘I just guessed’.
Accept explanations in the form of numerical indications on
the number sequence. Explanation must be sufficiently clear
to enable the calculation of missing number.
1
[2]
M3.
9 (dots)
6 (crosses)
Both to be correct for 1 mark.
[1]
M4.
(10, 7) (12, 7) (10, 10)
All correct, in any order for 1 mark.
[1]
Page 12 of 20
M5.
(a)
–100 written in the left-hand box.
Do not accept 100–
1
(b)
150 written in the right-hand box.
1
[2]
M6.
Chart completed as shown:
[1]
M7.
Award TWO marks for the sequence completed as shown:
If the answer is incorrect, award ONE mark for two numbers correct.
Accept answers as fractions, eg ,¾, 1½
Accept for ONE mark
• the number in the third box is 96
AND
• the number in the first box is half of the number in the
second box eg
Do not award any marks if all numbers are whole numbers.
Up to 2
[2]
M8.
Award TWO marks for the correct answer of
Page 13 of 20
If the answer is incorrect, award ONE mark for
either
1m0.8 in the first box
or
a number in the second box, which is 6.5 greater than the answer given in the first box.
Numbers must be in the correct order.
Up to 2
[2]
M9.
Award TWO marks for all three numbers correct as shown:
•
a multiple of 9
•
a square number
•
a factor of 96
OR
If the answer is incorrect, award ONE mark for two numbers correct.
Up to 2
[2]
M10.
(a)
AND
1
(b)
An explanation which recognises that the numbers in circles
are multiples of 5, eg
•
Because all the circles are multiples of 5.
•
Because 35 is in the five times table.
Both numbers must be correct for the award of the mark.
Answers may be written in either order.
Do not accept vague or arbitrary explanations, eg
• ‘Because you keep on adding 5’;
• ‘Because the circles are 5 more each time’.
U1
[2]
Page 14 of 20
M11.
Award TWO marks for a correct number written in each
of the four boxes.
even
not even
a square
number
0 OR 4 OR 16
OR 36 OR 64
1 OR 9 OR 25
OR 49 OR 81
not a square
number
even AND
not a square AND
less than 100
odd AND
not square AND
less than 100
If the answer is incorrect, award ONE mark for three boxes completed correctly.
Accept more than one number in each box, provided all are
correct.
Up to 2
[2]
M12.
Award TWO marks for all four factors, as shown:
1, 2, 5, 10
If the answer is incorrect, award ONE mark for:
•
three factors correct and none incorrect
OR
•
four factors correct and one incorrect.
Accept factors written in any order.
All four factors and no incorrect numbers must be
given for the award of TWO marks.
Up to 2
[2]
M13.
Any odd numbered multiple of 10, ie 10 OR 30 OR 50 OR 70 OR 90 OR
any number ending with any of the pairs of digits above.
1
Page 15 of 20
An explanation which recognises that all multiples of 20 are also multiples
of 10, eg:
•
‘Because all the numbers in the 20 times table are also in the 10 times table’
•
‘Because all multiples of 20 are multiples of 10’
•
‘Because 20 is in the 10 times table’
•
‘All multiples of 20 go in box A because 10 goes into them’
•
‘20 is a multiple of both 20 and 10, and so is 40, 60, etc’
•
‘Because if it’s not a multiple of 10, it can’t be a multiple of 20’
•
‘Because if it is a multiple of 20, it has to be a multiple of 10’
•
‘Because 10 is a factor of 20’.
Do not accept vague or arbitrary explanations, eg:
• ‘Because 40 is a multiple of 10’
• ‘Because they would be in box A instead’
• ‘Because all the multiples of 10 are multiples of 20’
• ‘Because 10 is a multiple of 20’.
1
[2]
M14.
[1]
M15.
Award TWO marks for numbers written in the correct regions as shown:
If the answer is incorrect, award ONE mark for any three numbers written in the correct regions.
Page 16 of 20
Do not accept numbers written in more than one region.
Accept alternative indications such as lines drawn from the
numbers to the appropriate regions of the diagram.
Lines need not touch the time line provided the intended accuracy
is clear.
Up to 2
[2]
M16.
(a)
71
72
73
81
82
83
91
92
93
74
94
75
76
77
78
79
80
85
86
87
88
89
90
95
96
97
98
99
100
1
(b)
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
98
99
100
Do not award the mark if more than one number is circled.
Accept alternative unambiguous indications, eg numbers ticked,
crossed or underlined.
1
[2]
Page 17 of 20
M17.
An explanation which gives a counter-example to illustrate that not all numbers
ending in 4 are multiples of 4, eg:
•
‘14 is not a multiple of 4’
•
‘4, 24 and 44 are multiples of 4, but not 14 and 34’
•
‘14 or 34 don’t work’
•
‘54’
OR
an explanation which recognises that only numbers ending in 4 which have
an even number of tens are multiples of 4, eg:
•
‘It has to have an even number of 10s as well, like 20 or 40’
•
‘14, 24, 34, 44, 54, 64 – only half of them are’
•
‘4 doesn’t go into 10 so 14 isn’t’.
No mark is awarded for circling ‘No’ alone.
Do not accept vague or incomplete explanations, eg:
• ‘Some numbers end in a 4 but aren’t multiples of 4’
• ‘16 doesn’t end in 4’
• ‘Not all multiples of 4 end in 4’
• ‘24 is a multiple of 4 but the next one isn’t’
• ‘4, 8, 12, 16, 20, 24 etc’.
If ‘Yes’ is circled but a correct, unambiguous explanation is given,
then award the mark.
U1
[1]
Page 18 of 20
M18.
An explanation which gives a counter-example to illustrate that halving a number that ends
in 8 does not always give a number ending in 4, eg:
•
’18 doesn’t work’
•
‘It could end in a 9’
•
‘Double 49 is 98’
•
’58 ÷ 2 = 29’
•
‘Half of 8 is 4 but half of 18 doesn’t end in 4’
•
’18, 28, 38, 48, 58, 68 – only half of them work’
•
‘It has to have an even number of 10s, like 28 or 88’
•
‘38’
No mark is awarded for circling ‘No’ alone.
Do not accept vague or incomplete explanations, eg:
• ‘Half of them don’t’
• ‘Half of 28 is 14’
• ‘Double 44 is 88’
If ‘Yes’ is circled but a correct, unambiguous explanation is given,
then award the mark.
U1
[1]
M19.
Award TWO marks for a multiple of 15 which is greater than 100, eg
105 OR 120 OR 135 OR 150 OR 300
Accept more than one answer if all are correct.
If the answer is incorrect, award ONE mark for evidence of appropriate method, eg:
Accept for ONE mark 30, 45, 60, 75 OR 90
← Not spotting matching number (105)
← One step size incorrect (96 to 98)
← One step size incorrect (75 to 80)
← Multiple greater than 100 but not calculated
Answer need not be obtained for the award of ONE mark.
Up to 2
[2]
Page 19 of 20
Page 20 of 20