Linear, square, Fibonacci-style and growing-difference patterns.
OftenIn many papers, especially GL AssessmentAbout 60 seconds a question in the test
The big idea
Look at the differences between terms. If they are the same, it is a linear sequence. If the differences themselves change steadily, look at the second difference.
Know special sequences: square numbers (1, 4, 9, 16…), cube numbers (1, 8, 27…), triangular numbers (1, 3, 6, 10…) and Fibonacci-type sequences where each term is the sum of the previous two.
Tips that save marks
Write differences underneath the sequence.
If nothing obvious works, try two interleaved sequences.
Check your rule works for every term, not just the first two.
A worked example
2, 5, 10, 17, 26, ?
Differences: 3, 5, 7, 9.
Differences go up by 2 → next difference is 11.
26 + 11 = 37.
Now try five
Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.
Question 1Aim for about 60 seconds
Each row and each column of this grid follows a pattern. What is the missing number?
9
11
?
15
17
19
21
23
25
Show the worked answer
Answer: E, 13
How to work it out
Along each row the numbers go up by 2; down each column they go up by 6.
So the missing number is 13.
Check it against its row and its column.
Why the other options are wrong
A (19): One step too far down the column.
B (17): This mixes up the row step and the column step.
C (15): This goes one step too far along the row.
D (7): This uses the number above; the pattern goes up as you go down.
Question 2Aim for about 60 seconds
Each row and each column of this grid follows a pattern. What is the missing number?
8
17
26
15
24
33
?
31
40
Show the worked answer
Answer: C, 22
How to work it out
Along each row the numbers go up by 9; down each column they go up by 7.
So the missing number is 22.
Check it against its row and its column.
Why the other options are wrong
A (20): This mixes up the row step and the column step.
B (29): One step too far down the column.
D (31): This goes one step too far along the row.
E (15): This uses the number above; the pattern goes up as you go down.
Question 3Aim for about 60 seconds
Each row and each column of this grid follows a pattern. What is the missing number?
12
15
18
?
18
21
18
21
24
Show the worked answer
Answer: B, 15
How to work it out
Along each row the numbers go up by 3; down each column they go up by 3.
So the missing number is 15.
Check it against its row and its column.
Why the other options are wrong
A (14): A near miss: check the working again.
C (18): This goes one step too far along the row.
D (16): A near miss: check the working again.
E (12): This uses the number above; the pattern goes up as you go down.
Question 4Aim for about 60 seconds
What is the next number in the sequence?
78, 71, 64, 57, 50, ?
Show the worked answer
Answer: A, 43
How to work it out
Write the gaps between the numbers to find the rule.
Take away 7 each time, so the next number is 43.
Question 5Aim for about 60 seconds
What is the next number in the sequence?
25, 36, 49, 64, 81, ?
Show the worked answer
Answer: E, 100
How to work it out
Write the gaps between the numbers to find the rule.
These are the square numbers, so the next number is 100.
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