Teach your child to write the gap between each pair of numbers, then look for the rule in the gaps.
Practice test 1 is free. No card needed.
Number patterns are solved by finding the rule in how much each number grows or shrinks, then carrying it on. If your child is in Year 5 now, they meet these in Quantitative Reasoning on 6 March 2027.
Checked by the SelectiveReady team on 12 October 2026 · Updated 27 October 2026 · How we check facts
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It's a list, a string of beads or a grid that grows by a rule, and your child finds the next or missing number. The handbook says Quantitative Reasoning asks children to look at information carefully, find patterns and relationships, solve problems, and spot similarities and differences. A number pattern is the plainest test of the patterns part.
Quantitative Reasoning is the third of the four tests, after Reading Comprehension and the writing. It has 35 questions in 35 minutes, so a pattern that won't settle is worth marking and coming back to.
These three are our own, in the ASET style: a missing number, a bead string and a grid that snakes. Each shows the answer and the working, so you can read them together.
As you read, write the gaps out together under the numbers. Talk through how the gaps show the rule, and why the other options break it.
What number is missing from this pattern? 1, 4, 9, 16, ___, 36
Answer: B
Answer: B
Look at the gaps between the numbers: 3, 5, 7, and then 9, so the missing number is 16 + 9 = 25. Check it: 25 + 11 = 36. These are also 1 × 1, 2 × 2, 3 × 3 and so on. 23 is tempting because it repeats the gap of 7 instead of growing it.
Sophie threads beads onto a string in this order: 1 red, 1 blue, 1 red, 2 blue, 1 red, 3 blue, and so on, with one more blue bead after each red bead than the time before. How many beads are on the string when she has just threaded the 8th red bead?
Answer: D
Answer: D
Count the red and blue beads separately. Before the 8th red bead there are 7 groups of blue beads: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 blue beads. Add the 8 red beads: 28 + 8 = 36. 44 is tempting, but it also counts the 8 blue beads that come after the 8th red one.
Noah writes the counting numbers in rows of 6. The first row goes left to right, the second row goes right to left, the third row goes left to right, and so on, as the table shows. Which number will be directly below 130?
| Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 |
| 12 | 11 | 10 | 9 | 8 | 7 |
| 13 | 14 | 15 | 16 | 17 | 18 |
| 24 | 23 | 22 | 21 | 20 | 19 |
Answer: A
Answer: A
Each row holds 6 numbers, so row 22 holds 127 to 132. Even-numbered rows run right to left, so 130 is in column 3. Row 23 holds 133 to 138 and runs left to right, so its column 3 number is 135. 136 is tempting because it adds a whole row of 6, but the rows change direction, so that shortcut fails.
Write the gaps first, and test other ideas only if the gaps don't settle. Gaps are the quickest thing to check, and rough working is fine in the question booklet, but markers never see it, so writing them down costs nothing. These steps are ours, taken from the working above.
Take each number from the next one and write the answer below. In the first question the gaps are 3, 5, 7, so each gap grows by two.
Doubling, square numbers such as 1 × 1, 2 × 2, 3 × 3, or two patterns taking turns are the next ideas to test.
When two things repeat, like red and blue beads, count each colour separately, then add them.
For a far-off number, work out which row or group it falls in rather than writing every number out.
Put it back in and see the pattern carry on. In the first question, 25 + 11 = 36 confirms it.
The wrong options in our questions come from three slips: a gap kept the same, a count that runs too far, and a shortcut across a grid. After you read them together, ask which slip might catch your child, and check for it on the next pattern.
Practise out loud, a few minutes at a time. The handbook suggests about a minute per question, so find the rule first and add the clock later.
Three questions show the method; a full test shows whether your child still finds the rule against the clock. Practice test 1 is free and timed like the real one, and its results show which skills cost marks. More worked questions: ASET quantitative reasoning sample questions.
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.