A matrix is a sequence folded into a square, and it gives you something a straight sequence never does: two independent routes to the same answer.
Most children use one of them. Using both is what turns this from a guess into a check.
Non-verbal and spatial reasoning together carry 25% of the marks, according to the partnership entrance test page, and it is the section nothing in primary school prepares a child for.
A sequence folded into a square
You are shown a grid, usually three by three, with one box empty, and five options. The rule runs across each row and separately down each column.
So the missing box is not answering to one pattern. It is answering to two, and they have to agree.
Rows first, then columns
- Read the top row left to right. What happens from box one to box two, and then to box three?
- Test that rule on the second row. If it holds, you have the row rule. If it does not, your rule is wrong, and better to know now.
- Apply it to the row with the gap and predict the answer.
- Now read the columns and work out the column rule the same way.
- Check your prediction against the column. It must satisfy both.
- Only then look at the options.
Step five is the whole value of this question type. If the row says one thing and the column says another, you have misread one of them, and you have caught it before answering.
What can change
| Check | Typical rule |
|---|---|
| Number | Dots increase by one along the row |
| Shading | Shading moves round, or alternates |
| Rotation | A quarter turn per box |
| Position | An element moves one corner each step |
| Combination | The third box combines the first two |
| Cancellation | Lines in both of the first two disappear in the third |
Those last two are worth teaching explicitly, because children rarely guess them. In a combination matrix the third box is the first two overlaid. In a cancellation matrix, anything appearing in both disappears, and only what is unique survives.
Where the marks go
- Using only the rows. Half the information, and no check.
- Testing the rule on one row only. Confirm it on a second.
- Reading the options first. Predict, then look.
- Not writing anything down. "+1 dot, turn 90" in the margin costs three seconds.
the partnership's familiarisation guide demonstrates only two non-verbal types, Figures alike and Hidden shapes, and says plainly that the real test contains types it does not show. So treat any list of question types, including this one, as the best available picture rather than a syllabus.
See our guide to series and sequences, which uses the same checking order.
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The column is a free check, and nobody uses it
Matrices are a topic where children do half the work and then guess. They read across the rows, find something that fits, and pick the option that looks closest.
What they miss is that the missing box has to satisfy its column as well. That is a second, independent route to the same answer, and it is free. If the row and the column disagree, you have misread one of them, and you have found that out before committing.
I would teach the checking order explicitly, because every one of these non-verbal topics needs to be taught. Very few children work the rules out from an example on their own, and matrices are among the ones where a confident wrong method can go unnoticed for months.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
How do you solve matrix questions in the 11+?
Read the top row and work out the rule, confirm it against the second row, then apply it to the row containing the gap. Then read the columns and check your prediction satisfies the column rule too, because the missing box must answer to both.
Why are matrices easier than straight sequences?
Because they give two independent routes to the same answer. A straight sequence offers one pattern and no way to check it, while a matrix lets the column confirm what the row told you.
What is a combination matrix?
One where the third box in a row is the first two overlaid. A related type is cancellation, where anything appearing in both of the first two boxes disappears and only the unique features survive. Children rarely guess either, so both are worth teaching explicitly.
What should my child check in a matrix question?
Number, shading, rotation and position first, then whether the row works by combination or cancellation. Writing the rule in the margin, such as plus one dot and turn ninety, stops a child losing the thread.
Should my child look at the options first?
No. Work out the rule, predict the missing box, and only then look. A child who reads the options first will often talk themselves into one that matches half the rule.