Figure matrices · nonverbal reasoning

Figure matrix questions, with both rules to find

A grid of figures with one cell left empty. One rule runs across the rows, a different rule runs down the columns, and the missing figure has to satisfy both at once. Finding one rule and stopping is the single most common way to get these wrong.

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How the puzzle is built

  • 1The grid is usually two by two or three by three, with the bottom right cell empty.
  • 2Reading across a row, exactly one thing changes: the colour, the shading, the number of shapes, or the shape itself.
  • 3Reading down a column, a different thing changes. The two rules are independent, which is what makes the puzzle more than pattern spotting.
  • 4The answer has to obey both. Options are built so that each one obeys exactly one rule, which is why a half-solved matrix still feels convincing.

The method, in order

Worth saying out loud the first few times. The order matters more than the speed.

  1. 1. Read one full row first, not the whole grid

    Say out loud what changes from the first cell to the second, then the second to the third. One property, named.

  2. 2. Now read one full column the same way

    A different property should be changing. If it looks like the same one, you have probably misread the row.

  3. 3. Predict the answer before looking at the options

    Describe the missing cell in words: "three of them, green, dotted." Prediction is what stops a plausible option from talking you out of a correct reading.

  4. 4. Check your prediction against every option, not just the first match

    If two options fit, one of your two rules is wrong. Go back to the grid rather than choosing between them.

Where figure matrices questions turn up

CogATthe Nonverbal battery, where it is usually the first item type children meet
NNATas reasoning by analogy and serial reasoning, which use the same grid logic
CAT4 and InViewthe nonverbal reasoning sections
SOF olympiad papersLogical Reasoning, where the grid is often three by three with a picture rule

The four ways children go wrong

These are not guesses. They are what the wrong options in a real question are built from, which is why each one feels reasonable at the time.

Finding the row rule and answering

The fix: Always check the column too. Options are built specifically to reward a half-solve.

Reading colour as the rule when it is shading

The fix: Say the property out loud. "Solid, outline, dotted" is a different rule from "green, blue, amber", and mixing them up puts you one option off.

Counting shapes wrong on the last row

The fix: Count them again. A three-shape cell drawn in a triangle arrangement reads as two at a glance.

Choosing an option that is nearly right

The fix: Nearly right is built on purpose. If your predicted description does not match exactly, it is not the answer.

Questions parents ask

What is a figure matrix question?
A grid of figures with one cell missing. A rule governs how the figures change across each row and a different rule governs how they change down each column, and the missing figure must satisfy both. It measures reasoning with no reading and no arithmetic.
Why does my child find two answers that both look right?
Because that is how the wrong options are built. Each one satisfies one of the two rules but not the other. When two options both look right, it is a signal that one of the rules has been misread, not that the question is unfair.
What rules appear in figure matrices?
The common ones are: a property changes step by step (shading, colour), a count increases, a shape gains a side, or a figure rotates by a fixed amount. Harder items combine two of these, and the hardest apply a rule to a property you have to notice first.
Which tests use figure matrices?
The CogAT nonverbal battery, CAT4 and InView nonverbal reasoning, and SOF olympiad logical reasoning sections. The NNAT uses the same grid logic under different names, reasoning by analogy and serial reasoning.
How should a child approach a matrix they cannot see the rule in?
Change what they are looking at. Ask "what is the same in every cell?" before "what changes?" Eliminating the constants usually leaves the rule visible, and it works when staring at the whole grid does not.
Are figure matrices the same as pattern completion?
No, though they are often confused. Pattern completion asks which piece fits a hole in a single design. A matrix asks you to apply a rule to produce a new figure. The first is matching, the second is reasoning.
At what age do figure matrices get hard?
The two-by-two version with one changing property is accessible from around six. Three-by-three grids with two independent rules are a genuine step up and are where most of the difficulty in a test sits, usually from about grade 3.

Practise the whole test

One skill at a time is how you fix a weakness. A full timed test is how you find out whether it is fixed.

CogAT practice →NNAT practiceOlympiad papers

Other reasoning skills: paper folding, pattern completion, figure classification.