Matrices (3×3 grids) is one of the standard non-verbal reasoning patterns in GL Assessment-style 11+ papers, and it rewards method over talent more than almost any other question type. The child is shown a grid of nine cells with one cell left blank, and must choose the option that completes it. Children who learn to interrogate each shape systematically routinely overtake 'naturally spatial' peers who guess. This guide gives you the exact step-by-step method, the traps that catch careful pupils, and the free practice to lock it in.
What a matrix question looks like
In a 3×3 matrix you see a grid of nine boxes. Eight contain shapes; one — usually the bottom-right cell — is empty. Beneath or beside it sit five answer options, labelled A to E, and you mark your choice on a separate answer sheet. The grid is governed by rules that run across each row and down each column at the same time. Your job is to work out both rules and find the single option that obeys them. Expect several matrix questions in a GL NVR paper; in reasoning-heavy regions, NVR can carry a large share of the total marks, so this is a type worth mastering rather than muddling through.
The step-by-step method
Treat every matrix the same way. A fixed routine stops you staring blankly and burns fewer seconds:
- Scan the top row left to right. Ask what changes from cell one to cell two to cell three. Does a shape rotate, add a line, change shade, grow, or multiply?
- Name the row rule out loud in your head. For example, 'the arrow turns 90° clockwise each step' or 'one extra dot is added each time'.
- Now read the first column top to bottom. Find the column rule the same way. It is usually different from the row rule.
- Predict the missing cell. Apply the row rule to the third row and the column rule to the third column. Both must point to the same answer.
- Match to an option, then eliminate. Reject any option that breaks either rule. The correct answer satisfies the row rule and the column rule together.
If neither rows nor columns give a clean pattern, check the diagonals — a minority of papers hide the rule there. Always confirm your pick against a second property before committing.
Attributes to scan in every cell
Most matrices combine two or three simultaneous changes. Train your child to run through a fixed checklist so a second, quieter change is never missed:
- Number of shapes or elements (counting rules are the most-missed of all)
- Shading or fill — black, white, striped, dotted
- Size — growing or shrinking across the grid
- Orientation — rotation angle or which way an arrow points
- Position — where a shape sits inside its cell
- Line thickness and style (solid vs dashed)
- Symmetry and added or missing lines
A worked example
Imagine the top row shows a triangle, then a triangle with one internal line, then a triangle with two internal lines. The row rule is 'add one line each step'. Now read down the first column: a small shape, a medium shape, a large shape. The column rule is 'the shape grows each step'. The missing bottom-right cell must therefore be a large triangle with two internal lines. Any option that is large but has one line, or has two lines but is small, is a trap. Only the option satisfying both rules is correct — that is the whole discipline of matrices in one picture.
The classic traps
These are the errors that cost marks even for able children:
- Solving from the row only. The row rule alone often fits two options; the column rule is what separates them.
- Missing a counting rule. A change in the number of dots or lines hides easily under a more obvious style change.
- Confusing rotation with reflection. A shape that turns is not the same as its mirror image — check a distinctive corner.
- Falling for a red herring option. Papers include a 'nearly right' distractor that matches one rule but breaks the other.
Timing and pacing
GL NVR papers are tightly timed at roughly 35 to 50 seconds per question, with no calculator and a separate answer sheet. Use a simple pacing plan: read the grid, name both rules, eliminate, mark. If a matrix resists after about 40 seconds, note it, mark your best-guess option (never leave a multiple-choice blank), and return if time allows. A steady rhythm beats sinking two minutes into one stubborn grid.
| Element | Typical GL figure |
|---|---|
| Paper length | ~50 minutes |
| Seconds per question | 35–50 |
| Format | Multiple choice, answers A–E |
| Scoring | Standardised Age Score (SAS), ~69–141 |
How marking works
Raw scores are converted to a Standardised Age Score that adjusts for your child's exact age in months, so a younger child is not disadvantaged against an older classmate. The SAS usually runs from about 69 to 141, with 100 the average; many grammar schools look for around 111 or above, though exact pass marks vary by area and year. Getting the harder matrix questions right lifts that standardised score, which is why targeted practice on this one type pays off.
How to practise this type
Work in short, focused bursts — ten questions, mark, then review every error out loud: 'what property did I miss?' Our free NVR worksheet sets isolate matrices so the method becomes automatic, the full NVR types list maps the wider territory, and timed mock papers knit the types back together at exam pace. Round it off in the revision hub, and check the key 11+ dates so your plan is paced to test day.
Frequently asked questions
Why are two rules involved in one matrix?
Each 3×3 grid is governed by a rule that runs across the rows and a separate rule that runs down the columns. The correct answer must satisfy both at once, which is why solving from the row alone often lands on a trap option.
How long should a matrix take?
Budget roughly 35 to 50 seconds. If you are stuck after about 40 seconds, mark your best guess and move on — you can return if time allows, and a blank scores nothing on a multiple-choice paper.
What score does my child need?
NVR is marked as a Standardised Age Score, age-adjusted and usually between about 69 and 141. Many grammar schools need around 111 or above, but the exact qualifying mark depends on your area and the year, so check your specific centre.