Non-Verbal Reasoning Matrices

A matrix is a grid of figures with one cell left empty, most often 3 by 3, sometimes 2 by 2. Work out the pattern and pick the figure that fills the gap.

In the test the whole grid is called the big square and each cell a small square. The gap can be any cell, not just the corner.

Only two lines can decide the answer: the gap's own row and its own column. Five cells in a 3 by 3, not nine. The rest confirms your rule, it does not find it.

The method

Five beats: gap it, cross it, name it, fill it, check it.

1. Gap it. Say which cell is empty. "Top row, middle column."
2. Cross it. Read the row that crosses the gap, then the column. Ignore the rest for now.
3. Name it. Say which of the four grids below you are in. That tells you how to finish.
4. Fill it. Say the whole missing figure out loud before you look. Shape, size, shade, and where every mark sits.
5. Check it. Cross out on one feature at a time, starting with the one you are surest of.

Expect the row and the column to say different things. The second is usually what splits the last two options. Two options still standing means a rule you have not found.

A 2 by 2 grid is an analogy in a box. Read it across: top-left is to top-right as bottom-left is to what? Then check it downwards.

About 30 to 35 seconds for a 3 by 3, and about 15 for a 2 by 2.

Rules to watch

Name the grid first. There are only four kinds.

• Stepping. Something changes by the same amount along the row: one more dot, a quarter turn, a size up. Carry the step on into the gap.
• One of each. Every row and column holds the whole set, like sudoku. The answer is the one missing from the gap's row and column. Just cross out.
• Row and column. The row decides one thing and the column decides another. Say the answer as a pair. "The row says black, the column says triangle."
• Built. The middle cell of each row is made from the two on either side: joined, stacked, overlapped, or one taken away. If the gap is an end cell, work backwards: what would you need to start with to get that middle?

Then scan the cell itself with the SHAPES+S.

• S — Shade. White, grey, hatched (thin diagonal lines) or black? The most common change of all. Shades swap, or one shape hands its shade to another. Judge a tone against the figure next to it, not from memory.
• H — How many. Count them. A shape can appear, vanish, split, double, or copy itself to each side.
• A — Angle. A quarter turn clockwise, a half turn, or reflected — flipped over like a mirror? Watch one corner. A turn walks it round the shape. A mirror jumps it straight across.
• P — Place. Moved, traded jobs, or gone inside? A small item becomes the big frame, the middle swaps with the corners, loose shapes tuck into containers, a whole ring shifts one place clockwise.
• E — Edges. A different shape? More sides? A solid line gone dashed?
• S — Size. Bigger or smaller?
• +S — Symmetry. Does the figure fold onto itself? Down the middle, across the middle, or the same upside-down. Fold the whole figure, not just its outline. Symmetry is rare in this type of question — check it last if all others fail.

Watch for these traps

Every wrong figure gets most of the grid right. It breaks one thing on purpose.

• Borrowed from another row. Much the most common. It obeys the column but belongs to another row, or the other way round. Say the answer as a pair, and check both halves.
• Right figure, wrong size. Size never feels like a rule, so you stop looking once the shape is settled. Put a size in your prediction.
• Turned, but a part stayed behind. The figure turns, but a dot or a tag slides somewhere else instead of riding round with it. Follow that mark.
• A mirror instead of a turn. They look alike on a nearly symmetrical shape. Find the mark off to one side: a turn walks it round, a mirror jumps it across.
• Right shape, wrong shade. Shaded when it should be white, or the other way round. Say the shade out loud too.
• A copy of the cell next door. Visibly part of the grid, so it feels like it belongs. Usually it forgot to turn or step on.
• Something the grid has never shown. A shade, shape or mark in no other cell. If you never found the rule, new looks like missing. Every part of your answer should already appear in the gap's row or column.

Try these yourself

Now have a go yourself — tap the figure that completes the grid.

Related

• The complete 11+ question-type guide
• NVR: Series — one row of the same idea
• NVR: Analogies — what a 2 by 2 grid really is

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