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Academy11+

11+ Non-verbal reasoning · Topic explained

NVR matrices

Which picture fills the gap in the grid?

The big idea

Find the rule across the full rows (and down the columns), then use it to fill the gap.

Picture it

Sudoku with shapes: every row has one of each.

Key words

matrix
a grid of pictures following a rule
row
a line of pictures going across
column
a line of pictures going down

Worked examples

  1. 1Warm-up

    Which picture fills the gap?

    • Across the top row, the circle turns black.
    • So the square turns black: a black square.
  2. 211+ standard

    Which picture fills the gap?

    • Each row has a circle, a square and a triangle…
    • …and one white, one grey, one black.
    • Missing: a white square.
  3. 311+ standard

    Which picture fills the gap?

    • Each row counts up: 1, 2, 3, then 2, 3, 4…
    • The last row: 3, 4, 5 dots.
  4. 411+ standard

    Which picture fills the gap?

    • Across each row the arrow turns a quarter clockwise.
    • Left, then up: the gap points up.

The common mistake

The mistake

Only look along the row with the gap.

Instead

Learn the rule from the complete rows first, then check it down the columns.

Why: The row with the gap is missing the evidence; the full rows show the rule.

Where it comes up in the 11+

Matrices are a big part of GL NVR and CEM-style non-verbal tests: 2 by 2 grids first, then 3 by 3.

The video

Video coming soon

We're making a short video that explains nvr matrices step by step. Until then, everything it covers is on this page.

Free printable

NVR matrices worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. In a 2 by 2 grid the top row goes: small circle, big circle. The bottom row starts with a small star. What fills the gap?

    • a big star
    • a small star
    • a big circle
    • a small circle
    Show the answer

    a big star

    Across each row the shape grows.

  2. 2. Each row has one white, one grey and one black shape. A row has white and black. What's missing?

    • grey
    • white
    • black
    • striped
    Show the answer

    grey

    One of each shading per row.

  3. 3. Where do you find the rule first?

    • in a complete row
    • in the row with the gap
    • in the answer options
    • in the corners
    Show the answer

    in a complete row

    Full rows show the whole rule.