NVR: 3x3 matrices with figures

A free preview from the Athena Learning Library — the same lesson registered students learn from.

In this lesson: Complete a 3x3 matrix by combining the row rule and the column rule.

Before you start

You already read grids every day — a school timetable is rows and columns working together. A matrix puzzle is the same idea, played with shapes.

Watch it happen

Crack a matrix: rows first, then columns

3 by 3 grid: row 1: a pale blue hexagon, a white hexagon, a dark grey hexagon; row 2: a pale blue triangle, a white triangle, a dark grey triangle; row 3: a pale blue square, a white square, missing. The missing figure is a dark grey square.

Nine squares, one missing. The eight figures you can see obey a rule across every row and down every column.

Step 1 of 4

The idea

A matrix is a grid, here three rows by three columns, with one box missing. Each row follows a rule across, and each column follows a rule down. The missing box must obey both rules at the same time, and that is what makes it findable.

Tackle one feature at a time. First choose a feature, such as the main shape, and read across the complete top row: how does it change from box to box? Then check that the second row does the same thing. Next read down the columns to see whether the same feature also follows a downward rule. Repeat with the other features: shading, size, direction and number of dots or parts.

Write each rule in words beside the grid. Now build the missing box feature by feature: the row rule gives some features, the column rule gives others, and together they should describe one complete figure. Finally, test your figure against every row and column it belongs to. If it breaks even one rule, a feature is wrong, so recheck that feature only.

Worked example

A 3 by 3 grid of figures follows a rule across every row and down every column. The bottom-right square is missing. Which figure belongs there?

3 by 3 grid: row 1: a light grey star, a light grey hexagon, a light grey diamond; row 2: a pale blue star, a pale blue hexagon, a pale blue diamond; row 3: a black star, a black hexagon, missing. The missing figure is a black diamond.

Read across the rows first. Row 1: a light grey star; a light grey hexagon; a light grey diamond. Row 2: a pale blue star; a pale blue hexagon; a pale blue diamond. The same kind of change runs across both rows.
Now check down the last column: a light grey diamond, then a pale blue diamond, then the missing square. The missing figure has to keep the column rule as well as the row rule.
So the missing figure is a black diamond: in this grid, each column uses one shape, and the shading moves one step along (black → light grey → pale blue) down each column.

Answer: A black diamond — in this grid, each column uses one shape, and the shading moves one step along (black → light grey → pale blue) down each column.

Try one yourself

Another grid, with its bottom-right square missing. Which figure belongs there?

3 by 3 grid: row 1: a dark grey hexagon, a white hexagon, a black hexagon; row 2: a dark grey triangle, a white triangle, a black triangle; row 3: a dark grey circle, a white circle, missing. The missing figure is a black circle.

Watch out

Using only the row rule or only the column rule — the missing box must satisfy both.
Trying to track every feature at once; separate shape and dot count and the rules become easy.
Assuming the shape stays the same down a column just because it stays the same across a row.

Quick check

Try these on your own first — then reveal each answer.

1. Which figure completes this grid?

3 by 3 grid: row 1: a black pentagon, a black triangle, a black star; row 2: a white pentagon, a white triangle, a white star; row 3: a blue pentagon, a blue triangle, missing. The missing figure is a blue star.

2. Which figure completes this grid?

3 by 3 grid: row 1: a blue circle, a white circle, a dark grey circle; row 2: a blue pentagon, a white pentagon, a dark grey pentagon; row 3: a blue triangle, a white triangle, missing. The missing figure is a dark grey triangle.

Practise this concept

Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.

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