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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Squares, Squares and More Squares

#### The diagram shows a square
dissected into seven smaller squares.

Can a square be dissected into any number of squares?

Can you dissect a square into: two, three, four, five ... $n$ other squares?

#### Can you justify your findings?

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Age 11 to 14

Challenge Level

Can a square be dissected into any number of squares?

Can you dissect a square into: two, three, four, five ... $n$ other squares?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?