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### Number and algebra

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### Working mathematically

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### Advanced mathematics

# Folding Squares

*You might like to try A Parallelogram Trisection and Folding Fractions next.*

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Age 14 to 16

Challenge Level

Start with a square...

## Fold to create a diagonal running from bottom left to top right. |
## Find the midpoint of the base by folding. |
## Fold the paper again, joining the top left corner to the midpoint of the base. |
## What fractions of the diagonal do you think your new fold has created? |

Measure the two sections of the diagonal and compare their lengths.

What do you notice?

Is this what you expected?

Is this what you expected?

Can you produce a convincing mathematical argument or proof that justifies what you have found?