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# Tilted Squares

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### Consecutive Numbers

Links to the University of Cambridge website
Links to the NRICH website Home page

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30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

*Tilted Squares printable sheet*

It's easy to work out the areas of squares drawn on a grid if they are oriented in the usual way:

**Can you find a quick and easy method to work out the areas of tilted squares?**

Here are some squares with a tilt of 1:

Notice anything special about their areas?

Can you predict the areas of other squares with a tilt of 1?

What about squares with a tilt of 2? Or 3? Or 4? Or...?

Notice anything interesting?

**Can you make any conjectures about the areas of tilted squares?**

**Can you prove your conjectures?**

*You might like to use the interactivity below to help you to draw tilted squares.*

Full Screen tablet/mobile friendly version

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.