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Rectangle Tangle

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

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Dividing a Cake

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?


Stage: 2 Challenge Level: Challenge Level:1


How can you cut a doughnut into eight equal pieces with only three cuts of a knife?

Why do this problem?

This problem requires a good understanding of the concept of fractions and challenges children to visualise 3D shapes.

Possible approach

You might decide to ask this question orally to start with, without giving the group any visual clues at all. Give pupils time to think on their own, then talk to a partner, then share initial ideas altogether.

In order to come to work on a solution, make sure pairs are encouraged to jot down/draw anything that might be useful.

You could test out ideas at the end with a real doughnut or a bagel!

Key questions

How could you make your first two cuts?
How could you turn the doughnut so you can make another cut?

Possible extension

This sheet gives some ideas for extending the challenge, for example by looking at other 3D shapes, or by focusing on an A4 sheet or paper.

Possible support

Using play dough or plasticene to make a doughnut-shape and then to try cutting it, will help children who find the visualisation difficult.