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### Number and algebra

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# Overlapping Again

## Overlapping Again

You may want to look at Overlaps before you try this problem.

Here are some pairs of shapes:

What overlap shape would you get if you overlapped them halfway across each other?

Here are some more pairs of shapes. What overlap shapes would you get this time?

Which of these overlap shapes did you find?

**Why do this problem?**

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

You may want to look at Overlaps before you try this problem.

Here are some pairs of shapes:

What overlap shape would you get if you overlapped them halfway across each other?

Here are some more pairs of shapes. What overlap shapes would you get this time?

Which of these overlap shapes did you find?

This problem, as Overlaps, focuses on encouraging children to visualise - in this case to picture an image in their head. There are also valuable opportunities for them to apply their knowledge of properties of shape, and to use appropriate vocabulary.

Visualising can be a very useful way of getting into a problem, but it can also help at other stages of the problem-solving process. Providing opportunities like this for your class to practise visualising will help them to become familiar with its uses and to regard it as a legitimate skill to draw upon.

What are the two shapes you are thinking about?

Looking at the overlaps where the sides are diagonal, which shapes could they have come from?

Can you imagine gradually moving one shape across the other one?

Learners who need more of a challenge could try Quadrilaterals.

Suggest trying this simpler version of the problem.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?