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# Rabbit Run

## Rabbit Run

Ahmed wants to build an outdoor run for his rabbit.

He has decided that it will go against one wall of the shed.

Ahmed has some wooden planks to use for the other sides of the rabbit run. Some are 4m long, some 5m and some 6m.

If he uses three planks, he will be able to make the rabbit run in the shape of a quadrilateral.

What quadrilaterals would he be able to make if he uses three planks the same length?

Why?

What quadrilaterals would he be able to make if he uses two planks the same length and one a different length?

Why?

What quadrilaterals would he be able to make if he uses three planks which are all different lengths?

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Age 7 to 11

Challenge Level

- Problem
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Ahmed wants to build an outdoor run for his rabbit.

He has decided that it will go against one wall of the shed.

Ahmed has some wooden planks to use for the other sides of the rabbit run. Some are 4m long, some 5m and some 6m.

If he uses three planks, he will be able to make the rabbit run in the shape of a quadrilateral.

What quadrilaterals would he be able to make if he uses three planks the same length?

Why?

What quadrilaterals would he be able to make if he uses two planks the same length and one a different length?

Why?

What quadrilaterals would he be able to make if he uses three planks which are all different lengths?

This problem will challenge pupils' knowledge of the properties of quadrilaterals. It is a good context for 'proof by exhaustion'.

It might be useful to have some plastic quadrilaterals available so that the children can refer to them during the task. Children should be encouraged to 'prove by exhaustion' that they have found all possible shapes.

This problem could be extended into compiling minimum sets of criteria to distinguish different quadrilaterals from each other. For example:

a rhombus and a kite

a rhombus, a kite and a square

a rhombus, a kite, a square and a rectangle.