How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?

Rabbit Run

Age 7 to 11 Challenge Level:

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?

You may like to use the interactivity below to help try out your ideas. Click on the buttons to choose a particular length plank. You can move a plank by clicking near its centre and dragging it. You can rotate a plank by clicking and dragging on one of its ends.

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

Possible approach

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.

Key questions

Possible extension

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.