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Three Squares

What is the greatest number of squares you can make by overlapping three squares of the same size?

3 squares

You could try this interactivity. Click on the edge of any square to drag it.

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Why do this problem?

This problem is fantastic for reinforcing the properties of a square. Its exploratory nature will engage children and encourage them to experiment with mathematical ideas.

Possible approach

You could begin by using the interactivity to arrange just two squares in different ways and asking children to count the number of squares made in each case. It would be helpful if learners were invited to draw round each square they could see on the interactive whiteboard so that the squares were made easily visible. There might be some debate about which are squares and this gives the group the opportunity to remind each other of a square's properties.

Once they are familiar with the idea, introduce the main problem and suggest they work in pairs. If it is not possible for everyone to be at a computer to use the interactivity, then you could print squares on three different OHTs for children to manipulate themselves. It would also be useful to have squared paper available for jottings, rough working and recording.

In the plenary, you could use the interactivity to share solutions. It would also be worth talking about how children went about the problem. Did they record as they went along? If so, what and why? You may find that some learners drew an arrangement so that they could count the squares more easily by marking in colour. Others might have recorded an arrangement as a reminder of the largest number of squares they had found so far.

Key questions

How many squares can you make by overlapping two large squares?
How do you know that is a square?
Can you move the large squares so that you create more squares?

Possible extension

Some children could try using four squares in the same way, or they could use equilateral triangles instead.

Possible support

Learners could start by looking at two squares and using this interactivity will help .