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Can you make five differently sized squares from the interactive tangram pieces?


This activity investigates how you might make squares and pentominoes from Polydron.


Make a cube out of straws and have a go at this practical challenge.

Cuisenaire Squares

Age 7 to 11
Challenge Level

Cuisenaire Squares

Have a look at this picture:


What do you notice?
What do you wonder?

How would you describe what you see?

These patterns have been made using Cuisenaire rods.  
Try recreating the picture using rods or using this interactivity:

What will the next square look like?
And the next one?

How would you describe the pattern in full?
Can you describe the pattern in a general way?

Why do this problem?

This problem encourages children to make conjuctures and generalisations, and it may lead into discussions about square numbers.

Possible approach

Ideally, learners would have real Cuisenaire rods to use, so that they can solve this problem practically as well as virtually. If they are not already familiar with Cuisenaire rods, it is essential to give them time to 'play' before having a go at this activity.

Introduce the task by showing the image. Try not to say anything by way of explanation, simply ask, "What do you notice? What do you wonder?".  Give learners a few minutes of thinking time on their own before suggesting that they talk to a partner.  Invite pairs to share their noticings, or wonderings, with the whole group, writing them up on the board without offering comment yourself. Encourage members of the class to respond to anything you have written. How do they know the images are all squares?

Introduce Cuisenaire, either the physical rods, or the interactivity. If you do not have real rods, it would be useful for children to have access to the interactivity in pairs, for example on a tablet or computer. Invite learners to try to recreate the picture first and then to continue the pattern. You could ask a few pairs to create the next squares in the sequence on the interactive whiteboard, or under a visualiser with real rods. Each time, encourage the class to explain how we know that the image is definitely the next one in the sequence.

Give pairs, or groups of four, a chance to articulate the general pattern and to rehearse the wording until they are happy that it is clear. As a whole class, refine the general 'rule' together. Learners might refer to the rods in the previous picture to describe what a particular image looks like. They may begin to refer to the rods using a numbered length, but that is certainly not necessary. 

Possible extension

Children could create their own pattern, perhaps based on rectangles, and then make similar conjectures and generalisations.

Possible support

By encouraging learners to use real Cuisenaire rods to have a go at this problem, or the interactivity, everyone will be able to get started. Some children may find it helpful to draw rods on squared paper.