Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Polydron

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

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

Possible Pieces

Age 5 to 11
Challenge Level

We are going to look at possible jigsaw pieces.

The kind of jigsaw we're looking at is rectangular, with straight edges.

Some of the most common jigsaw shapes are a bit like these three pieces below:

So, for each jigsaw piece we start with a square template, then some sides have a peg. The edge pieces of the jigsaw have one or two straight sides.

We will only use pieces that have at least one peg and one hole.

Challenge 1

Using pieces that have at least one peg and one hole, find all the possible ways of making a rectangular jigsaw three pieces wide and two pieces deep, with straight edges all the way around. All six pieces should be different.

Challenge 2

Find all the possible pieces that have at least one peg and one hole.

Challenge 3

Read all of this one before starting!

Again, only use pieces that have at least one peg and one hole and none the same.

Find as many possible ways of making a two by four rectangular jigsaw, starting with this piece in the top left-hand corner.

Before you start making/drawing/constructing pieces, think carefully and then estimate how many possible arrangements there will be and be able to explain your reasoning to others.

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