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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?

Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Calendar Cubes

Age 7 to 11
Challenge Level

Why do this problem?

There is a variety of ways to approach this problem. Some children will need a couple of blank cubes to write on and try out their ideas. Others will need the visual prompt of the cubes but record on paper. Others still will not use the cubes at all, interpreting the information and making it into a logic problem. The discussions about which methods worked for which child can be very fruitful.

Possible approach

Display a couple of large dice (dots or numerals will do) and ask the children to say the numbers which are represented by placing them next to each other - 66, 23 etc. Ask what the largest number could be, and the smallest.

Then pose the problem and allow some time for the children to 'get into' it, bringing them back after a short time to share what they have found out or know already and how they are beginning to work.

When several children have found solutions, ask them to check with each other whether they are the same. Bring the group back together and spend some time asking different children to explain their thinking. Draw attention to the similarities and differences between the methods. Was there one method that was the most elegant or were they all pretty good? Keen children could then make the cubes and a dodecahedron to complete their calendar.

Key questions

What is the largest number we need to display? The smallest?
Are there any numerals we need lots of times?
Are there numerals we only need once?

Possible extension

The problem as it is posed is a closed question. The making of the cubes offers some room for additional challenge as there will be some children who will have solved the problem but will not be particularly dextrous when making the finished objects.

Possible support

Offer all children blank cubes and sticky paper to label the sides. Many will realise they actually don't need the cubes but can work out the solution by rearranging the bits of paper into two piles. Working in pairs can be more fruitful than working alone.