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.

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

Building with Longer Rods

Building with Longer Rods

This activity has been particularly created for the most able.

When you have completed Building with Rods then go further with this challenge of using rods that are $3$ units long.

Same rules as before - so just to remind you; here are two solutions that fit the rule.

Here are two that don't fit the rule as the small cubes have to be lined up squarely, with no overlapping.

The challenge is to find all the possible ways of stacking the rods, keeping the blue rod on the bottom, the red rod in the middle and the green rod on top.

What do you think will happen if you try the same activity with rods that are $4$ long?

What do you think will happen if the rods are $5$ long?

Why do this problem?

This activity is specially designed for the highest-attaining pupils that you ever come across. It acts as a further extension to Building with Rods and Three Sets of Cubes, Two Surfaces. It's an activity that is intended to give opportunities for pupils to explore a spatrial situation using their intuition and flair.  It also provides them with an opportunity to create a system for solving such problems.

Possible approach

As this is designed for the highest attaining, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.

Key questions

Tell me about what you have found.
Can you describe the ways that you arrived at these shape arrangements?
How did you construct these on the computer?