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?

Fake Gold

Why do this problem?

This problem is an exercise in logical thinking. It is a good opportunity to insist on a precise explanation with justification.

Possible approach

You could wrap up four identical boxes in gold paper and tell the story, using a balance to compare the weights. Pose the question and ask the children what should be done first, and why.

For each subsequent action, ensure that a reason is given. If incorrect suggestions are made, do not correct them but carry out the actions anyway. If children challenge them, ask for justifications.

When a satisfactory solution has been reached and everyone is happy, pose the question about nine bars and give the children some time to work on it in pairs. You might choose to give each pair a large piece of paper to record their thinking, which they can then share with the rest of the class.

You could then confirm a correct solution practically.

Key questions

What would happen to the balance if the weights were eqaul?
What would happen if they weren't?

Possible extension

This version of an old favourite is made easier by specifying that the fake weight is light. A suitable extension might be to see what the minimum number of weighings would be if it wasn't known whether the fake was light or heavy.

Possible support

Done practically, the first part of this activity becomes accessible for all.