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?

Room Doubling

Why do this problem?

This is an excellent investigation because it is suitable for learners of all ages (including adults!). It is similar to some ideas that have come from using Cuisenaire rods, in particular the red block [2].

Possible approach

Perhaps you could relate to any experiences that the pupils have had with alterations like these in their own homes. It is valuable to let most pupils have access to doing it practically as well as just on squared paper as people think in so many different ways. Encourage all kinds of recording - some pupils may get into using symbols to represent the rooms.

Key questions

Tell me how you have thought about the way you can get answers.

Possible extension

Children could search for patterns by going to much larger houses with $10$ to $15$ rooms across while still two wide. They could have a look at thoes houses which are symmetric and/or those that are a reflection in design to others. Try here for more!

Possible support

Give pupils copies of the pictures and maybe make some models out of Lego.