Problem Teachers' Notes Hint Solution

This problem is a challenging context in which to explore area. It involves logical thinking combined with some trial and improvement.

Organise the children in to small groups for this task, making sure that squared paper, coloured pens/pencils, coloured paper, scissors, rulers and calculators are available.

Present the task to the class, either by having the problem on an interactive whiteboard, or using this copy of the problem . Give groups a few minutes to discuss initial ideas about how to tackle it and then invite them to share some thoughts. Encourage approaches which do not rely solely on trial and improvement. For example, some groups may have thought about the area of the rectangle and therefore the possible lengths of its sides.

Give the class time to tackle the problem using whatever equipment they need (it would be handy for each group to have a copy of the problem ) and then draw them together to share their conclusions and different ways of working. Some may have made the different sized squares, others may have been happy to draw or sketch arrangements of squares. Ask some of the groups to explain their thought processes and invite other learners to ask them questions to clarify anything that isn't clear.

What do you know about the rectangle?

How could you try fitting the squares together?

Tiles on a Patio is an investigation based on similar ideas which would make a good follow-on activity.

It might help to have some sets of squares already cut out ready for use.