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Shape Products

Age 11 to 14 Challenge Level:

Why do this problem?

This problem helps students become familiar with the idea of a symbol (in this case a shape) representing a number. They will need to work systematically and use their knowledge of multiplication and division in order to solve the problem.

Possible approach

These printable resources may be useful:      Shape Products
Shape Products - Support

In order to introduce the idea of a shape representing a number, you could start the lesson by having some shapes representing numbers in addition sums. For example:
square + rectangle=5, circle + square = 11, rectangle + rectangle = 8
Ask students to talk to each other about how they would work out what each shape stands for in the calculations above, and then ask them to share their strategies. In this case the last sum is actually the most helpful to start with.

You could then display the first of these slides and explain the task. Ask the students to think on their own about where they might start. Invite them to share their ideas with a partner and work together using the worksheet. If they need some more clues, the Support worksheet has four extra clues - these are also available on the second slide.

Once students have finished, challenge them to tackle the extension questions on the sheet. In a final plenary, discuss the strategies that students used to work out the value of each shape, and the order in which they used the different clues.

Key questions

What is special about clues C and D?
What is unusual about clues F and H?

Possible extension

The problems Cryptarithms and What's it Worth? require similar thinking processes to this problem and would be good ones for students to try next.

Possible support

Students could prepare for this activity by initially tackling Missing Multipliers.

It may be appropriate for some students to start this activity with the Support worksheet with all 12 clues. Some students may like to cut out the 12 clues and move them around in order to more easily compare pairs that contain the same shape.