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Super Value Shapes

Age 7 to 11
Challenge Level

Super Value Shapes

Each of the following shapes has a value

triangle 4
circle 8
rectangle 15

What is the total value of the following two shapes when you put them together?

circle rectangle

How about these? triangle circle circle
Tell us about this triangle rectangle triangle

Use a combination of shapes to show the following values. Can you find more than one way to show the values?
20, 27, 35, 36, 50, 66 and 100

Can you find some numbers between 5 and 50 that cannot be made using these shapes?

Why do this problem?

Children enjoy breaking codes. This set of problems requires substitution skills and is a way of introducing basic algebra concepts to young children. Drawing the results will assist children to make the association between symbol and value.

Possible approach

To make the work more concrete, have pattern block shapes available. Values can be written on sticky labels and put on the shapes until children feel confident enough to work more abstractly by transfering the assigned value to the shape.
It is important to put a number like 29 into the set, because there is no solution for this total. The children could be asked for suggestions about changing the given values so that a solution could be found.
Once the original solutions are found, ask the children to find alternative solutions and to discuss the possibilities offered.

Key questions

Tell me about how you found different shapes for the same total.
How would you like to record your answers?

Possible extension

As an extension children can be asked to choose a shape that they can add to the three that are given and then to give it a value.
Using the four shapes, can the children find new ways to show the given values? Have the children make up problems for friends or neighbours to solve.

Possible support

Make sure you have something to represent each shape that they can handle. It would be good to have many of each so that the children can keep their solutions in front of them and don't need to break each one up to make new ones.