Generic Proof

Generic proof involves carefully selecting an example which enables anyone to see, in that example, the general structure.  The tasks below offer opportunities to use generic proof.  They form part of our Mastering Mathematics: Developing Generalising and Proof Feature.

Two Numbers Under the Microscope

Age 5 to 7 Challenge Level:

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

Odd Times Even

Age 5 to 7 Challenge Level:

This problem looks at how one example of your choice can show something about the general structure of multiplication.

Take One Example

Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

Take Three Numbers

Age 7 to 11 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Three Neighbours

Age 7 to 11 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Square Subtraction

Age 7 to 11 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?