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?

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?

Three Neighbours

Age 7 to 14
Challenge Level

Take three consecutive numbers and add them together. What do you notice?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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