Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Generic Proof

### Two Numbers Under the Microscope

### Odd Times Even

### Take One Example

### Take Three Numbers

### Square Subtraction

### Three Neighbours

Or search by topic

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.

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.

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.

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.

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?

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?

Age 7 to 14

Challenge Level

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