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.
article
Take one example
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.
problem
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.
problem
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.
problem
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?
problem
Three neighbours
Age
7 to 14
Challenge level
Take three consecutive numbers and add them together. What do you notice?
problem
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?