Reasoning, convincing and proving

problem
Round a hexagon

Age

7 to 11

Challenge level

This problem shows that the external angles of an irregular hexagon add to a circle.
problem
Walking round a triangle

Age

5 to 7

Challenge level

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
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?
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
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
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
Polynomial interpolation

Age

16 to 18

Challenge level

Can you fit polynomials through these points?
problem
Particularly general

Age

16 to 18

Challenge level

By proving these particular identities, prove the existence of general cases.
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
What's happening?

Age

5 to 7

Challenge level

Shapes are added to other shapes. Can you see what is happening? What is the rule?