Many of the problems in this feature include proof sorting activities which challenge you to rearrange statements in order to recreate clear, rigorous proofs. There are also a selection of "dodgy proofs" where your challenge is to find out where the logic breaks down.
Plus magazine has a selection of interesting articles about proofs here.
What does it all add up to?
Impossible sums
Which numbers cannot be written as the sum of two or more consecutive numbers?
Difference of odd squares
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
Direct logic
Can you work through these direct proofs, using our interactive proof sorters?
Adding odd numbers (part 2)
Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?
KS5 proof shorts
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.