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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.
problem
What does it all add up to?
Age
11 to 18
Challenge level
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem
Impossible sums
Age
14 to 18
Challenge level
Which numbers cannot be written as the sum of two or more consecutive numbers?
problem
Difference of odd squares
Age
14 to 18
Challenge level
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
problem
Direct logic
Age
16 to 18
Challenge level
Can you work through these direct proofs, using our interactive proof sorters?
problem
Adding odd numbers (part 2)
Age
16 to 18
Challenge level
Can you use Proof by Induction to establish what will happen when you add more and more odd numbers?
list
KS5 proof shorts
Age
16 to 18
Challenge level
Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.