Reasoning, convincing and proving
problem
Pythagoras Proofs
Age
11 to 16
Challenge level
Can you make sense of these three proofs of Pythagoras' Theorem?
problem
Mathdoku
Age
7 to 11
Challenge level
Complete the Mathdoku grid using the clues. Can you convince us that the number you have chosen for each square has to be correct?
problem
An Easy Way to Multiply by 10?
Age
7 to 11
Challenge level
Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
problem
Unravelling Sequences
Age
7 to 11
Challenge level
Can you describe what is happening as this program runs? Can you unpick the steps in the process?
article
Why dialogue matters in primary proof
In this article for Primary teachers, Ems explores three essential features of proof, all of which can be developed in the context of primary mathematics through talk.
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
Impossible sums
Age
14 to 18
Challenge level
Which numbers cannot be written as the sum of two or more consecutive numbers?
problem
Different Products
Age
14 to 16
Challenge level
Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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?