Reasoning, convincing and proving

problem
A city of towers

Age

5 to 7

Challenge level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
problem
Colouring triangles

Age

5 to 7

Challenge level

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
problem
Noah

Age

5 to 7

Challenge level

Noah saw 12 legs walk by into the Ark. How many creatures did he see?
problem
Let's investigate triangles

Age

5 to 7

Challenge level

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
problem
Adding all nine

Age

11 to 14

Challenge level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
problem
Calendar capers

Age

11 to 14

Challenge level

Choose any three by three square of dates on a calendar page...
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NRICH starter problem selection

On this page we give a selection of good starter activities for those new to NRICH
$Breaking the Equation ' \Empirical Argument = Proof '$

article
Breaking the equation 'empirical argument = proof '

This article stems from research on the teaching of proof and offers guidance on how to move learners from focussing on experimental arguments to mathematical arguments and deductive reasoning.
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Proof: a brief historical survey

If you think that mathematical proof is really clearcut and universal then you should read this article.
article
Symmetric tangles

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!