![Noah](/sites/default/files/styles/medium/public/thumbnails/content-98-10-letme1-icon.gif?itok=m27sCnq8)
Reasoning, convincing and proving
![Noah](/sites/default/files/styles/medium/public/thumbnails/content-98-10-letme1-icon.gif?itok=m27sCnq8)
![Adding all nine](/sites/default/files/styles/medium/public/thumbnails/content-01-09-bbprob1-icon.gif?itok=2iAxlA4H)
problem
Adding all nine
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!
![Calendar Capers](/sites/default/files/styles/medium/public/thumbnails/content-01-01-bbprob1-icon.jpg?itok=NedgmNOj)
![NRICH starter problem selection](/sites/default/files/styles/medium/public/thumbnails/nrich-starter-problem-selection.png?itok=QBSjj5l9)
page
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 '](/sites/default/files/styles/medium/public/thumbnails/content-id-6664-icon.jpg?itok=ek8-LdKl)
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.
![Proof: A Brief Historical Survey](/sites/default/files/styles/medium/public/thumbnails/content-id-5996-icon.jpg?itok=Jyo4ys0K)
article
Proof: A Brief Historical Survey
If you think that mathematical proof is really clearcut and
universal then you should read this article.
![Symmetric Tangles](/sites/default/files/styles/medium/public/thumbnails/content-id-5746-icon.jpg?itok=r8ngRfHK)
article
Symmetric Tangles
The tangles created by the twists and turns of the Conway rope
trick are surprisingly symmetrical. Here's why!
![An introduction to proof by contradiction](/sites/default/files/styles/medium/public/thumbnails/content-id-4717-icon.jpg?itok=yHHT3-Ae)
article
An introduction to proof by contradiction
An introduction to proof by contradiction, a powerful method of mathematical proof.
![Primary Proof?](/sites/default/files/styles/medium/public/thumbnails/content-id-2838-icon.jpg?itok=8KxGpROL)
article
Primary Proof?
Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.
![The Golden Ratio, Fibonacci Numbers and Continued Fractions.](/sites/default/files/styles/medium/public/thumbnails/content-id-2737-icon.jpg?itok=bDkJETlD)
article
The Golden Ratio, Fibonacci Numbers and Continued Fractions.
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.