Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Can you find different ways of creating paths using these paving slabs?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Use your knowledge of place value to try to win this game. How will you maximise your score?

This article for primary teachers suggests ways in which we can help learners move from being novice reasoners to expert reasoners.

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

In this article for primary teachers we consider in depth when we might reason which helps us understand what reasoning 'looks like'.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Are these statements always true, sometimes true or never true?

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

This problem looks at how one example of your choice can show something about the general structure of multiplication.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . .

Are these statements always true, sometimes true or never true?

What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.