There are **96** NRICH Mathematical resources connected to **Mathematical reasoning & proof**, you may find related items under Thinking Mathematically.

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

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

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

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

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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?

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

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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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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?

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Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

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Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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Which set of numbers that add to 10 have the largest product?

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Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!

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Without doing lots of calculations, can you decide which of these number sentences are true? How do you know?

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Max and Bryony both have a box of sweets. What do you know about the number of sweets they each have?

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Can you find out which 3D shape your partner has chosen before they work out your shape?

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

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

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

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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

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Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

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

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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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.

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Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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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Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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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.

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A huge wheel is rolling past your window. What do you see?

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

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.

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. . . .

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

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Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

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If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?