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There are 56 NRICH Mathematical resources connected to Reasoning, convincing and proving, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Reasoning, convincing and provingIn each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
Can you use the clues to complete these 4 by 4 Mathematical Sudokus?
Can you find out which 3D shape your partner has chosen before they work out your shape?
Use your knowledge of place value to try to win this game. How will you maximise your score?
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Are these statements always true, sometimes true or never true?
Are these statements always true, sometimes true or never true?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
How many possible symmetrical necklaces can you find? How do you know you've found them all?
Take three consecutive numbers and add them together. What do you notice?
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?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This problem looks at how one example of your choice can show something about the general structure of multiplication.
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Can you find different ways of creating paths using these paving slabs?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.
This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.
These tasks provide opportunities for learners to get better at proving, whether through proof by exhaustion, proof by logical argument, proof by counter example or generic proof.
This article for primary teachers suggests ways in which we can help learners move from being novice reasoners to expert reasoners.
In this article for primary teachers we consider in depth when we might reason which helps us understand what reasoning 'looks like'.
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 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.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
Complete the Mathdoku grid using the clues. Can you convince us that the number you have chosen for each square has to be correct?
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.
Can you describe what is happening as this program runs? Can you unpick the steps in the process?
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 significant food for thought.
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 this?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?