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Games. Generalising. Working systematically. Counting. Interactivities. Mathematical reasoning & proof. Creating and manipulating expressions and formulae. Visualising. PrimaryGames-Number. Factors and multiples.There are 27 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
Online
Age 7 to 11 Challenge 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.
Always, Sometimes or Never?
Age 5 to 11 Challenge Level:
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Sprouts Explained
Age 7 to 18
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. . . .
Neighbourly Addition
Age 7 to 14 Challenge Level:
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
A Bag of Marbles
Age 5 to 7 Challenge Level:
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Two Numbers Under the Microscope
Age 5 to 7 Challenge Level:
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
Next-door Numbers
Age 5 to 7 Challenge Level:
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Always, Sometimes or Never? Number
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Take One Example
Age 5 to 11
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.
Square Subtraction
Age 7 to 11 Challenge Level:
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?
Odd Times Even
Age 5 to 7 Challenge Level:
This problem looks at how one example of your choice can show something about the general structure of multiplication.
Problem Solving, Using and Applying and Functional Mathematics
Age 5 to 18 Challenge Level:
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.
Primary Proof?
Age 5 to 7
Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.
Logic
Age 7 to 14
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.
Paradoxes
Age 7 to 14
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.
What Do You Need?
Age 7 to 11 Challenge Level:
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?
Take Three Numbers
Age 7 to 11 Challenge Level:
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Cows and Sheep
Age 7 to 11 Challenge Level:
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Making Pathways
Age 7 to 11 Challenge Level:
Can you find different ways of creating paths using these paving slabs?
Walking Round a Triangle
Age 5 to 7 Challenge Level:
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?
Three Neighbours
Age 7 to 11 Challenge Level:
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Always, Sometimes or Never? KS1
Age 5 to 7 Challenge Level:
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Always, Sometimes or Never? Shape
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Breaking the Equation ' Empirical Argument = Proof '
Age 7 to 18
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.
Air Nets
Age 7 to 18 Challenge Level:
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Add 3 Dice
Age 7 to 11 Challenge Level:
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. . . .
NRICH is part of the family of activities in the Millennium Mathematics Project.