# Resources tagged with: Mathematical reasoning & proof

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### There are 35 results

Broad Topics > Thinking Mathematically > Mathematical reasoning & proof

### Next-door Numbers

##### Age 5 to 7Challenge Level

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

### Square Subtraction

##### Age 7 to 11Challenge 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 7Challenge Level

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

### Take Three Numbers

##### Age 7 to 11Challenge Level

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

### Less Is More

##### Age 5 to 11Challenge Level

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

### Always, Sometimes or Never? Number

##### Age 7 to 11Challenge Level

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

### What Do You Need?

##### Age 7 to 11Challenge 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?

### 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.

### Three Neighbours

##### Age 7 to 11Challenge Level

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

##### Age 5 to 11Challenge Level

Who said that adding couldn't be fun?

### Reasoning: the Journey from Novice to Expert (article)

##### Age 5 to 11

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

### Two Numbers Under the Microscope

##### Age 5 to 7Challenge Level

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

### Always, Sometimes or Never? KS1

##### Age 5 to 7Challenge Level

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

### Making Pathways

##### Age 7 to 11Challenge Level

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

### Cows and Sheep

##### Age 7 to 11Challenge Level

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

### Always, Sometimes or Never?

##### Age 5 to 11Challenge Level

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

### Reasoning: Identifying Opportunities (article)

##### Age 5 to 11

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

### Interactive Balance

##### Age 5 to 11Challenge Level

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

### True or False?

##### Age 7 to 11Challenge Level

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

### 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.

### Equivalent Pairs

##### Age 5 to 7Challenge Level

Can you match pairs of cards which show the same amount?

##### Age 7 to 14Challenge Level

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

### Sweetie Box

##### Age 5 to 11Challenge Level

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

### Online

##### Age 7 to 11Challenge 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.

### Add 3 Dice

##### Age 7 to 11Challenge 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. . . .

### A Bag of Marbles

##### Age 5 to 7Challenge Level

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

### Walking Round a Triangle

##### Age 5 to 7Challenge 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?

### 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.

### Guess What?

##### Age 7 to 11Challenge Level

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

### 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. . . .

### Always, Sometimes or Never? Shape

##### Age 7 to 11Challenge Level

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

### Problem Solving, Using and Applying and Functional Mathematics

##### Age 5 to 18Challenge 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.

### 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.