# Resources tagged with: Mathematical reasoning & proof

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### There are 96 results

Broad Topics > Thinking Mathematically > Mathematical reasoning & proof

### 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?

### 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!

### Making Pathways

##### Age 7 to 11Challenge Level

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

### 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?

### 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 11 to 14Challenge Level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

### 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?

### Tis Unique

##### Age 11 to 14Challenge Level

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

### Aba

##### Age 11 to 14Challenge Level

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

### 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.

### 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?

### 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.

### 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.

### Eleven

##### Age 11 to 14Challenge Level

Replace each letter with a digit to make this addition correct.

### 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'.

### Gabriel's Problem

##### Age 11 to 14Challenge Level

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

### 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?

### Always, Sometimes or Never? Number

##### Age 7 to 11Challenge Level

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

### 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?

##### Age 5 to 11Challenge Level

Who said that adding couldn't be fun?

### More Mathematical Mysteries

##### Age 11 to 14Challenge Level

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

### The Genie in the Jar

##### Age 11 to 14Challenge Level

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

### Largest Product

##### Age 11 to 14Challenge Level

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

##### Age 7 to 14Challenge Level

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

##### 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. . . .

##### Age 11 to 14Challenge Level

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

### Even So

##### Age 11 to 14Challenge Level

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

### Chocolate Maths

##### Age 11 to 14Challenge Level

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

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

### 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?

### One O Five

##### Age 11 to 14Challenge Level

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

### Sticky Numbers

##### Age 11 to 14Challenge Level

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

### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

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

### Guess What?

##### Age 7 to 11Challenge Level

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

### Take Three from Five

##### Age 11 to 16Challenge Level

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?

### Seven Squares - Group-worthy Task

##### Age 11 to 14Challenge Level

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?

### 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.

### Top-heavy Pyramids

##### Age 11 to 14Challenge Level

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

### 9 Weights

##### Age 11 to 14Challenge Level

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?

### Always the Same

##### Age 11 to 14Challenge Level

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

### Is it Magic or Is it Maths?

##### Age 11 to 14Challenge Level

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

### Calendar Capers

##### Age 11 to 14Challenge Level

Choose any three by three square of dates on a calendar page...

### Greetings

##### Age 11 to 14Challenge Level

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How. . . .

##### Age 11 to 14Challenge Level

A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .

### Clocked

##### Age 11 to 14Challenge Level

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?

### 1 Step 2 Step

##### Age 11 to 14Challenge Level

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?

### Air Nets

##### Age 7 to 18Challenge Level

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

### Elevenses

##### Age 11 to 14Challenge Level

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

### Dicing with Numbers

##### Age 11 to 14Challenge Level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

### Not Necessarily in That Order

##### Age 11 to 14Challenge Level

Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?