Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Number problems at primary level that require careful consideration.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Can you complete this jigsaw of the multiplication square?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Use the information to work out how many gifts there are in each pile.

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

How would you count the number of fingers in these pictures?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

There were 22 legs creeping across the web. How many flies? How many spiders?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Here is a chance to play a version of the classic Countdown Game.

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

This number has 903 digits. What is the sum of all 903 digits?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?