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

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?

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?

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

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.

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

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

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

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

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?

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

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

56 406 is the product of two consecutive numbers. What are these two numbers?

Can you complete this jigsaw of the multiplication square?

Number problems at primary level that require careful consideration.

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

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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

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

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

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

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

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

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

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

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.

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?

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

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

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?

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

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.

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?

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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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. . . .

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?

Number problems at primary level that may require determination.

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

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