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?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you replace the letters with numbers? Is there only one solution in each case?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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 problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Can you complete this jigsaw of the multiplication square?

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?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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.

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

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.

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.

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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.

A game that tests your understanding of remainders.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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

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?

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?