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?

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?

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

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?

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

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

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 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?

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.

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

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.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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.

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?

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

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

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 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!

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?

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,. . . .

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

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?

Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

A game that tests your understanding of remainders.

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

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

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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?

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

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?