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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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

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?

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?

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

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?

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

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!

Can you complete this jigsaw of the multiplication square?

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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

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

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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

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?

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

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.

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!

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?

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

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

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.

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

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

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

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

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

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?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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?

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.

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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,. . . .

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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

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

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?

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?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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.

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