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

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 problem is designed to help children to learn, and to use, the two and three times tables.

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

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?

A game that tests your understanding of remainders.

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!

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 complete this jigsaw of the multiplication square?

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?

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

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

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.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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?

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

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

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 your logical reasoning to work out how many cows and how many sheep there are in each field.

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?

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?

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!

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,. . . .

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

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

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

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

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?

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

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?

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?

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

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.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?