A game that tests your understanding of remainders.

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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 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?

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

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

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?

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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.

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?

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 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 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?

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

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

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.

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

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

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

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.

Ben’s class were making 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 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.

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Given the products of adjacent cells, can you complete this Sudoku?

Can you complete this jigsaw of the multiplication square?

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

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

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?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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?

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

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?

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

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

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?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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

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?