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

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?

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?

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

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.

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!

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

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

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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

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?

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!

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

Can you complete this jigsaw of the multiplication square?

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

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?

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?

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 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?

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

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?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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

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?

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

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

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

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?

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?

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?

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

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?

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

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

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

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?

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

This task combines spatial awareness with addition and multiplication.

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

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?

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 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,. . . .