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

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?

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?

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

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?

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

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?

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.

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?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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?

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?

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?

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?

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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?

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

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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

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.

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

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

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?

This number has 903 digits. What is the sum of all 903 digits?

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.

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

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

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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,. . . .

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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

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?

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

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!

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

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?

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?

Can you complete this jigsaw of the multiplication square?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

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?

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