During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

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.

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

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.

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?

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

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

Can you complete this jigsaw of the multiplication square?

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?

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

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

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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.

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

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?

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. . . .

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

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?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

This article for teachers suggests ideas for activities built around 10 and 2010.

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?

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

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

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

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?

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

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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.

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

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

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

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

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?

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,. . . .

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

Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.

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

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

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?

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

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?