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?

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

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

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

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?

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?

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

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?

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

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.

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?

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.

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?

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?

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

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?

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

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!

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

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

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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.

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

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

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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

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

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

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 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?

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

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

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

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?

A game that tests your understanding of remainders.

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?

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.

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?

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

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?

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