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?

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

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.

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?

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?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

Can you complete this jigsaw of the multiplication square?

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

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

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

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

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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.

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

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?

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

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

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

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

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?

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

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

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

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

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

Can you work out some different ways to balance this equation?

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

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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 sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

This task combines spatial awareness with addition and multiplication.

Are these statements always true, sometimes true or never true?

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

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

This challenge combines addition, multiplication, perseverance and even proof.

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?

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