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

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

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?

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

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?

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

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?

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?

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?

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

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?

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?

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?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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?

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?

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?

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 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?

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Can you complete this jigsaw of the multiplication square?

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

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.

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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

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.

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 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,. . . .

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

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

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?

Resources to support understanding of multiplication and division through playing with number.

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

This problem is designed to help children to learn, and to use, the two and three times tables.

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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

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

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

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

This task combines spatial awareness with addition and multiplication.