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

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

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?

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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.

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.

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?

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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?

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

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

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

56 406 is the product of two consecutive numbers. What are these two numbers?

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

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

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

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

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. . . .

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?

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

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

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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.

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

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?

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?

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?

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?

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?

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?

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?

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

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.

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?

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

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?

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

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

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,. . . .

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?

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

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?

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

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