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.

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

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?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

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

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

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.

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.

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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!

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

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?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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?

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

Can you find different ways of creating paths using these paving slabs?

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

This task combines spatial awareness with addition and multiplication.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Use the information to work out how many gifts there are in each pile.

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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.

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

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

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Play this game and see if you can figure out the computer's chosen number.

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

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.

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

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