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?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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?

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

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

This task combines spatial awareness with addition and multiplication.

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?

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?

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?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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?

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

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

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

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

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

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.

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

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

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.

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

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.

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.

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

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?

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.

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.

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?

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

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

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.

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

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?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?