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?

Number problems at primary level that may require resilience.

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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

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

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?

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

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

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

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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?

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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?

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

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?

This task combines spatial awareness with addition and multiplication.

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 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?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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?

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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!

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

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

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

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?

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

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?

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?

How would you count the number of fingers in these pictures?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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

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?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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

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

A game that tests your understanding of remainders.