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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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 replace the letters with numbers? Is there only one solution in each case?

Can you complete this jigsaw of the multiplication square?

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?

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.

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

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.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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?

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?

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?

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. . . .

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?

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?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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

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

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.

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

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

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?

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

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?

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

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!

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

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.

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?

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

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

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

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?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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

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

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

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

Have a go at balancing this equation. Can you find different ways of doing it?

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

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