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

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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

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

Number problems at primary level that require careful consideration.

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

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 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?

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?

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

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.

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 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?

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

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 complete this jigsaw of the multiplication square?

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

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?

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

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.

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 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?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

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?

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?

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

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!

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

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?

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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?

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?

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?

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

This task combines spatial awareness with addition and multiplication.

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.

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