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

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'.

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

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?

Number problems at primary level that require careful consideration.

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.

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?

Can you find what the last two digits of the number $4^{1999}$ are?

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

Number problems at primary level that may require determination.

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

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?

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

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

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?

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?

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.

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?

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

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.

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?

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

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

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

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?

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

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

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?

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

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

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?

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

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 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?

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?

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

This task combines spatial awareness with addition and multiplication.

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?