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

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

This article for teachers suggests ideas for activities built around 10 and 2010.

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

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 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.

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?

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

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

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?

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?

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

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

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

Find a great variety of ways of asking questions which make 8.

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.

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?

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

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

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

Can you complete this jigsaw of the multiplication square?

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?

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?

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

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?

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

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.

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. . . .

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.

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

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

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

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

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?

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

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?

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

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

Resources to support understanding of multiplication and division through playing with 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?