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.

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?

Number problems at primary level that require careful consideration.

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

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?

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

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.

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?

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?

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.

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

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

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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

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

Can you score 100 by throwing rings on this board? Is there more than way to do it?

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?

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

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

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?

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?

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?

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?

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?

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

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

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?

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?

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.

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Number problems at primary level that may require determination.

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

This number has 903 digits. What is the sum of all 903 digits?

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

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

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