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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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

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?

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

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?

Number problems at primary level that require careful consideration.

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

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?

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?

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?

Number problems at primary level that may require determination.

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?

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.

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

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?

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.

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?

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

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

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

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.

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?

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

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?

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

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

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?

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?

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

This task combines spatial awareness with addition and multiplication.

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

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

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

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.

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?

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