Number problems at primary level that require careful consideration.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

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

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

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

How would you count the number of fingers in these pictures?

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

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

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

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

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

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?

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

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 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 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.

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.

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

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.

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

There were 22 legs creeping across the web. How many flies? How many spiders?

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?

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

This task combines spatial awareness with addition and multiplication.

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?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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.

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?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Here is a chance to play a version of the classic Countdown Game.

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?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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

Number problems at primary level that may require determination.