This task combines spatial awareness with addition and multiplication.

This challenge combines addition, multiplication, perseverance and even proof.

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Can you find all the ways to get 15 at the top of this triangle of numbers?

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

This challenge is about finding the difference between numbers which have the same tens digit.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

This article suggests some ways of making sense of calculations involving positive and negative numbers.

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Can you use the information to find out which cards I have used?

Dotty Six is a simple dice game that you can adapt in many ways.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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.

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

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

There are nasty versions of this dice game but we'll start with the nice ones...

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

How can we help students make sense of addition and subtraction of negative numbers?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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 use the numbers on the dice to reach your end of the number line before your partner beats you?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?