This task combines spatial awareness with addition and multiplication.

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

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

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?

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.

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

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?

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?

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?

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

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?

Delight your friends with this cunning trick! Can you explain how it works?

An environment which simulates working with Cuisenaire rods.

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?