Generate large numbers then give the values of each digit.

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

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

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.

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.

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...

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?

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?

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?

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?

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

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?

Can you make square numbers by adding two prime numbers together?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

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?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Find a great variety of ways of asking questions which make 8.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

Can you find different ways of creating paths using these paving slabs?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?