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

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

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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.

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

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 problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

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

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Number problems at primary level to work on with others.

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

What is the sum of all the digits in all the integers from one to one million?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

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?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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

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

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

These two group activities use mathematical reasoning - one is numerical, one geometric.

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.