In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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?

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.

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

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

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

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

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?

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

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.

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

A game for 2 players. Practises subtraction or other maths operations knowledge.

If you have only four weights, where could you place them in order to balance this equaliser?

Number problems at primary level to work on with others.

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

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

Can you hang weights in the right place to make the equaliser balance?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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?

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.

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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

Number problems at primary level that require careful consideration.

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

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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?

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?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

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.