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

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

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

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.

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

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

In this game for two players, the aim is to make a row of four coins which total one dollar.

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?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

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.

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.

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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

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

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

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?

What do you notice about these squares of numbers? What is the same? What is different?

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

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

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

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?

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

Got It game for an adult and child. How can you play so that you know you will always win?

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.

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?