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

Dotty Six is a simple dice game that you can adapt in many ways.

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

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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

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

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?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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.

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

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

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

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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?

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 arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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!

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?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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

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?

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?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

Use the number weights to find different ways of balancing the equaliser.

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?

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?

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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.

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

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

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.

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

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.