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

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

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

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?

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

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

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

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.

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.

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?

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?

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

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

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

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

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

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

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

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

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?

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

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.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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

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

This article for teachers suggests ideas for activities built around 10 and 2010.

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

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.

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

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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?

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.

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?

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?

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?

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

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?