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

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?

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?

How would you count the number of fingers in these pictures?

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...

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

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.

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

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

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

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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

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

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

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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.

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?

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

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?

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?

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?

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

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

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

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

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

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?

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

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

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

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?

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

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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?

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

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.