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?

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

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?

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

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

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their 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?

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

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

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?

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

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

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

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

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

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?

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

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

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.

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

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.

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?

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?

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?

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

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 players. Practises subtraction or other maths operations knowledge.

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

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

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

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

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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