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 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?

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

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

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

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

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

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

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

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

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

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?

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?

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

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

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

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

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

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

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.

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?

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

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

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

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?

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

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?

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

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?

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

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.

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

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

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?

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

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

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?

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?

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

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?

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

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

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