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?

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

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

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?

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

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

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

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?

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.

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

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

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

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.

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

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.

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 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.

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

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

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?

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?

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

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?

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

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

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?

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?

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.

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

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!

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?

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

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

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

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