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

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?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

How can we help students make sense of addition and subtraction of negative 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?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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

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

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 these head, body and leg pieces to make Robot Monsters which are different heights.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

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

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Investigate the different distances of these car journeys and find out how long they take.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

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

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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.

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Investigate what happens when you add house numbers along a street in different ways.

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

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?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?