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

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?

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

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?

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

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?

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

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

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?

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?

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?

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.

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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

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

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

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

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.

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.

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.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

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

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

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.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Where can you draw a line on a clock face so that the numbers on both sides have 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?

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?