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

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

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?

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?

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

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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?

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

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

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

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?

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

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?

There were 22 legs creeping across the web. How many flies? How many spiders?

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?

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?

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.

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

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

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

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

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?

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?

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?

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

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?

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

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

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

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

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

Find a great variety of ways of asking questions which make 8.

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .