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

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?

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?

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

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

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?

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?

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?

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?

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

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

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

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?

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

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

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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?

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?

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

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?

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?

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

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

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

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

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

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

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

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

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?

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 the 'double-3 down' dominoes to make a square so that each side has eight dots.

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

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

Use these four dominoes to make a square that has the same number of dots on each side.

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

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?

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.

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.

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

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