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

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

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. . . .

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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?

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?

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

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

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

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

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.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

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

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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?

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

Are these statements always true, sometimes true or never true?

This task combines spatial awareness with addition and multiplication.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Number problems at primary level to work on with others.

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?

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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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 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?

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

Number problems at primary level that require careful consideration.

Number problems at primary level that may require determination.

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?

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?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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