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?

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.

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

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?

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

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

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?

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?

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?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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

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.

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

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?

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

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

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.

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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

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

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?

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

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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?

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?

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?

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

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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.

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

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.

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.

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

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

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

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

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?

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!

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 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?