Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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.

Use the information to work out how many gifts there are in each pile.

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?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

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

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

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.

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

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?

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.

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?

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

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

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

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?

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.

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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.

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?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

How would you count the number of fingers in these pictures?

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!

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.

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

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?