Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Can you make square numbers by adding two prime numbers together?

These two group activities use mathematical reasoning - one is numerical, one geometric.

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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.

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?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

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

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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!

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.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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.

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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!

This dice train has been made using specific rules. How many different trains can you make?

Got It game for an adult and child. How can you play so that you know you will always win?

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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. . . .