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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

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

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

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?

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.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

Can you work out some different ways to balance this equation?

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 order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

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

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?

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.

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

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!

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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 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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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!

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?