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?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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!

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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?

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

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.

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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

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.

Can you hang weights in the right place to make the equaliser balance?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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?

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

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!

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

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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

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?

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?

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?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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.

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!

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

Find all the numbers that can be made by adding the dots on two dice.

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

If you have only four weights, where could you place them in order to balance this equaliser?

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?

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