In how many ways can you stack these rods, following the rules?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

If you had 36 cubes, what different cuboids could you make?

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

What could the half time scores have been in these Olympic hockey matches?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Can you use the information to find out which cards I have used?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

How many models can you find which obey these rules?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

This activity investigates how you might make squares and pentominoes from Polydron.

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

A challenging activity focusing on finding all possible ways of stacking rods.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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?

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.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Investigate the different ways you could split up these rooms so that you have double the number.