Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Can you find all the different ways of lining up these Cuisenaire rods?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

How many trapeziums, of various sizes, are hidden in this picture?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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 create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Can you use this information to work out Charlie's house number?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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?

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 the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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?

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

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!

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

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

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?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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.

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?

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?

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?