How many different symmetrical shapes can you make by shading triangles or squares?

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

Use the clues about the symmetrical properties of these letters to place them on the grid.

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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.

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

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

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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?

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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?

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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

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

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

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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.

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.

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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

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.

These practical challenges are all about making a 'tray' and covering it with paper.

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?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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?

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?

An investigation that gives you the opportunity to make and justify predictions.

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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!

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

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