Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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.

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?

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?

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

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

What happens when you try and fit the triomino pieces into these two grids?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

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

How many different shapes can you make by putting four right- angled isosceles triangles together?

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

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.

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?

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?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

How many models can you find which obey these rules?

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

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

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

This challenge is about finding the difference between numbers which have the same tens digit.

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

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

Can you find out in which order the children are standing in this line?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

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

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.

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?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

My coat has three buttons. How many ways can you find to do up all the buttons?

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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

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.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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

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