Can you fill in the empty boxes in the grid with the right shape and colour?

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?

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?

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?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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?

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

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

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

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

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

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

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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?

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

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

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.

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?