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

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.

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?

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

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.

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

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?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

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

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

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

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?

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?

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

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?

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?

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.

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?

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?

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

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?

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?

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?

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

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

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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

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?

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?

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?

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

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

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

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

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?

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

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?

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

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

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?

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?