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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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?

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

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

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.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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

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

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

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

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

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?

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

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.

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

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

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

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?

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

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?

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?

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

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

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?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Can you find all the different triangles on these peg boards, and find their angles?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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?

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?

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?

How many possible necklaces can you find? And how do you know you've found them all?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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?