Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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?

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

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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?

How many trapeziums, of various sizes, are hidden in this picture?

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

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?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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?

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 working in a systematic way will ensure none are left out.

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

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

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?

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?

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

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

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

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.

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

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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

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?

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?

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

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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?