Explore the triangles that can be made with seven sticks of the same length.

These pictures show squares split into halves. Can you find other ways?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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?

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

What do these two triangles have in common? How are they related?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

An activity making various patterns with 2 x 1 rectangular tiles.

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?

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?

Can you put these shapes in order of size? Start with the smallest.

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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?

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?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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?

This activity investigates how you might make squares and pentominoes from Polydron.

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Can you make five differently sized squares from the tangram pieces?

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Can you make the birds from the egg tangram?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?