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

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

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

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

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

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?

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?

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?

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

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?

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

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

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?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

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.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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?

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

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?

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

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

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?

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

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

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

What is the greatest number of squares you can make by overlapping three squares?

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

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

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

For this activity which explores capacity, you will need to collect some bottles and jars.

In this activity focusing on capacity, you will need a collection of different jars and bottles.

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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?

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