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

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

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?

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

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

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

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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?

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?

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.

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

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

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

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

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

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

Can you visualise what shape this piece of paper will make when it is folded?

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

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

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

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

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

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Can you lay out the pictures of the drinks in the way described by the clue cards?

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

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Can you make the birds from the egg tangram?

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

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

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?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

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

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!