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

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?

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

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

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

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

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

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?

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?

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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

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

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?

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?

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

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

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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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

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

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.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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?

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

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

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?

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

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

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

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?

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

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Make a flower design using the same shape made out of different sizes of paper.

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

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

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?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

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?

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

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

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

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