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

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

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

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

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

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.

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

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

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

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

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

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

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?

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

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?

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?

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

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?

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?

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

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 cube out of straws and have a go at this practical challenge.

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

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

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

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 ...

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

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?

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

Can you make the birds from the egg tangram?

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?

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

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

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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?

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?

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

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?

Here is a version of the game 'Happy Families' for you to make and play.

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

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

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