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

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

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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?

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

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

Can you cut up a square in the way shown and make the pieces into a triangle?

Reasoning about the number of matches needed to build squares that share their sides.

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

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

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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

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

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

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

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

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

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

The challenge for you is to make a string of six (or more!) graded cubes.

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.

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 the birds from the egg tangram?

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

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?

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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 ...

Follow these instructions to make a three-piece and/or seven-piece tangram.

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?

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

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

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?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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

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

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