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

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

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

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

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

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

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?

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

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

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

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

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

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

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?

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?

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?

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?

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 ...

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

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

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

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?

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.

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

Use the tangram pieces to make our pictures, or to design some of your own!

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

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?

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?

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?

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 make the birds from the egg tangram?

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

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?

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?

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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

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

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

How can you make a curve from straight strips of paper?

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

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