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

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?

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?

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

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

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

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?

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 ...

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

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

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

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

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

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

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

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

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

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

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

How many models can you find which obey these rules?

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

Can you make the birds from the egg tangram?

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

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.

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?

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

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?

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.

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

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?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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

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?

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?

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

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

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

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?

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

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?

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.