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.

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

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?

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?

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?

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?

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

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

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

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?

Can you make the birds from the egg 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?

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

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

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

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

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

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 ...

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

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

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?

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

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

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

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

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?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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.

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

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?

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?

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