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?

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 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?

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

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?

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

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

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?

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

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

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

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?

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

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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

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?

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 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?

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

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

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

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

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?

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

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

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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

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

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 ...

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

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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?

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?

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Can you make the birds from the egg tangram?

How many models can you find which obey these rules?

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?