Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

Follow these instructions to make a five-pointed snowflake from a square of paper.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

This activity investigates how you might make squares and pentominoes from Polydron.

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Can you deduce the pattern that has been used to lay out these bottle tops?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

What do these two triangles have in common? How are they related?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

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?

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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

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?

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

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

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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?

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

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

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

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?

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

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

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Can you make the birds from the egg tangram?

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?

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?

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

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

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

These practical challenges are all about making a 'tray' and covering it with paper.

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.

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?

How many models can you find which obey these rules?

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

How can you make a curve from straight strips 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?