Challenge Level

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?

Challenge Level

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Challenge Level

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

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Challenge Level

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

Challenge Level

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

Challenge Level

Can you make the birds from the egg tangram?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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 ...

Challenge Level

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

Challenge Level

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

Challenge Level

Make a mobius band and investigate its properties.

Challenge Level

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

Challenge Level

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