Can you make the birds from the egg tangram?

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?

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

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?

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.

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

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

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

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.

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

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 ...

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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?

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.

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

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

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?

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

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?

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?

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

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

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

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

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

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?

Use the tangram pieces to make our pictures, or to design some of your own!

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?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Delight your friends with this cunning trick! Can you explain how it works?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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

Reasoning about the number of matches needed to build squares that share their sides.

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?

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

How many models can you find which obey these rules?

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

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?

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?