Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Can you make the birds from the egg tangram?

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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

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

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

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?

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

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

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

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

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?

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

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 ...

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

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

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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

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?

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

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?

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.

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

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?

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

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?

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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

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

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

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

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.

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?