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?

Can you make the birds from the egg tangram?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

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

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?

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

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 ...

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?

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

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?

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

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

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

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

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

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

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.

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?

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

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

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

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

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

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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?

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

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?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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

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

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.

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

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?

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 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?

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

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

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

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

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

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

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

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?