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?

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?

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

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

Can you make the birds from the egg tangram?

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

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

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

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

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

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

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 ...

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

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.

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

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

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?

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?

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?

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?

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?

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?

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

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

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

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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.

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

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

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

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

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

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?

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

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

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?

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