Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

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

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?

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

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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

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

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?

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?

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

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.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

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

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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

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?

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

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

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

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?

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

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?

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

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

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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

Can you make the birds from the egg tangram?

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?

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 see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

Can you logically construct these silhouettes using the tangram pieces?

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

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

Can you put these shapes in order of size? Start with the smallest.

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