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?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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?

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?

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

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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 each work out the number on your card? What do you notice? How could you sort the cards?

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?

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

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.

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

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

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

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

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

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

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

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?

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

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

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

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

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?

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

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

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

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?

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?

How many models can you find which obey these rules?

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?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

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?

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.

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?

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

These pictures show squares split into halves. Can you find other ways?

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