Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

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

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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

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

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?

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

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

For this activity which explores capacity, you will need to collect some bottles and jars.

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

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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?

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

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

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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

In this activity focusing on capacity, you will need a collection of different jars and bottles.

Can you make five differently sized squares from the tangram pieces?

Explore the triangles that can be made with seven sticks of the same length.

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

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

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?

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

Can you lay out the pictures of the drinks in the way described by the clue cards?

Can you make the birds from the egg tangram?

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

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

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

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

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

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?

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?

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.

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

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

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

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

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?

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?

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 ...

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