Can you put these shapes in order of size? Start with the smallest.
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?
What shapes can you make by folding an A4 piece of paper?
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?
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.
Make a flower design using the same shape made out of different sizes of paper.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Can you visualise what shape this piece of paper will make when it is folded?
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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Can you cut up a square in the way shown and make the pieces into a triangle?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
These pictures show squares split into halves. Can you find other ways?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
What do these two triangles have in common? How are they related?
This practical activity involves measuring length/distance.
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?
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.
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you make five differently sized squares from the interactive tangram pieces?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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 ...
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 split each of the shapes below in half so that the two parts are exactly the same?
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?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Can you each work out what shape you have part of on your card? What will the rest of it look like?
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
Can you make the birds from the egg tangram?
Exploring and predicting folding, cutting and punching holes and making spirals.
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?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you lay out the pictures of the drinks in the way described by the clue cards?
You'll need a collection of cups for this activity.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
Reasoning about the number of matches needed to build squares that share their sides.
This activity investigates how you might make squares and pentominoes from Polydron.