Reasoning about the number of matches needed to build squares that share their sides.
Make a cube out of straws and have a go at this practical challenge.
Make a flower design using the same shape made out of different sizes of paper.
Can you visualise what shape this piece of paper will make when it is folded?
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 ...
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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.
Can you cut up a square in the way shown and make the pieces into a triangle?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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 by folding in this way? Why not create some patterns using this shape but in different sizes?
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 shape is made when you fold using this crease pattern? Can you make a ring design?
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 make the birds from the egg tangram?
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 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?
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?
Follow these instructions to make a three-piece and/or seven-piece tangram.
In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.
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?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Follow these instructions to make a five-pointed snowflake from a square of paper.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
These practical challenges are all about making a 'tray' and covering it with paper.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
This practical activity involves measuring length/distance.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
How do you know if your set of dominoes is complete?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
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?
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?
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
How many models can you find which obey these rules?
Can you create more models that follow these rules?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
How can you make a curve from straight strips of paper?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
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?
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Can you make five differently sized squares from the interactive tangram pieces?