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?
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.
What shapes can you make by folding an A4 piece of paper?
Can you visualise what shape this piece of paper will make when it is folded?
Can you each work out what shape you have part of on your card? What will the rest of it look like?
Make a flower design using the same shape made out of different sizes 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?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Can you deduce the pattern that has been used to lay out these bottle tops?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Did you know mazes tell stories? Find out more about mazes and make one of your own.
Follow these instructions to make a five-pointed snowflake from a square of paper.
Make a mobius band and investigate its properties.
Surprise your friends with this magic square trick.
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Follow these instructions to make a three-piece and/or seven-piece tangram.
Here is a version of the game 'Happy Families' for you to make and play.
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?
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
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.
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
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 make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
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 ...
Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
How can you make a curve from straight strips of paper?
A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?
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?
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.
How do you know if your set of dominoes is complete?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
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?
Make a ball from triangles!
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
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?
This activity investigates how you might make squares and pentominoes from Polydron.