Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
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?
Follow these instructions to make a five-pointed snowflake from a square of paper.
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Can you describe what happens in this film?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Here is a chance to create some Celtic knots and explore the mathematics behind them.
Can you deduce the pattern that has been used to lay out these bottle tops?
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.
Make an equilateral triangle by folding paper and use it to make patterns of your own.
Did you know mazes tell stories? Find out more about mazes and make one of your own.
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
What shapes can you make by folding an A4 piece of paper?
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
What do these two triangles have in common? How are they related?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you make the birds from the egg tangram?
Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
Make a mobius band and investigate its properties.
Surprise your friends with this magic square trick.
Can you each work out what shape you have part of on your card? What will the rest of it look like?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
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?
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?
Ideas for practical ways of representing data such as Venn and Carroll diagrams.
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
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?
Can you visualise what shape this piece of paper will make when it is folded?
Make a flower design using the same shape made out of different sizes of paper.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
The challenge for you is to make a string of six (or more!) graded cubes.
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Follow these instructions to make a three-piece and/or seven-piece tangram.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Can you create more models that follow these rules?
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?
We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
This activity investigates how you might make squares and pentominoes from Polydron.
Here is a version of the game 'Happy Families' for you to make and play.