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Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Cut it Out

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Bryony's Triangle

Age 7 to 11
Challenge Level

Bryony's Triangle

Watch the video in which Bryony demonstrates how to make a flower from a square of paper. (If you can't see the control bar, zoom out in your browser.)
She then sets you a challenge: what fraction of the original square of paper is the shaded triangle?

We would love to hear how you approach this problem.
You may want to send us in pictures or photos along with your explanations.

Thank you to Bryony Black for giving us permission to use this problem.

Why do this problem?

The practical aspect of this task will appeal to many children.  It offers an opportunity for learners to share their understanding of fractions with each other as they work to solve the problem.

Possible approach

You could begin by watching the video straight through all together and then talking about the task as a whole group so that everyone feels confident to have a go.  It might be worth playing it again all through before handing out squares of paper.  You could then play the video a third time in short sections as learners fold their own paper.  
Alternatively, you could demonstrate the folding yourself if you are not able to use the video in the classroom.
Once all learners have made the flower, give them a chance to talk in pairs about the fraction part of the challenge.  It might be that at this point, more squares of paper are needed which could be folded again and annotated.  After some time, you could ask pairs to join together to form groups of four so that each pair has chance to explain their thinking so far.
You might give each group or pair a piece of large paper for them to record their ideas, which could then be presented to the rest of the class.    

Key questions

How might you use the folds of your flower to help?
What fractions of the piece of paper can you see using the folds? 
How could you split the paper in half using the fold lines?  A quarter ...?  

Possible extension

Some children might like to have a go at Fraction Fascination.

Possible support

You could encourage children to open out the flower and draw lines on the square over the fold lines to mark halves, quarters etc. You may want to have scissors and coloured pencils/pens available too.  It might be appropriate to offer a different paper-folding task which is more accessible.  You could challenge children to find a fraction contained within that, which perhaps requires fewer 'steps'.