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Important The images in this presentation are only for use by the Ri and owners of the images. Please contact maths@ri.ac.uk if you would like to use them.maths@ri.ac.uk

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What else can the Ri offer you? http://www.rigb.org/http://www.rigb.org/ see the ‘Teacher’ section under ‘Education’

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Ri Mathematics Masterclasses: Clothworkers’ Foundation Mathematics in Design: Esmée Fairbairn Foundation Engaging mathematics for all: QCA Acknowledgements

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Resources Flexibility of use: Whole class with extension for the G&T Only G&T after school Exceptional day, e.g. STEM day …

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Warm-up Can you fold a square of paper out of an A4 sheet? Discuss with your pair how you did it and why it works

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Folding fractions Can you fold an A4 sheet of paper in halves? Can you fold a sheet of paper in quarters? What other fractions can you fold perfectly?

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Discuss Follow the fold. What is the fraction folded?

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Can you prove it? Can you prove it is 1/3? Can you explain how it works? 1/3

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Explain why the two triangles below are similar Activity

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Compare the base of the red and blue triangles. What can you say about the heights of the two triangles? The side of square is 1 unit. What is the height of the blue triangle? Activity

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Optional slide Activity Find the ratios between the sides of the triangles shown.

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Can you explain how it works? Step 1: set an origin and use coordinate axes. Write down the equations of the straight lines through the point P. Step 2: use simultaneous equations to work out the horizontal coordinate of the point P. l2l2 l1l1 l 3 P

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Fold again… On the same square, use the folds made to fold the line of equation x=1/3.

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Fold a few more lines… On a fresh square of paper, fold the lines with the equations below. (Set an origin, x-axis, y-axis beforehand.) Y = x Y = 2x Y = 4x Y = 8x Y = 1-x Y = 3x

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Explore Can you extend the method for perfect fifths? How? ??...

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Fifths and other fractions ??...

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For the teacher

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To reflect on How do you implement this activity in the classroom? –How do adapt it to different year groups? –Which competences addresses? –What are the possible pitfalls? –What if someone says that folding paper is not mathematics? –What is the point? –What are the benefits of such an activity for sixth formers? –What have you learnt today as a teacher? –What is the value of working in groups? –What are your thoughts on using the style of this session as your teaching style? –How can I address differentiation of pupils? (one way is using pupils that picked-it-up quicker as helpers)

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Using GeoGebra It is free: www.geogebra.org.www.geogebra.org It is easy to learn and easy for pupils to learn to use it themselves. Because it is free they can have it too. Some teachers share resources on a Geogebra wiki (just use Google to find it). Can use online version if you cannot install it. Requirements: Java enabled PC or Mac. Can use an ‘export’ facility to create a html file with your work (if you want to share your work in the school’s VLE)

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