Sticks and Shadows

Paul Lockhart’s excellent book Measurement (a constructive follow-up to his infamous diatribe about the start of maths education, A Mathematician’s Lament), includes this gem:

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I adapted for mixed-ability Yr9 class. Some students were thinking deeply about the shape of the curve, others were practicing measuring angles and lengths and plotting coordinates.

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From formal to concrete
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Multiple ways to measure the shadow…

 

Geogebra app proved the most popular, since the least brainpower required to use it. Maybe only give this to the students once they have struggled with a physical metre-ruler or the unit circle first?

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Lovely conversations about how a shadow can have a negative length, and why we would want to think of the metre-ruler sticking straight into the ground and still casting a shadow.

Some students found four squares representing 30 degrees a challenge. Which graph is correct?

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Spot the difference.
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Student explanation
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