Lesson 15 Circle functions

Episode 3 (Extension)

Reasoning Resources: Paper, scissors (optional)
Value of the comparison between area and circumference in real-life situations.
Visual clues are often ambiguous. Give pupils the real-life context of daffodil bunches sold in two different sizes. One size is half the circumference of the other and half its price. /s that fair? Which is the better buy?

Any example of familiar bunching is possible: sweet sticks, incense, baby carrots, asparagus etc. The pupils have to assume that the sticks are of the same type and packed in the same way.
To be convinced that four small bunches have the same area as one large one may take time, and practical experience with paper and scissors! Accept that this looks fair if pupils suggest that it does, but that we need to think more deeply. Leave pairs and groups to argue the case. You may wish to give them paper and scissors. discussion pupils should recognise that they must compare areas. They may use newly
acquired knowledge to argue their ideas. Some pupils may also think that the area of the large bunch is equivalent to about three small bunches, using pi inappropriately, rather than 4.
Looking deeper into the
real-life situation involves
measurement, calculation
and reasoning.


Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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