Prompt 17: Understanding the Area of a Circle

1. My applet – Cell 2: Area of a Circle
2. My applet – Cell 4: Circle Area through Integration
3. Popular Applet: Anthony Or: Area of Circle

Questions:

1. In regards to Cell 1, students require Pythagoras’ Theorem to find the area of the inscribed triangle. Would you ever set this as a question after a unit on Pythagoras?
2. Cell 2, 3 and 4: The parallelogram method may be the most common way of understanding the formula. However, the triangle method may lead more seamlessly into deriving the formula with calculus. Does this affect your decision of which method you show earlier on in school?
3. The How-before-Why debate is a popular one right now. Would you ensure students knew how to use the formula before promoting understanding or vice-versa? How about if you go backwards from a parallelogram or a triangle into a circle – does drawing on what students already know about areas of shapes change your response to this question?