Reflection: Connection to Prior Knowledge Constructing an Argument for the Circumference Formula - Section 1: Scaffolded Argument

 

Before jumping into this lesson, it helps if students have had experience dealing with the trigonometry of regular polygons inscribed in circles. It also helps if they've been exposed to the concepts and notation of limits, and asymptotic behavior of functions.

Prior to teaching this lesson, I had taught another lesson entitled Functions Involving Areas of Regular Polygons Inscribed in Circles. That lesson turned out to be much-needed primer for the current lesson. For example, in that lesson students already had experience expressing the perimeter of an inscribed regular polygon in terms of the radius. I can't imagine having to teach them how to do that in this lesson in addition to making the argument for the circumference formula. Students also had experience in that lesson, performing structural analysis and using technology to analyze the asymptotic behavior of functions. Speaking of asymptotic, all of the vocabulary students need in this lesson was developed in that lesson as well.

So all of this to say that there is a significant amount of prior knowledge students need to have before tacking this lesson and I strongly recommend taking time and effort to build that prior knowledge in advance of this lesson.

  Prerequisite Knowledge
  Connection to Prior Knowledge: Prerequisite Knowledge
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Constructing an Argument for the Circumference Formula

Unit 11: Measurement and Dimension
Lesson 1 of 6

Objective: SWBAT construct a semi-formal argument to establish that the circumference of a circle is 2(pi)r

Big Idea: Circular Argument? In this lesson, students use structural analysis, trigonometry, and limits to show that the circumference of a circle is twice the product of pi and the radius.

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