Reflection: Developing a Conceptual Understanding Constructing Tangents to Circles - Section 3: Construction 2: Tangent from a Point Outside the Circle


It's really important to me that my students actually understand why the constructions they are doing work. Why? Because ultimately what they're learning is how to use tools of geometry, not how to follow directions.

Many of my students merely want to memorize the steps and call themselves knowing the constructions. These same students are confounded when they are presented with construction problems (e.g., construct a square with the same area as a given rectangle). I want my students to be trained in how a compass and straightedge, but beyond that I want them to know the geometric relationships that explain why the constructions work.

To ensure that this happens, I try to always include a prompt that asks students to explain why this construction works. In this way, I can be more confident that they are seeing the constructions in the same way they would a proof (each step has a reason) instead of seeing them as magic recipes that produce the desired effect without us having a clue as to how.

  Promoting Conceptual Understanding of Constructions
  Developing a Conceptual Understanding: Promoting Conceptual Understanding of Constructions
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Constructing Tangents to Circles

Unit 8: Circles
Lesson 4 of 5

Objective: SWBAT construct tangents to circles at a specified point and from a point outside the circle and explain why the constructions work.

Big Idea: More than just recipes...Constructions are more like proofs, and in this lesson, students will need to understand the reasons why they work.

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Math, Geometry, circles
  65 minutes
tangent from outside
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Environment: Suburban
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