## Reflection: Rigor Polygons: Introduction & Investigation - Section 1: What is a Polygon?

A task doesn't need a lot of bells and whistles to be a rich task.  This period of dialogue and debate about the definition of a simple polygon became very high level in my classroom.  Achieving this level of rigorous discourse requires a few simple things, in my personal experience.

The teacher should:

• be willing to entertain questions that they themselves may find perplexing
• never tell a student, "No, that's not a -----," but instead, when presented with a student error/misunderstanding, should ask guiding questions to eventually lead them to a change in thinking.  (What makes you say that?  What is the definition of a simple polygon?  What kind of sides do you see on your polygon? and so on).
• encourage students who persist when they hit the point of cognitive dissoance
• be willing to sometimes say, "I don't know" or "I'm not sure" and then elaborate upon the steps s/he will take to find the needed information
• model the fun in thinking about perplexing questions and the limits of definitions (the arbitrary point at which a line becomes a really thin rectangle - conceptually very abstract)

The students should:

• explain their reasoning in complete sentences
• be allowed to attempt to justify a "wrong" answer. The student who thought he could draw a 2 sided polygon is a great example of the productive use of "incorrect" thinking. His illustrations on the board led to very rich conversations in my class.

A Rich Conversation About Simple Polygons - Constructing Viable Arguments & Critiquing the Reasoning of Others
Rigor: A Rich Conversation About Simple Polygons - Constructing Viable Arguments & Critiquing the Reasoning of Others

# Polygons: Introduction & Investigation

Unit 11: Geometry in Architecture
Lesson 1 of 9

## Big Idea: Interacting with polygons and testing the definitions can be engaging, fun and build a powerful, individualized understanding. (Lesson updated: January 6, 2015)

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Standards:
Subject(s):
Math, Geometry, engineering
60 minutes

### Jennifer Valentine

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