## Reflection: Student Led Inquiry Interior and Exterior Angle Sum of Polygons - Section 1: Regular Hexagon Construction and Exploration

Teaching this lesson, I was reminded just how powerful student conjectures are!  My students often amaze me with how they think when they...

• notice important ideas and make their observation sound completely natural
• wonder aloud about relationships (meaningful or not) and their peers follow their thinking so completely
• conjecture about possibilities in ways that lead us in the right direction

It’s even more surprising to me that my students don’t often notice the power of their mathematical thinking!  Few of them recognize the power of their insight and how truly interesting their thinking is!

To me, this is a lesson that lends itself to some of the key values and messages I want my students to consider all the time:

• EVERY student is capable of wondering about something that is mathematically valuable
• We can all get better at justifying our reasoning and explaining our thinking clearly and precisely
• Learning is so much more enjoyable when engaging your own thinking

While I circulated the room as students worked in their groups today, I was able to grab several student’s work, displaying each under the document camera. Sharing snippets of the interesting thoughts and questions that emerged in the room, along with strategic approaches to the investigation (e.g., color coding a well-labeled diagram) made the lesson flow with more consistency.

In my classroom it is often the case that student work is what inspires others to want to put on a new lens, to think differently, or to reconsider the value of a nagging question that emerged for them.  As I shared different pieces of student work, I noticed how student work influenced (and perhaps drove) the kinds of discussions groups were having.  Several groups, for example, began to wonder how they could prove several ideas around special quadrilaterals (a regular hexagon can be divided into two congruent isosceles trapezoids, a regular hexagon has an infinite number of similar kites and rhombuses, etc.).  Several students began to see that equilateral triangles and 30-60-90 triangles seemed to be everywhere and wondered why that was the case (good exposure for a later lesson special right triangles)!

Student Led Inquiry: Using Student Work to Surprise Students with Their Own Wondering and Conjecturing

# Interior and Exterior Angle Sum of Polygons

Unit 8: Discovering and Proving Polygon Properties
Lesson 2 of 9

## Big Idea: Through investigating a variety of polygons with different numbers of sides, students will discover the interior and exterior angle sum for any polygon.

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Standards:
Subject(s):
Math, Geometry, polygons (Determining Measurements), properties of polygons, angle sum theorem, Constructions
92 minutes

### Jessica Uy

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