In this Do Now, students will review the algebra skills needed to solve problems requiring students to use the formula for sum of the interior angles of polygons and also the formula for exterior angle theorem of polygons.
This activity provides students with an introduction to polygons with a strong focus on the vocabulary related to polygons. This overview will help to provide the basis with which we will discuss more complicated polygons, like parallelograms, in future lessons.
The pair-share at the beginning helps students to work on making math vocabulary their own while using mathematical precise language (MP 6). I have included possible student answers in the resources. You can use them as is to scaffolded student conversation or you may remove the sample answers prior to creating handouts for your students.
Students will complete an exploration that will guide them through how to derive the formula for the sum of interior angles in any polygon. Students will use repeated reasoning (MP7) to discover the degrees in multiple polygons, like quadrilateral, pentagon, hexagon and decagon. This video from Khan Academy provides a great overview for you and students, and can be used as a review this class or for absent students.
I have found that the hardest part of deriving the formula is helping students to jump from numerical values (like a 5 sided figure has 540 degrees) to using the variable "n." The (n-2) part is tricky for students but the video does a nice job of explaining this at around minute 5. Once you have the formula, students can then explain each piece of the formula again to a partner or to the whole class. The derivation of this formula leads directly into the next formula, the measure of each interior angle in a polygon.
The activity/homework can be completed in class or at home by students. These questions focus on applying the formulas for sum of the interior angles in a polygon and the exterior angles in a polygon.
The exit ticket is a quick, formative assessment of students' learning on the sum of the interior angles of a polygon. This exit ticket can easily be extended by asking students to find the measure of each interior angle in an octagon.