Exterior and Interior Angles: Teacher Notes

Overview

In this activity students will investigate angle properties of polygons.

Important Mathematical Ideas The sum of the interior angles of a polygon is fixed and is determined by the number

of sides. The sum of the exterior angles of a polygon is a constant.

Prior Knowledge Understanding of geometry terms (including diagrams) (e.g., supplementary angles,

interior angles, exterior angles of polygons).

Common Misconceptions The sum of the exterior angles of a polygon changes based on the number of sides. The interior angles of a polygon are always equal even when the polygon is not

regular.

Information to Support/ Enhance/ Extend Learning Students are asked to keep a journal for each unit in the course. It should contain

notes of important mathematical ideas with examples and new vocabulary. ePortfolio may be used for these journal entries. Students can make individual choices whether this is a paper or digital personal

resource. Consider a variety of formats as alternatives to journal entries (e.g., student note,

pair/share, group discussion, exit card, poster, electronic posting). Develop a Word Wall and continue it throughout the unit as new vocabulary and

terms arise that require clarification (e.g., polygon, triangle, quadrilateral, rectangle, square, pentagon, hexagon, octagon, regular polygon, irregular polygon, interior angle, exterior angle).

Students need access to Geometer's Sketchpad (GSP) which is Ministry licensed. Sketchpad explorer can be used for iPads and tablets.o to use this ministry-licensed software on home computers, students need an

authorization codeo Sketchpad Explorer is a free iPad app that allows the user to interact with pre-

made sketches in Sketchpad

Minds On

Task 1: Types of Polygons Students will:

o investigate the properties of polygons using an interactive o complete the Types of Polygons worksheet

Sample solutions posted with Teacher Notes in the vLEChallenge students to find interesting images of different types of polygons to display on the Word Wall

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Exterior and Interior Angles: Teacher Notes

This investigation can be extended to include convex polygons and concave polygons

Action

Students can Pair-Share their predictions for Exterior Angles and Interior Angles of Polygons before doing their investigations

Task 2: Exterior Angles of a Polygon Investigation Students will:

o predict the sum of all the exterior angles of a polygono predict whether the sum of all the exterior angles will be the same for different

types and sizes of polygonso investigate the sum of the exterior angles of a triangle, quadrilateral and a

pentagon using the GSP sketcho record their observations in the Exterior Angles of a Polygon Record Sheeto check with provided sample solutionso reflect back on their earlier prediction and adjust if necessary

Journal Prompts and Sample Responses1) What is the sum of all the interior angles of a polygon?

I know it is 1800 for a triangle and 3600 for a square or rectangle.2) Will the sum of all the interior angles be the same for different types and sizes of

polygons? The sum of all interior angles will not be the same for different types and sizes of polygons.

Task 3: Interior Angles of a Polygon Investigation Students will:

o use GSP to investigate the sum of the interior angles of a triangle, quadrilateral and a pentagon

o record their observations in the Interior Angles of a Polygon Record Sheeto examine the relationship between the number of sides of a polygon and the sum

of the interior angleso look for a pattern between the number of sides in a polygon and the number of

interior triangles that can be created using its vertices (n - 2)o look for a relationship between the number of interior triangles and the sum of the

interior angles of a polygon (n - 2), 1800

o extend the pattern for polygons with more sideso check with sample solutions providedo reflect back on their earlier prediction and adjust if necessary

Consider having students graph the sum of the angles vs. number of sides of a polygon and “see” the relationship as a graphical representation

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Exterior and Interior Angles: Teacher Notes

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Exterior and Interior Angles: Teacher Notes

Consolidation

Task 4: Exterior Angles of Polygons Practice Students will:

o complete the practice questionso check answers with solutions provided

Can be used as a Think/Pair/Share.

Task 5: Interior Angles of Polygons Practice Students will:

o complete the practice questionso check answers with solutions provided

Can be used as a Think/Pair/Share.

Task 6: Assignment 1: Exterior and Interior Angles of Polygons Assignment posted with the unit. Solutions posted with Teacher Notes in the vLE.

Task 7: Student Reflection Students are asked to reflect on their understanding of this topic. These reflections can be used as assessment for learning to help determine next

steps for individual students.

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