Download How Many Degrees?

Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 31962
How Many Degrees?
This lesson facilitates the discovery of a formula for the sum of the interior angles of a regular polygon. Students will draw all the diagonals from one
vertex of various polygons to find how many triangles are formed. They will use this and their prior knowledge of triangles to figure out the sum of
the interior angles. This will lead to the formulation of a formula for finding the sum of interior angles and the measure of one interior angle.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Interactive Whiteboard, Basic
Calculators, LCD Projector, Overhead Projector
Instructional Time: 1 Hour(s) 30 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: regular polygons, interior angles, triangle, angle sum of a triangle, diagonal, degrees, formula, sum
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: Guided or Open Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
Students will find the sum of the angle measures of a polygon and the interior angle of a regular polygon.
Prior Knowledge: What prior knowledge should students have for this lesson?
Classify triangles by sides and angles, classify a polygon by the number of sides (specifically quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons,
decagons, dodecagons and n-gons).
The formative assessment used at the beginning of the lesson will serve as a review and allow instructor to assess competency of the prior knowledge.
Guiding Questions: What are the guiding questions for this lesson?
How many degrees are in a triangle?
How many triangles are in a square?
Can we divide any polygon into triangles? How would this help us to determine the amount of degrees in the polygon?
How can we continue with this strategy as we look at a pentagon?
Introduction: How will the teacher inform students of the intent of the lesson? How will students understand or develop an
investigable question?
Instructor will explain that we are going to "discover" more information about regular polygons. The worksheet (attached) "Degree" will be handed out.
Degree.docx
Degree answers.docx
Instructor will demonstrate how to draw all the diagonals from one vertex and count the number of triangles formed.
page 1 of 3 Students will continue in their groups to complete the worksheet. Instructor will monitor student learning and facilitate students in developing the pattern which leads
to the formula for finding the sum of the angles of a regular polygon.
Investigate: What will the teacher do to give students an opportunity to develop, try, revise, and implement their own methods to
gather data?
Students will be investigating how the degrees of a triangle can be used to find the sum of degrees in any regular polygon. Students will then extend this concept and
investigate how to determine the measure of one interior angle of a regular polygon.
As the teacher circulates and observes student performance, ask the Guiding Questions to assist and assess student understanding.
Analyze: How will the teacher help students determine a way to represent, analyze, and interpret the data they collect?
Students will place their information on the worksheet provided. They will analyze the pattern developed by drawing all the diagonals from one vertex for a square
through a decagon. By reviewing the data, students will develop a formula for finding the sum of interior angles of a regular polygon. Students will then extend this
knowledge and develop a method for finding the measure of one interior angle.
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Instructor will facilitate a discussion about the discoveries of the day and have students summarize. Use the appropriate Guiding Questions to help facilitate this
discussion.
The summative assessment for this lesson will then be given to the student which will assist the students in determining their understanding of the material. This will
be handed in as they leave.
Summative Assessment
This assessment will be used as an "exit quiz."
Assessment will be handed out during the last 5 minutes of class, to be handed in as student leaves.
This is included as an attachment named "Understand."
Understand[3].docx
Formative Assessment
Instructor will use a challenge problem dealing with missing measures of angles in a triangle to assess students knowledge regarding triangles, missing angles, and
complementary and supplementary angles. Challenge problem is attached and named "Find The Missing Angles." This problem may be displayed on overhead or
document camera.
Find the missing angles.docx
Find the missing angles answers.docx
Feedback to Students
The feedback to students is noted within each lesson phase.
Be sure to point out 2 common misconceptions. Students sometimes misread the following 2 questions:
Questions that ask you to find the number of degrees in the sum of the interior angles of a polygon.
Questions that ask you to find the number of sides of a polygon.
Hint: When working with the angle formulas for polygons, be sure to read each question carefully for clues as to which formula you will need to use to solve the
problem. Look for the words that describe each kind of formula, such as the words sum, interior, each, exterior and degrees.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
This activity works well in groups of two or four. Students will discuss the material together and facilitate each other in discovering the formula. Students with specials
needs will be placed in groups that have strengths which will assist with any special needs .
This activity could also be done on a smart board or using a document camera. Students could then participate together and follow along with what is presented.
Extensions:
This lesson could extend to the next day by introducing exterior angles and finding the sum of the exterior angles of various regular polygons.
Suggested Technology: Document Camera, Computer for Presenter, Interactive Whiteboard, Basic Calculators, LCD Projector, Overhead Projector
Special Materials Needed:
Attached Worksheets
ruler
basic calculator
SOURCE AND ACCESS INFORMATION
page 2 of 3 Contributed by: deborah velez
Name of Author/Source: deborah velez
District/Organization of Contributor(s): Seminole
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.8.G.1.5:
Description
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles
created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an
argument in terms of transversals why this is so.
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