Teacher: R. DelSignore Date: November 24, 2003
Class: Geometry Grade Level: 9
Unit: Polygons Lesson: Angles of Polygons
PA Academic Standards: 2.9.8.J: Analyze geometric patterns (e.g., tessellations, sequences of shapes) and develop descriptions of the patterns.
2.3.8.C: Measure angles in degrees and determine relations of angles.
2.3.8.D: Estimate, use and describe measure of distance, rate, perimeter, area, volume, weight, mass, and angles
Goal of this lesson:
For students to discover the relationship between the sides of a polygon and the number of diagonals that can be drawn from one vertex, the number of triangles that those diagonals form, and the sum of the interior angles of that polygon.
3. List of key questions with answers
4. Answer key to transparency
5. Cooperative Learning Work Sheet
6. Extra pencils
7. Working markers
8. Overhead projector
9. Class notes
1. Locate page number of lesson in textbook
2. Test markers to make sure they work
3. Make sure projector works
4. Prepare class notes
5. Prepare list of key questions and answers
6. Make transparency sheet
7. Complete transparency sheet
8. Make Cooperative Learning Work Sheet
9. Make Cooperative Learning Answer Key
Instructional Objectives (Student-centered, observable, and precise statements of what students will be able to do):
TSWBAT determine the number of diagonals that can be drawn from exactly one vertex of an n-sided polygon.
TSWBAT count the number of triangles that are formed from the diagonals of an n-sided polygon.
TSWBAT calculate the sum of the interior angles of an n-sided polygon.
Introduction (attention getter, anticipatory set, discrepant event, open-ended problem scenario, engagement):
For this lesson, I will be using the Hunter Model. I will begin by reviewing the material we did in the last class about the properties of triangles recalling information such as the sum of the interior angles, the number of sides, and the number of angles, etc. I will ask the students these questions as a review and also have several examples on the board to lead into the new material. This will be my anticipatory set from which I will base the material from this class on. (10 minutes)
Developmental Activities (Instructional components that provide opportunities for students to make progress toward intended instructional objectives):
I will begin the bulk of the lesson will be a question and answer period where I will direct the students to learn from their own responses to my questions. I will begin class by putting the transparency of the polygons on the overhead. There are pictures of a triangle, a quadrilateral, a pentagon, and a hexagon along with a chart that records the number of sides, the number of diagonals, the number of triangles formed from these diagonals, and the sum of the interior angles of these polygons. I begin with the column that has the number of sides and ask the students how many sides each polygon has. I will then move on to the next column which is the number of diagonals that can be drawn from exactly one vertex. I will remind the students that the definition of a diagonal is a line segment that joins two nonconsecutive vertices, and ask them how many diagonals can be drawn from a single vertex of each one of these. I will then pose the question, “What can be said about the relationship of the number of sides of the polygon to the number of diagonals?” Using the answers I will ask them to develop a formula to represent this relationship. Next, I will go onto the next column header: the number of triangles formed from these diagonals. (This should be apparent because of the drawings on the overhead.) After asking the students to help me fill in the column, I will then ask them the question, “What can be said about the relationship of the number of sides of the polygon to the number of triangles formed from the diagonals?” Again, using the responses from the students, I will ask them if they can derive a formula for the relationship between the number of sides and the number of triangles formed from the diagonals. Finally, moving on to the final column on the transparency, I will discuss the sum of the interior angles of each polygon. Recalling, the material presented in the previous class that the interior angles of a triangle must equal 180 degrees, I will point out to the students that we successfully divided each polygon into smaller triangles and ask them if they have any guesses as to how to find the sum of the angles of a polygon. After several responses from the students, I will ask them, “What is the relationship between the number of triangles formed from the diagonals and the sum of the interior angles?” Then I will ask the students if they can come up with a formula representing this relationship. (15 minutes)
At this point I will ask the students if they have any questions about what we have just gone over. I will answer any questions if they are any and if not, I will move on to the next activity. (5 minutes)
The next activity of the class will be a cooperative learning experience. I will hand out a worksheet asking some of the same relevant questions that I asked during the question and answer period. The students will be in groups that I have already predetermined. While they work on this, I will be walking around monitoring the students’ progress on the assignment. At the end of the period, each student will be required to hand in their own paper. (15-20 minutes)
Assessment/Evaluation (How you and the students will know that they learned. May be formative or summative):
The diagnostic assessment for this lesson will be based on the responses at the beginning of class regarding the review of the concepts of the triangle. This will allow me to get a feel for how much the students learned from the last class.
The formative assessment for this lesson will be conducted during the question and answer period that will take up a good portion of the period. This will give me an insight as to how well the students are following the new material I will be presenting. It will be imperative that I do not call on the same students over and over again, so that I can get an overall view of how ALL of the students are grasping the concept.
Finally, the summative assessment will take place as I grade the work sheets the students hand in to me at the end of class. Also, the homework that is due for the next class will show me who is getting it and who may need some extra help.
Conclusion (Closure; a planned wrap-up for the lesson):
As a conclusion to the lesson, I will make sure there are no final questions. I will give the students an opportunity to ask any questions they may have about the material. If there are no questions I will assign the homework that is to be completed before the following class when we will go over it.
Accommodations/Adaptations for Students with Special Needs:
In order to accommodate the student with a learning disability, who requires visual aids to support all audial activities, I will be using the overhead projector for most of the lesson. The transparencies on the overhead will not only have the visual aids that the student requires, but also, there will be a complete list of significant questions. I will not, however, provide any of the students with copies of the transparency until the end of the lesson, as to keep their focus and promote their own note taking during class.
The beginning of the class where we review the properties of a triangle, I will be using a PowerPoint presentation to help the students review.
During the bulk of the lesson, I will be using an overhead projector to instruct the students on the properties of polygons.