Title: Polygons and their interior angles
Name: Lauren Johnson
Date: April 27, 2006
Grade/ Age: Eighth grade; ages 13-16
Purpose:

For students to become familiar with using technology, such as GSP, while constructing different polygons. Also, the purpose of the lesson is for students to find a relationship between the sum of the degrees of the interior angles to the number of sides of a polygon.
Standards:
P2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.
Intermath Alignment:
What is the sum of the angles of a triangle? of a quadrilateral? of a pentagon? of a hexagon? What is the sum of the angles in convex polygons in terms of the number of sides? Move the mouse pointer over the picture for a hint.
Objectives:

After constructing different polygons in GSP (situation), the students will be able to determine the sum of interior angles of any polygon when given the number of sides (learned capability) to help develop their critical thinking skills in geometry
(object) by finding a relationship between the sum of degrees of interior angles and the number of sides of a polygon (action) by observing the different constructions of polygons (constraints).
Materials:

GSP/ computer lab

Pencil

Paper

Essential Questions:

What is a polygon?

Where can I find polygons outside of school?
Procedure:
1.
Grab students attention by having students identify different types of polygons in the classroom and naming each type of polygon. (7 min)
2.
Then, have students find a partner to work with. (3min)
3.
Have the students create a chart on a piece of paper that has three different sections (the sections should be labeled as follows: name of polygon, number of sides, and sum of interior angles) – (5min)
4.
Take students to the computer lab and have them open GSP.- (5min transition)
5.
Students will then construct three random points and connect them with line segments to form a triangle (3 sided polygon).
6.
Then, the students will use the calculate button to measure the degrees of each angle in the figure.
7.
Once students have found each angle’s degree measurement, the students will add the angles together to find the sum of the degrees in a three-sided polygon.- (steps
3-6 will take approximately 10 min)
8.
Have students construct a 4 sided, 5 sided, and 6 sided polygon, along with measuring each interior angle and finding the sum of all the interior angles. Have the students record the data in their chart.- (30 min)
9.
Finally, have students explore the relationship between the number of sides and the sum of interior angles in any polygon to derive a formula finding the interior angles of a polygon. (Provide the students with scaffolding by having them calculate the difference between the number of sides and the sum of the interior angles). – (20 min)
Closure:

Discuss the findings and discoveries of the students GSP exploration of polygons.
Transition:

Connect to next lesson by having students think about the measure of the exterior angles and how they would find out that information. What knowledge would they use?
Assessment:

Observe the activity as students work in GSP and determine if students found the correct formula for the sum of interior angles of a polygon.
Evaluation:

Have students print out their constructed polygons (3, 4, and 5 sided) and look for at least 50% of the students with the correct formula.

Reflection:
After completing the lesson, it was apparent that most students were not able to come up with a formula even after I provided them with the hint of calculating the difference between the number of sides and the sum of the interior angles. I should have allowed my lesson plan to focus on just one aspect, like the sum of the interior angles in a triangle and then I could have had the students to identify the different types of triangles that can be formed from the different angle measurement. I could then even follow with how many non-overlapping triangles can be formed in a quadrilateral, pentagon, and hexagon. This would then provide my students with the scaffolding they need to build a bridge in their learning gap.