Heather Mcneill

Heather McNeill

Title: What’s My Rule?

Description: Students will develop the rule for figuring out the total degrees of the interior angles of regular polygons.

Subject(s): Geometry

Educational Level: 9-11

Introduction: The sum of the interior angles of polygons can be determined by considering the number of triangles inside the polygon. Consider a triangle; it has no diagonals so there is only one triangle inside (itself) and its interior angles sum to 180 degrees. A quadrilateral can be cut into two triangles thus the sum of the interior angles for a quadrilateral is 2(180) = 360 degrees. This pattern follows for all regular polygons.

Group Size: Individual & Pairs

Learning Objective(s): - Students will be able to formulate the correct formula for finding the sum of the interior angles of regular polygons by the end of the lesson.

Guiding Question: How do the interior angles change from one regular polygon to another, why does knowing what the interior angles are matter?

Materials: - Computer lab - “Adding It Up” student activity sheet

Procedures:

1. To begin the lesson the teacher should review familiar vocabulary terms with the students. These terms should include: polygon, concave, convex, regular polygon, irregular polygon, and triangulation.

2. Students should then each have a computer and exploring the following link: http://illuminations.nctm.org/ActivityDetail.aspx?ID=9

With this activity the students should begin to consider patterns and evaluate what they are noticing.

3. Next, students are to construct a formula which relates the number of sides to the number of interior angles.

4. Have the students discuss in pairs their findings and compare their student created formulas. Heather McNeill

5. Next pass out the Adding It Up activity sheet, students are to follow the instructions and answer the questions. http://illuminations.nctm.org/Lessons/AddingItAllUp/AddingItAllUp- AS.pdf

6. As a class, discuss the answers to the activity sheet. Then ask the students where they see polygon and specifically triangles in the real-world. (roof trusses, bridges, etc.) Parts of polygons and triangles are used a lot in building construction since it helps to create stronger structures. What professions would need to know the angle measures of the interior angles? (Engineers, architects, construction workers, etc.)

Assessment: “Adding It Up” activity sheet.

Benchmark(s): MA.912.G.2.2 - Determine the measures of interior and exterior angles of polygons, justifying the method used.

Beginning (1) Developing (2) Accomplished (3) Exemplary (4)

Lesson Instructional goals Instructional goals Instructional goals and Instructional goals and Foundations and objectives are and objectives are objectives are stated. objectives clearly not stated. stated but are not stated. easy to understand. Learners have an Learners cannot tell understanding of what Learners have a clear what is expected of Learners are given is expected of them understanding of what them or what they some information and what they should is expected of them and should know. regarding what is know. what they should be expected of them. able to do. Guiding questions Guiding questions are not stated. Guiding questions provide structure, Guiding questions are vague. purpose and meaning provide structure, to lesson purpose, and a compelling interest in the lesson.

Instructional Instructional Some instructional Most instructional Instructional strategies Strategies strategies are strategies are strategies are appropriate for learning missing or strategies appropriate for appropriate for outcome(s). Strategy used are learning outcome(s). learning outcome(s). based on a combination inappropriate. of practical experience, Some strategies are Most strategies are theory, research and based on a based on a documented best combination of combination of practice. practical experience, practical experience, theory, research and theory, research and documented best documented best practice. practice.

Assessment Method for Method for Method for assessing Method for assessing Heather McNeill

assessing student assessing student student learning and student learning and learning and learning and evaluating instruction evaluating instruction is evaluating evaluating instruction is present. clearly delineated and instruction is is vaguely stated. authentic. missing. Can be readily used Assessment is for expert, peer, Can be readily used for teacher dependent. and/or self-evaluation. expert, peer, and/or self-evaluation.

Technology Selection and Selection and Selection and Selection and Use/levels of application of application of application of application of integration technologies is technologies is technologies is technologies is inappropriate (or beginning to be appropriate for appropriate for learning nonexistent) for appropriate for learning environment environment and learning environment learning environment and outcomes. outcomes. and outcomes. and outcomes. Some technologies Technologies applied to Technologies applied enhance enhance learning. applied do not affect learning. learning. Technology level of Technology level of integration is adaptation Technology level of integration is adoption or above. integration is entry or above.

Organization Lesson plan is Lesson plan is Lesson plan is Complete package and unorganized and not organized, but not organized and neatly presented in well Presentation presented in a neat professionally presented. organized and manner. presented. professional fashion.

Attributes of No attributes of One or two attributes Two attributes of Three or more Meaningful meaningful learning of meaningful meaningful learning attributes of meaningful Learning are present learning are present are present learning are present but borderline or superficial learning

Attributes of meaningful learning – Active & Cooperative

Level of integration – Adoption, Adaption, Transformation

Use of technology to support learning – Visualize concepts & Web based resources