Hyde Park High School Teacher Lesson Plan

1. Hyde Park High SchoolTeacher Lesson Plan Grades: 10 & 11 Content: Geometry (Section H3) Mr. Prospere, Mr. Erilus, Mr. Coriolan

2. Rationale/Background For the past two weeks, 10th and 11th grade students have been studying areas of parallelograms, areas of triangles, trapezoids and rhombi in their geometry class.This lesson builds from previous lesson and is geared toward helping students develop and apply new geometry concepts.The students have already mastered certain concepts such as triangle, quadrilateral, polygon, etc. in this lesson, they will learn how to find the area of regular polygon, a concept related to MCAS standards.

3. Content objectives: At the end of this lesson, student will be able to: a) find the area of a regular polygon b) …altitude of a right triangle and its area formula. Language Objectives: At the end of this lesson, student will be able to: a) describe how to find the area of a regular polygon b) write and add new terms in their vocabulary builder worksheets c) Define orally the theorem: Area of a regular Polygon

4. Materials: Paper Compass Ruler Protractor Straightedge Textbook: Glencoe Geometry(Section H3) - Chapter 11-3:areas of regular Polygons

5. Startup/Motivation: • Describe the difference between a regular and irregular polygon. Vocabulary Apothem Polygon Irregular Polygon Congruent Isosceles Vertex Radius Hexagon Altitude

6. Building Background Knowledge Based on the students’ Prior Knowledge, they can define and recognize the following: Definition of a regular polygon Recognizing characteristics of regular polygons Special Right Triangles (450- 450-900 & 300-600-900)

7. Define the word apothem to the students • A regular polygon can be divided into congruent isosceles triangles by drawing a line from each vertex to the center of the polygon. • The altitude of one of these triangles is calledapothem. • The area of the polygon can be determined by adding the areas of the triangles.

8. Strategies Have students identify from the figure the center of the circle, the radius of the circle, the apothem of the polygon and the sides of the polygon. Let a represent the length of the apothem and s represent the length of a side of the hexagon • since the apothem is perpendicular to a side of one of the six congruent triangle. • Ask students how to find the area of the triangle. • Have them write the formula

9. (continued…) • Area of one of the triangles=1/2bh=1/2sa (s represents the side and a the apothem) • Remind students that the triangles are congruent, therefore they have the same apothem. • Have them write the area of all the other isosceles triangles in the terms of the apothemaand the length of each sides. • Have them find the area of the hexagon by adding up the areas • Area= 1/2as+1/2as+1/2as+1/2as+1/2as+1/2as

10. (Continued…) • =(1/2)(6as) • =(1/2)(6s) (a) • since 6s represents thePerimeter(P) of the hexagon, • ask students to substitute P for 6s • Area=(1/2)Pa • student may use the above expression as a formula to find the area of a regular n-gon. • If students have difficulty finding the apothem of the polygon, explain to them how right triangle trigonometry may be used.

11. Key concept: Area of a regular polygon The area of a regular polygon is half the product of the apothem and the perimeter. • Have students express their ideas in writing and orally • they get help from their teachers to improve their language skills. • Rely on visual learning to assess ELL’s ability to use inductive reasoning. • Teacher may define words by using objects in the classroom as illustration. • Discuss students’ responses. They may describe the same pattern in more than one way

12. (continued…) • Use of index cards to illustrate key concepts • Have students use cooperative learning. They take turns with their partners to explain a concept in their own words and teacher makes correction • Have students practice reading in their math textbooks • English language learners may be unfamiliar with some words, teacher helps them break them into its prefix and its root scribe or if necessary, use students’ native language for better meaning and understanding.

13. Ongoing assessment • Have students make connection by taking them outside to observe and record real-world examples related to the lesson. • Connecting to prior knowledge • Have students choose a partner and have them draw a regular polygon (a square for example) with the radius of the circumscribed circle . Then ask them to use the area formula to calculate the area by first finding the apothem. • Have student work through examples and exercises in their math textbook.

14. (Continued…) • Encourage them to apply definitions, concepts,and theorems they have learned to solve problems. • Have them summarized the main ideas of the lesson in writing and verbally. • Ask them to add the new vocabulary terms to their previous vocabulary list. Practice/Application 1) Find the area of an equilateral triangle with apothem 6 inches. 2) Find the area of a square with radius 4 centimeters. 3) Find the area of a regular hexagon with side length 12 feet. Homework assignment: Chapter 11 unit 3: practice and apply, page 613 exercises 10-20 even numbers.