Hyde Park High School Teacher Lesson Plan

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Hyde Park High SchoolTeacher Lesson Plan

• Grades 10 11
• Content Geometry (Section H3)
• Mr. Prospere, Mr. Erilus, Mr. Coriolan

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• 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.

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• 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

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

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

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• 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)

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• 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 called
  apothem.
• The area of the polygon can be determined by
  adding the areas of the triangles.

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• 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

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(continued)

• Area of one of the triangles1/2bh1/2sa (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 apothem a
  and the length of each side s.
• Have them find the area of the hexagon by adding
  up the areas
• Area 1/2as1/2as1/2as1/2as1/2as1/2as

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(Continued)

• (1/2)(6as)
• (1/2)(6s) (a)
• since 6s represents the Perimeter(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.

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• 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 ELLs 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

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(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.

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• 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.

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(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.
•