Right Triangle Geometry - Lesson Plan

Objectives

Teaching Plan A (2 Days, 50 Minutes Each)

The Right Triangle Geometry lesson can be approached in one of two ways, depending on students' understanding of right triangle geometry prior to beginning the lesson.Teaching Plan A assumes that students have not yet been introduced to certain principles of right triangle geometry, including the Pythagorean Theorem, Sum of Angles, and Definition of Sine, Cosine, and Tangent. If your students are already familiar with these principles, you may refer to Teaching Plan B.

DAY1 (50 Minutes)

Introduce Applications of Right Triangle Geometry (10-15 minutes)

The objective of this section is to introduce students to the types of problems that can be solved using right triangle geometry.

  1. Using a computer projector, demonstrate how to go to the eNLVM website, go to your school and class, and login. (5 minutes)
  1. Ask students to login to the eNLVM and direct them to the Right Triangle Geometry lesson. Have them read or work through the Motivation section. This section describes problems that can be solved using right triangle geometry. Since the purpose of this section is to motivate, students do not have to answer the questions the first time through. However, you may ask students to return to this section at a later time to answer the questions. (5-10 minutes)

Discuss Principles of Right Triangle Geometry (30 minutes)

The objective of this section is to introduce the basic principles of right triangle geometry needed to solve for unknown values of a right triangle.

  1. Have students turn off their computer monitors. Display the first activity of the Motivations section using the computer projector. On the whiteboard, identify the known and unknown values of the right triangle used in the activity. Discuss the Definition of Tangent and the Pythagorean Theorem as ways to solve for the unknown values. (10-15 minutes)
  2. Explain the Definition of Sine and Cosine and their applications. Also, describe how to use the Sum of Angles to find the value of an unknown angle when two angles are known. (15 minutes)

    If your access to computers is limited, you may consider presenting these principles as part of an earlier lesson. If so, please refer to Teaching Plan B.
  1. As a supplemental teaching tool, you may go to the Practice section of the Right Triangle Geometry lesson (using the computer connected to the projector) and solve several problems using the Right Triangle Solver. As appropriate, you may direct your students to follow along on their computers.

DAY 2 (50 Minutes)

Solve Problems Using Right Triangle Geometry

The objective of this section is to help students apply and master the principles of right triangle geometry by solving problems.

  1. Ask students to login to the eNLVM and go to the Right Triangle Geometry lesson.
  2. Using one of the following methods, introduce students to the Right Triangle Solver (used in the Practice Section) and teach them how to use it:
    • On the computer projector, go to the Practice section and demonstrate how to use the Right Triangle Solver.
    • Ask students to go to the Introduction section and read about using the Right Triangle Solver. These directions are accompanied by screen shots of the tool.
    • Ask students to go to the Introduction section and view the Flash video describing how to use the Right Triangle Solver.
  1. Have students go to the Practice section and complete 1 to 5 problems (or more) in both Activity 1 ("Normal" mode) and Activity 2 ("Just Do It" mode). The practice activities allow students to apply the principles of right triangle geometry in solving for unknown values of a right triangle. Activity 1 provides helps to the students, whereas Activity 2 does not. Both activities permit students to check their answers for feedback. Students who struggle with Activity 1 should be encouraged to use the hints for help. (20-30 minutes)

Assess Mastery (10-15 minutes)

The objective of this section is to assess students' mastery of the principles reviewed in this lesson.

  1. When students have completed the practice section, have them complete the Quiz. (10 minutes).
  1. With any class time remaining, display the quiz over the projector and discuss the answers to each question.

 

Teaching Plan B (2 Days, 70 Minutes Total)

Teaching Plan B assumes that students already have a basic understanding of certain right-triangle-geometry principles, including the Pythagorean Theorem, Sum of Angles, and Definition of Sine, Cosine, and Tangent.

DAY 1 (50 Minutes)

Review Applications and Principles of Right Triangle Geometry (15-20 minutes)

The objective of this section is to help students warm up to the lesson by reviewing several applications of right triangle geometry.

  1. Using a computer projector, demonstrate how to go to the eNLVM website, go to your school and class, and login. (5 minutes)
  1. Ask students to login to the eNLVM and direct them to Right Triangle Geometry lesson. Have them read and answer the questions in the Motivation section, explaining how they reached their solutions. (10-15 minutes)

Solve Problems Using Right Triangle Geometry (50 minutes)

The objective of this section is to help students apply and master the principles of right triangle geometry by solving problems.

  1. Using one of the following methods, introduce students to the Right Triangle Solver (used in the Practice Section) and teach them how to use it:
    • On the computer projector, go to the Practice section and demonstrate how to use the Right Triangle Solver.
    • Ask students to go to the Introduction section and read about using the Right Triangle Solver. These directions are accompanied by screen shots of the tool.
    • Ask students to go to the Introduction section and view the Flash video describing how to use the Right Triangle Solver.
  1. Have students go to the Practice section and complete 1 to 5 problems (or more) in both Activity 1 ("Normal" mode) and Activity 2 ("Just Do It" mode). The practice activities allow students to apply the principles of right triangle geometry in solving for unknown values of a right triangle. Activity 1 provides helps to the students, whereas Activity 2 does not. Both activities permit students to check their answers for feedback. Students who struggle with Activity 1 should be encouraged to use the hints for help. (20 minutes)

DAY 2 (30 Minutes)

Assess Mastery (15-20 minutes)

The objective of this section is to assess students' mastery of the principles reviewed in this lesson. Note that this section may be completed on Day 1, time permitting.

  1. Ask students to login to the eNLVM, go to the Right Triangle Geometry lesson, and complete the Quiz. (15 minutes).
  1. Display the quiz over the projector and discuss the answers to each question. (10-15 minutes)

Assessment

Credits

Lesson Design Bob Heal, Joel Duffin, Karen Perry
Web Development Alejandro Garcia, Neal Legler
Mathlets Alejandro Garcia
Images Denise Chandler, Alejandro Garcia, NASA

Correlation to Standards

Correlation to NCTM Standards

Geometry - Standard 2. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationship.

Correlation to Utah Standards

Correlation to Arizona Standards