Triangle Geometry - Lesson Plan

Teaching Plan A (2 Days, 50 Minutes Each)

This eModule can be approached in one of two ways, depending on students' understanding of triangle geometry prior to beginning the eModule.Teaching Plan A assumes that students have not yet been introduced to certain principles of triangle geometry, including the Law of Sines and Law of Cosines. If your students are already familiar with these principles, you may refer to Teaching Plan B.

DAY1 (50 Minutes)

Introduce Applications of Triangle Geometry (10-15 minutes)

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

Using a computer projector, demonstrate how to go to the eNLVM website, go to your school and class, and login. (5 minutes)

Ask students to login to the eNLVM and direct them to the Triangle Geometry eModule. Have them read or work through the Motivation section. This section describes problems that can be solved using the Law of Sines and Law of Cosines. Since the purpose of this section is to motivate, students do not have to answer the questions the first time through. However, you may work through the questions as a class or ask students to return to this section at a later time to answer the questions. (5-10 minutes)

Discuss Principles of Triangle Geometry (30 minutes)

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

Have students turn off their computer monitors. Display the first activity of the Motivations section (SOS Signal) using the computer projector. On the whiteboard identify the known and unknown values of the triangle used in the activity. Introduce the Law of Sines as a way to solve for the unknown values. As a class, practice using the Law of Sines by going to the next activity (Height of a Mountain) and solving the problem (10-15 minutes). Display the Playing Golf activity using the computer projector. On the whiteboard identify the known and unknown values of the triangle used in the activity and then introduce the Law of Cosines as a way to solve for the unknown values. As a class, practice using the Law of Cosines by solving the problem in the Two Ships activity (15 minutes). If you wish to have the students solve the motivation questions themselves at a later time, use examples of your own to teach the Law of Sines and the Law of Cosines. 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.

DAY 2 (50 Minutes)

Solve Problems Using Triangle Geometry

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

Ask students to login to the eNLVM and go to the Triangle Geometry lesson. Using one of the following methods, introduce students to the 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 Triangle Solver. Ask students to go to the Introduction section and read about using the Triangle Solver. These directions are accompanied by screen shots of the tool (5-10 minutes).

Have students go to the Practice section and complete 1 to 5 problems in both Activity 1 ("Normal" mode) and Activity 2 ("Just Do It" mode). The practice activities allow students to apply the principles of triangle geometry in solving for unknown values of a 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) If you wish, you may direct students to complete the second practice section dealing with the Motivation problems. Even if you answered these questions as a class, students may benefit from working through the problems on their own using the triangle solver (5-10 minutes).

Assess Mastery (10-15 minutes)

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

When students have completed the practice section, have them complete the Quiz. (10 minutes).
With any remaining class time, 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 triangle-geometry principles, including the Law of Sines and Law of Cosines.

DAY 1 (50 Minutes)

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

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

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

Solve Problems Using Triangle Geometry (50 minutes)

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

Using one of the following methods, introduce students to the 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 Triangle Solver. Ask students to go to the Introduction section and read about using the Triangle Solver. These directions are accompanied by screen shots of the tool.

Have students go to the Practice section and complete 1 to 5 problems in both Activity 1 ("Normal" mode) and Activity 2 ("Just Do It" mode). The practice activities allow students to apply the principles of triangle geometry in solving for unknown values of a 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) If you wish, you may have students complete the additional Practice section dealing with the Motivation problems. This could be useful if students struggled with answering the problems in the Motivation section.

DAY 2 (30 Minutes)

Assess Mastery (15-20 minutes)

The purpose 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.

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

Assessment

• Use class discussions to gauge the progress of the class and to identify common misconceptions.
• Walk around and observe individual students while they go through the lesson to identify individual progress and challenges.
• Use the quiz for the purpose of summative assessment and grading.

Credits

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.

• Grades 9-12: Use trigonometric relationships to determine lengths and angle measures.

Correlation to Utah Standards

• Geometry - 2.2.4. Find the missing parts of triangles using the Law of Sines and the Law of Cosines.