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## Lesson Plan

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This lesson provided by:
 Author: Becky Cornelius System: Lauderdale County School: Lauderdale County Board Of Education

General Lesson Information
 Lesson Plan ID: 26341 Title: Geometric Mean and Indirect Measurement Overview/Annotation: In this inquiry-based lesson, students will work in groups to gather measurements needed to approximate the height of a building. Students will discover how geometric mean can be used to find the lengths of missing sides of right triangles. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

Associated Standards and Objectives
Content Standard(s):
 MA2015 (9-12) Geometry 17. Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4] MA2015 (9-12) Geometry 21. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8]

Local/National Standards:

Alabama Course of Study 2009 standard is the same as the 2003 Course of Study

1.  In grades 9-12 all students should make decisions about units and scales that are appropriate for problem situations involving measurement.

2.  In grades 9-12 all students should make decisions about units and scales that are appropriate for problem situations involving measurement.

3.  In grades 9-12 all students should explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.

Primary Learning Objective(s):

Students will be able to use geometric mean to find the missing sides of right triangles.

Students will be able to use a tape measure to find distances.

Preparation Information
 Total Duration: 61 to 90 Minutes Materials and Resources: For each group: paper, tape measure, ruler, protractor Technology Resources Needed: Optional: LCD projector, calculators for students Background/Preparation: Students should be familiar with how to read a tape measure to the nearest 1/8"The teacher should locate an object outside that is too difficult to measure.  Possible objects are the top of a building, a flag pole, a light on the side of a building, etc.  The object should also have a flat ground surface to ensure accurate measurements.Students should have knowledge of Pythagorean Theorem, special right triangles, ratios, proportions, similarity

Procedures/Activities:

 Attachments:**Some files will display in a new window. Others will prompt you to download. GeometricMeanProblemsWithSolutions.rtf GeometricMeanProblems.rtf DiagramofExperiment.rtf

Assessment
 Assessment Strategies Informal assessment occurs throughout the lesson by observing the students' experiments, asking questions relative to their learning, and listening to responses and/or reading journal responses to explanations. For formal assessment, use the attached Geometric Mean Problems above for sample assessment questions.

 Acceleration: This lesson can be modified by increasing the level of difficulty of problems worked. Intervention: To assign students to groups, be sure to include a variety of ability levels in each group.  This will allow students who need extra assistance to have access to peer tutoring and peer coaching.  Following the lesson, students requiring further remediation will benefit from additional explanation from the teacher.  These students should also be allowed to work with the interactive lesson on Math Warehouse (link above).  Allowing these students the benefit of a visual representation of triangles and their geometric mean will help those having difficulty understanding the concepts.
 Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems. Presentation of Material Environment Time Demands Materials Attention Using Groups and Peers Assisting the Reluctant Starter Dealing with Inappropriate Behavior Be sure to check the student's IEP for specific accommodations.