**Lesson Title: Geometry Exploration Basic Trig Functions**

Topic/Focus Area: Trig Functions Used to Find Missing side of Right Triangles

**Subject(s):** Mathematics

480 North Imperial Ave.

Brawley, CA 92227

__Lesson Overview__

Students will be introduced to using trigonometry to solve for missing sides of right triangles by first looking at using a simple proportion to solve for a missing side. This involves comparing shadow lengths of known and unknown objects heights. When the question is posed, "What do you do if there is no shadow?", students will be introduced to the subject of trigonometry. Students will be given a sample problem and asked to propose theories on how it might be solved. Before any further information is given, students will be asked to take a pre-test on trig functions.

Next students will be briefed on the history of right triangles and trigonometry and the basic use of the SIN COS and TAN ratios by viewing and interacting with a Powerpoint presentation on the subject. Students will also view a Powerpoint presentation on a memory device used to remember these three key ratios. Students will be directed to several web sites where they can obtain additional information on the subject. Students will be given an objective check list that they will update and check off as the unit progresses. Students will then be expected to complete a worksheet on the basic use of SIN COS and TAN to solve for missing parts of a right triangle. Students will also interact with a trigonometry tutorial presented by Math Advantage 2000 and projected using a LCD projection unit. Finally students will take a post-test to evaluate their understanding and mastery of the material. The tests will be administered by using the Accelerated Math software currently being used in the classroom.

__Student Learning Objectives__

- Students will analize given right triangle problems and use the SIN, COS, and TAN ratios to solve for missing lengths of the sides of the triangles. Students will be assesed in their ability to accurately measure the component parts of the triangles, appropriately use the correct ratio, and consistently apply the trig functions to solve increasingly more complex problems. Students will demonstrate mastery in at least seven out of ten given problems.
- Given the SIN, COS, and TAN functions students will memorize the corresponding ratios and apply them as needed.
- Students will be able to apply Trig ratios to solve real world problems with the application and use of a Clinometer.

__Activities__

- Students will be given a pre-test that will be used to evaluate their understanding at the end of the unit .
- Sudents will be given example problem on solving for a missing length of the side of a right triangle using proportions to solve for the missing side. Example will involve measuring the length of the shadow of a tree with unknown height. Then comparing this to the shadow of an object whose height is known.

Students will then be asked how they could solve this problem without using shadows. (see sample problem worksheet) - Students will be assigned several web sites to visit to further their understanding of the usefulness of applied trig. (See web listings: Dave's Short Trig Course & Geometry Refernce Pages)They will use the web-quest handout (see attatchment) to complete this phase of the project.
- Next students will watch a PowerPoint presentation which will introduce the three basic trig ratio's SIN COS TAN. They will be given a Trig checklist and will take notes as they watch the presentation. The initial presentation will be followed up by a second PowerPoint presentation which will walk them through how to solve some real world application problems. (See PowerPoint presentations listed in file attatchment section)
- Students will then interact with a tutorial program, Math Advantage Trigonometry 2000. This will go over the trig ratios again, and introduce more sample problems. Students will add any additional information to their notes.
- Students will be given a worksheet which they will complete in groups of four. They will apply what they have learned to far. (See attatched file)
- Students will work on project to build a Clinometer and use it to calculate heights of various objects around town (see attachments).
- Students will take post-test to assess their understanding of the SIN COS TAN ratios after completing the unit.

__Resources__

SAT II: Subject Test Math Level IIc book published by REA

McDougal Littell Geometry book, published by Larson Boswell Stiff

Basic Trig Tutorial SIN COS TAN to solve Rt. Triangle Problem (math.about.com)

Geometry Reference Pages (student site) (math.rice.edu)

Huge Resource of Math Worksheets Pre-made (www.edHelper.Com)

Ask Dr. Math anything Great Resource (mathforum.org)

Dave's Short Trig Course (student site) (aleph0.clarku.edu)

ASK ERIC lessons and tutorials all subjects of Math (ericir.syr.edu)

Computer with Internet access, CD-ROM, scanner

Laser Printer

LCD Projection System

Accelerated Math Scantron Scanner

Math Advantage 2000 Trigonometry Software

Accelerated Math Software

Microsoft PowerPoint Software

__File Attachments__

Prior to starting the lesson, students will be given a pre-test on the material to be covered. Students will also be given an objective checklist which they must fill out to certify mastery of each objective. A post-test will then be administered to chart student progress. Advanced students can also complete an advanced web-quest project for further assessment.