Lesson Title: Geometry Exploration Basic Trig Functions
Topic/Focus Area: Trig Functions Used to Find Missing side of Right Triangles

Lesson Overview
Content Standards
Objectives
Activities
Resources
File Attachments
Assessment
Additional Comments

Subject(s): Mathematics

Grade Level(s): 9, 10

Name: Andrew McCandless
Taught: Math
Phone: 760-351-1091
E-mail: amccandless@brawleyhigh.org
School: Imperial Co. Office of Education
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.




Standards

Subject
: Mathematics
Grade
: Eight through Twelve
Strand
: Geometry

The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.


 
 
STAR California Standards Test Key Standard on the California Standards Test
Substrand:
19.0
Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
 

Student Learning Objectives


Activities

  1. Students will be given a pre-test that will be used to evaluate their understanding at the end of the unit .
  2. 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)
  3. 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.
  4. 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)
  5. 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.
  6. 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)
  7. Students will work on project to build a Clinometer and use it to calculate heights of various objects around town (see attachments).
  8. Students will take post-test to assess their understanding of the SIN COS TAN ratios after completing the unit.

Resources

Content Resources (books, articles, etc.)
SAT II: Subject Test Math Level IIc book published by REA

McDougal Littell Geometry book, published by Larson Boswell Stiff


Web Resources
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)


Hardware/Software Resources (computers, CD-ROMs, TV, VCR, etc.)
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

download the file Powerpoint lesson to teach SIN COS TAN ratios
  — Trig SOHCAHTOA Lesson Indians.ppt   (1.49 MB)

download the file Student Worksheet
  — Trig Worksheet.doc   (37.0 KB)

download the file Student Learning Objectives
  — COS SIN TAN Worksheet.doc   (32.5 KB)

download the file Sample Pre/Post Trig Test
  — lwf49 sample trig test.tif   (1.54 MB)

download the file Example problem using right triangle
  — How Tall is the Tree.doc   (26.0 KB)

download the file Web Quest Worksheet
  — Experiment Design Web Quest.doc   (60.5 KB)

download the file How to Build Clinometer Instruction Sheet
  — How to Build a Clinometer.doc   (103 KB)

download the file Photo Copy of Protractor for Clinometer
  — clinometer222.mix   (267 KB)

download the file Grading Rubric
  — Math Rubric Trig.htm   (5.63 KB)

download the file Data Sheet for Clinometer Experiment
  — Worksheet for Clinometer Experiment.xls   (25.0 KB)

download the file Final Presentation
  — Andy's Presentation.ppt   (3.96 MB)

download the file Trig Lesson with Example Problems
  — trig history powerpoint.ppt   (3.74 MB)

download the file Student Work Sample 1
  — MH work.tif   (5.20 MB)

download the file Student Work Sample 2
  — EG Work.tif   (1.61 MB)

download the file Student Work Sample 3
  — GM Work.tif   (1.76 MB)

download the file Student Work Sample 4
  — GM Work2.tif   (1.90 MB)

download the file Student Work Sample 5
  — GM Work3.tif   (1.64 MB)

download the file Pre and Post Test Results
  — Test Scores Pre and Post.xls   (17.5 KB)


Assessment
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.
Additional Comments