ctap 310 teaching with technology final presentation andrew mccandless basic trigonometry ratios...
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CTAP 310 Teaching with Technology
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Andrew McCandless
Basic Trigonometry RatiosBasic Trigonometry Ratios
Brawley Union High School, Brawley
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
Using Trig to Solve Rt. TrianglesUsing Trig to Solve Rt. Triangles
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
38 10
Focus Problem: Solving Using Proportions
How Tall is the Tree?The Shadow Knows!
At four in the afternoon a man who is 6 feet tall casts a shadow ten feet in 6length. If the tree casts a shadow of 38 feet, how tall is the tree?Use a proportion to solve this problem. (Question: could you solve this problem without using any shadows, or measuring the tree’s height?)
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
But how do you find the height of a building using only Right Triangles?
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
THE LESSON:
• Duration: 2 to 3 class periods
• Main Contents: 3 worksheets and Pre/Post Test
• Interactive Tutorial: Math Advantage 2000
• Internet Searching for additional Trig information
• Charting Data using Clinometer to find elevation
• Presenting Lesson on Microsoft PowerPoint
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
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.
California State Standards - Geometry
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
My Unit ObjectivesMy Unit ObjectivesObjective # 1Objective # 1 Students will memorize the SIN, COS, and Students will memorize the SIN, COS, and
TAN ratios for right triangles.TAN ratios for right triangles.
Objective # 2Objective # 2 Students will analyze problems and use the Students will analyze problems and use the correct SIN, COS, TAN ratios to solve for correct SIN, COS, TAN ratios to solve for missing parts of a right triangle.missing parts of a right triangle.
Objective # 3Objective # 3 Students will use the Internet to gain Students will use the Internet to gain additional information on the history and additional information on the history and uses of trigonometry.uses of trigonometry.
Objective # 4Objective # 4 Students will build Clinometer to apply Students will build Clinometer to apply what they have learned in real world what they have learned in real world problems.problems.
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
Fifth Period Geometry ClassFifth Period Geometry ClassTest Scores
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CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
Trigonometry Check List
Name __________________________________ Period: _______ Date: _______
When you finish you studies of trigonometry, you should be able to:
1.___ Know and explain the definitions of cosine, sine, and tangent
2.___ Use your calculator to find trigonometric values for given angle measures.
3.___ Use your calculator to find angle measures when given trigonometric values.
4.___ Find lengths of two sides of a right triangle when given one acute angle and one side.
5.___ Find the measures of the acute angles of a right triangle given the lengths of two sides.
6.___ Solve word problems involving angle of elevation and angle of depression.
7.___ Use trigonometry to solve word problems involving right triangles.
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
PowerPoint Presentation to help students learn and remember key ratios.
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
SIN= OPPHYP
COS=HYPADJ
OPPADJ
TAN=
SohCahToa
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
PowerPoint presentation on applied trigonometry.
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
Web Quest FormWeb Quest Form
Name: __________________________Date: ______ Period: ______ Name: __________________________Date: ______ Period: ______ ObjectiveObjective: To find out more about Trigonometry by researching web To find out more about Trigonometry by researching web
sites related to math.sites related to math. Where to LookWhere to Look: Geometry Reference Site:: Geometry Reference Site: www.math.rice.edu/~Lanius/geom/index.htmlwww.math.rice.edu/~Lanius/geom/index.html Dave’s Short Trig Course:Dave’s Short Trig Course: www.aleph0.clarku.edu/~djoyce/java/trig/index.htmlwww.aleph0.clarku.edu/~djoyce/java/trig/index.html ProcedureProcedure: Visit each site and find two or three ideas or concepts that : Visit each site and find two or three ideas or concepts that
interest you. Identify how they relate to our lesson on SIN, COS and interest you. Identify how they relate to our lesson on SIN, COS and TAN and right triangles.TAN and right triangles.
Other Site Addresses:Other Site Addresses: ObservationsObservations : : ConclusionsConclusions: : How have these sites helped you? What did you How have these sites helped you? What did you
learn? learn?
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
What Students Learned What Students Learned
Reviewed terms for parts of right Reviewed terms for parts of right triangletriangle
Learned three key trig ratiosLearned three key trig ratios Searching InternetSearching Internet Solving complex application problems Solving complex application problems
involving trigonometry functionsinvolving trigonometry functions How to build measuring device How to build measuring device
“clinometer”“clinometer”
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
WHAT I LEARNEDWHAT I LEARNED
Need more time for calculator practiceNeed more time for calculator practice Students love to see how math applies to Students love to see how math applies to
real life problemsreal life problems Students loved PowerPoint presentationsStudents loved PowerPoint presentations Finding quality material on Internet takes Finding quality material on Internet takes
time!!time!! Pre and Post Testing was really important!!Pre and Post Testing was really important!!
CTAP 310 Teaching with Technology
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MaryAnn Archer, Brawley Union High SchoolGeometry: Basic Trigonometry Ratios & Right Triangles
They Did a Great Job!!
5th Period Geometry Class 2002