Basic Trigonometry Ratios Andrew McCandless Brawley Union High School, Brawley FINAL PRESENTATION My Unit was Car Buying Today… I presented the unit to two classes of Geometry students, primarily 10th graders. They were familiar with PowerPoint, Excel and the Internet. They learned how to implement each of these more effectively throughout the unit in addition to learning mathematics involving decimals and percents. CTAP 310 Teaching with Technology

Using Trig to Solve Rt. Triangles Students looked through internet sites on new and used cars and chose their favorites. In my web-lesson I had links to several car buying sites they could access. Most were not too concerned with price. The $200,000 Hummer was a favorite.

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?) This “welcome” is information from my index page, I used this to introduce students to the basics of the new unit. 38 10

But how do you find the height of a building using only Right Triangles? As students searched the internet for their favorite vehicles, they wrote down cost information and loan payment information on worksheets I designed in my unit.

Duration: 2 to 3 class periods 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 The lesson began with a pre-test. The test focused on adding, subtracting, multiplying and dividing decimals. Then, the students were asked what the standard tipping rate at a restaurant was and to figure out the tip on a given price. Next, students had to apply a compound interest formula and then fill in a chart detailing how to find the total cost of a vehicle by considering tax, registration, warranty and down payments. Last they were to take loan interest rate information and monthly payments and create an accurate graph. The worksheets then practiced decimals, tipping and various percents and working with vehicle information. As well, we spent time in the computer lab searching the internet for car prices and loan payment information. In the end students created PowerPoint presentations in groups to summarize their findings and then took a Post-Test which was a slight variation on the pre-test.

California State Standards - Geometry 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.

My Unit Objectives Objective # 1 Students will memorize the SIN, COS, and TAN ratios for right triangles. Objective # 2 Students will analyze problems and use the correct SIN, COS, TAN ratios to solve for missing parts of a right triangle. Objective # 3 Students will use the Internet to gain additional information on the history and uses of trigonometry. Objective # 4 Students will build Clinometer to apply what they have learned in real world problems.

Fifth Period Geometry Class In the end growth is reflected throughout the test for this group of students This is a chart detailing each students score on the test, out of 16 total questions.

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. Students should be able to achieve up to level 5 on this list. Levels 6 and 7 are advanced.

The Journey of SohCahToa PowerPoint Presentation to help students learn and remember key ratios. PowerPoint served as a great assessment of student learning and Demonstrated student ability to synthesize their learning. The actual requirements as listed were graded according to a math rubric. The basic idea of their presentation graded involved: meeting the basic requirements as listed 2) all people in the group participating 3) Accuracy of information, especially correctness in their math problem – generally students worked out a compound interest problem or discussed tipping rates and decimal operations 4) the final area was in their general ability to have a smooth flowing presentation where they clearly elaborated on their information and explained what they learned.

SohCahToa OPP ADJ TAN= SIN= OPP HYP COS= HYP ADJ

PowerPoint presentation on applied trigonometry. Overall there was growth in student learning. This chart details the overall average score per question for all students. A score of 1 means that all students got that question correct. A score of 0 would indicate that no students got the question correct. I was not concerned with the beginning of the test were it shows decline. This was due to students just not being careful. The end of the test marked an area in graphing where there was no growth and I needed to address the topic of scaling axes properly in a more thorough manner. REACH FOR THE STARS

Web Quest Form Name: __________________________Date: ______ Period: ______  Objective: To find out more about Trigonometry by researching web sites related to math.  Where to Look: Geometry Reference Site: www.math.rice.edu/~Lanius/geom/index.html  Dave’s Short Trig Course: www.aleph0.clarku.edu/~djoyce/java/trig/index.html  Procedure: 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 TAN and right triangles. Other Site Addresses: Observations : Conclusions: How have these sites helped you? What did you learn? Throughout the unit I strove to keep the material clear and relevant. This including revising some of my initial plans.

What Students Learned Reviewed terms for parts of right triangle Learned three key trig ratios Searching Internet Solving complex application problems involving trigonometry functions How to build measuring device “clinometer”

WHAT I LEARNED Need more time for calculator practice Students love to see how math applies to real life problems Students loved PowerPoint presentations Finding quality material on Internet takes time!! Pre and Post Testing was really important!! The lesson preparation and assessment was very time consuming. I was glad to go through the process and implement a unit in math involving internet resources. Use of an LCD projector was totally new. Using a Laptop, a digital camera, and a scanner in my own class was also pretty new. What I wanted students to graph in Excel had to be refined greatly as well as what would work in Excel – which areas had to be highlighted, how the columns and rows would actually graph. The variety of using technology in teaching was great!

5th Period Geometry Class 2002 They Did a Great Job!!