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Unit 5 WebQuest - Internet Project

Trig Class Angles for Lessons in Lit Rocket

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
USA Today, November, 2000
     The groans from the trigonometry students immediately told teacher Michael Buchanan what the class thought of his idea to read Homer Hickam's October Sky.
    That was in January. This school year, Buchanan is being applauded for the project and gets credit for the idea to have all trig students - not just his students - at Chattahoochee High School in Alpharetta, Ga., read the book.
     Chattahoochee High School, which has an enrollment of about 2,700 students, is one of 400 schools in Canada and the USA using Hickam's autobiographical October Sky (Delacorte, $23.95) and his latest memoirs The Coalwood Way (Delacorte, $23.95) to teach lessons that go beyond typical classroom teachings.
     October Sky, originally titled Rocket Boys: A Memoir before Hollywood turned it into a movie and retitled it, takes place in 1957, the year the Russians launched Sputnik. Hickam, the son of a coal miner, nurtured a dream to send rockets into outer space. Although Hickam struggled in math, he and seven of his friends were encouraged by their teacher to pursue their dream and enter a national science fair. Hickam also had to fight his father's expectations that he one day would work in the coal mines with him.
     Hickam, who has developed an e-mail relationship with Buchanan and his students, says the main reason for his building rockets in 1957 was to have tangible proof of his goal to work as a NASA engineer.
     "When a man hired on at the coal mine, and my dad was the superintendent, the man had to tell him what it was he knew how to do. So in my simple way, I thought, 'Well, if I know how to build rockets,'" an application to NASA would mean more. "It was a simpleminded idea. What this proves to me is that if you have a reason to learn, then you will learn. That's why teachers are using the book," says Hickam, who espouses the three P's of a successful life: "passion, planning and perseverance."
     Lee Stiff, president of the National Council of Teachers of Mathematics, says there is merit in having projects that "engage students and get them to delve deeper into the mathematics and the sciences and such relationships as mathematics and social studies or mathematics and history. Those kinds of projects are worthwhile because they show young people that math is connected to a world outside itself and that mathematics can be useful."
   Buchanan says October Sky is not like a book about math; it's about teenagers. "I knew that part they would like," he says. "In the story, in order to accomplish what they would like, they had to teach themselves trig, calculus and physics. It's more about character development, career choices, sticking with what you believe, things like that. Each kid takes from it what he wants. Some see the connection between dealing with dad or with their brother, or getting focus in life. It kind of means something different to every kid."
   October Sky is more science related than math oriented, but "I know if they got interested in science, the math would follow," says Buchanan, who says he gave easy quizzes on the book.
     "It's an enrichment thing. They see the value in that."
     Chattahoochee High senior Bob Howard, 17, says that "it seemed a little weird" last year when Buchanan gave the reading assignment - in math, of all subjects. But it turned out to be "kind of a nice break" because Howard enjoys reading and didn't have to worry about "all the analysis and tearing apart" that's required of English assignments.
     Robin Kazmier, 18, a Chattahoochee graduate now in her freshman year at Northwestern University in Evanston, Ill., says she immediately identified with Hickam in the book.
     "I want to do geography and mapping. That involves a lot of math, and I'm not always great at it. The fact that (Hickam) struggled with a lot of math and had to work a lot on the side, I can identify in that sense," says Kazmier, who is taking accelerated calculus.
     "It was inspiring because it was anybody - no better than myself - who could reach his goals and accomplish his dreams. He didn't have any advantages, he just believed in himself and what he wanted to do," Kazmier says.
    Buchanan credits school librarian Becky Peace with getting the project off the ground by agreeing to purchase the books for his trigonometry class. Shortly afterward, local businessman Kent Curley donated $500 for book purchases, and the amount was matched by Roger Wise, a member of the Fulton County Education Foundation. Eventually, 90 students read the book the first year, and there was enough money for a similar project at a nearby school .
     "The school district encourages us to have alternate assessment avenues," Buchanan says, explaining that teachers must have a variety of ways to determine student achievement. So, he approached the library about the books. "Rather than give them a project they can go look up on the Internet, which they get in lots of classes, I thought it would be kind of cool to read a book."
     To assist teachers in their use of the book, Hickam and his wife, Linda Terry, an editor, have established a Web site with suggested lesson plans.
     Matthew Frye, 17, a senior who plans to attend The Citadel military college in Charleston, S.C., next year, says he earned a C-plus in Buchanan's class last year. But he still comes to school early to seek extra help with the math. Hickam's book "moved me in a way that I want to keep trying." He says he has even joined a rocket club that Buchanan is organizing at the school.
    

The Task
Your school is having a mathematics career information day. You plan to enter a display, either a poster or Web page, showing two applications of trigonometry that would relate to a possible career for you. As noted in the article at the beginning of this WebQuest, Homer Hickam and his friends used trigonometry to calculate the height traveled by their home-made rockets. Your display needs to contain the following information:

  • a clearly-labeled diagram illustrating each of two different trigonometry applications;
  • for each application, a sample calculation including appropriate numbers showing how the application is used;
  • the name of a career where each application would be used;
  • a paper describing and comparing the two careers you chose. Include anything that surprised you about the careers.

You will get some ideas about applications of trigonometry from the Exercises in your textbook in Lessons 13-1 and 14-2.

The Process
To successfully complete this project, you will need to complete the following items.

Guidance
Here are some additional questions and ideas you may want to consider for your project.

  1. What is the approximate cost to complete the training or education needed for each career you are featuring?
  2. What will the demand in the future be for each career?
  3. What can you expect for a salary for each career?
  4. In what parts of the country would each of the two careers be available? Would you need to live in an urban or rural area for each career?
  5. Is any additional education or training needed to advance in each of these careers?

Conclusion
Here are some ideas for concluding your project.

  • Present your project to your class or at a family night.
  • Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.
  • Write a paper describing and comparing the two careers you chose. Include anything that surprised you about the careers.
  • Interview a person with a career that uses trigonometry. Ask the person for several examples of their use of trigonometry on the job.

Questions

Lesson 13—1
Homer Hickam and his friends used the tangent ratio to calculate the maximum height reached by their rockets. The diagram shows that they assumed that the path of the rocket was vertical. They measured the baseline and used a theodolite to measure angle A.

Chart

  1. Suppose the baseline was 500 feet and angle A was 60°. What was the approximate maximum height reached by the rocket?
  2. Write a formula for calculating the maximum height of the rocket h given angle A and the length of the baseline b.
  3. On one particular day, Homer's two-foot long rockets reached a height of 2000 feet. Find three different baseline lengths and measurements for angle A that would result in a calculation of 2000 feet for the rocket's maximum height.

Lesson 14—2
As Elise was researching applications of trigonometry on the Internet, she discovered that some temperature data can be modeled by sine or cosine functions. The table shows the average monthly high temperatures for Boise, Idaho.

Chart

  1. Make a scatter plot of the data. Represent the months with numbers, for example, let January = 1, February = 2, and so on. Let the months be on the x-axis and the temperatures be on the y-axis. When you connect the points with a smooth curve, it should look like a sine curve.
  2. What is the amplitude a of the graph?
  3. Find 2 divided by the number of months in the table. Simplify the answer and leave in terms of . Let this value be b.
  4. Find the mean of the minimum and maximum temperature values. Call this value d.
  5. Look at your graph. It appears to be at its lowest point when
    x = 1. To find the horizontal translation of the sine curve, divide 1, the value of the lowest point, by your value for b. What is this value called c?
  6. An equation for the temperature data is y = a sin (bx - c) + d. Substitute the values you found for a, b, c, and d into this formula. Graph the scatter plot from part a and this function on the same graphing calculator screen. How well does the equation fit the temperature data?

 
 
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