[b]Lesson:[/b]
[b]Launch[/b]
(5 minutes)
Begin class by showing the following video to students (http://youtu.be/R0kMsYzO6sA). Direct students’ attention to the Ferris wheel in the video. Once the video is over, pose the question, “If we were to ride this Ferris wheel, how could we tell how far above the ground we were at any given moment?”
Allow students to think about the problem for a minute and then ask for ideas. If students seem to be hesitant to answer, ask the prompting question, “What would we need to know first before we could find our height?”
Write down students’ responses on the board and leave them there (they will be used in Part II of the activity.)
[b]Explore [/b]
(20-25 minutes)
Students will open the GeoGebra File and use the Investigating Trigonometric Transformations (Part I) handout to guide their explorations.
Teacher Questions:
*How does this graph compare to the parent function (taller/shorter, wider/narrower, higher/lower)?
*How are you determining what sliders you need to move to get the parent function to fit the new graph?
(10-15 minutes)
After student complete Part I of the handout, stop to discuss their findings. What do a, b, c, and d appear to do to the graph? What are strategies they found to transforming their parent function so it would fit the new graphs?
Introduce the official terminology (amplitude, period, phase shift, vertical shift). May need to emphasize b (the period) more than the others.
(20-25 minutes)
Students will work on Part II of the student handout (exploring the ferris wheel problem).
Teacher Questions:
*What are some of the critical locations on the ferris wheel? How does that translate over to the graph?
*Why is our graph only in quadrant 1? Why does it not hit the x-axis?
*What do each of the values mean in terms of the graph (diameter is 18, how does that affect the graph?; 20 second cycle, how will this affect the graph?)?
*What does the y-intercept of your graph represent? What do the highs and lows represent?
*For students that get this quickly, ask them how the graph and function would change if time started right after you got on the ride (so you’re at the bottom of the ferris wheel).
[b]Share/Summarize [/b]
Regarding Part I of the handout, inquire for each function that they are mapping the parent function to if it is this the only function that will work for each graph? (This will lead to a discussion of phase shifts).
Discuss why a sine function would be a good choice to model the path of a person riding a ferris wheel. Have students share their graphs and functions they created for the ferris wheel problem in Part II. What are other situations (real-world) where a sine function would be an appropriate model?
[b]Homework / Formative Assessment[/b]
Give Sine Transformations Handout (homework sheet). Students will practice basic skills with writing and graphing sine curves. A second application problem is also given where students will investigate a boat bobbing up and down in the water.
