Sample Trigonometric Lesson Plan
Unit 5: Day 6: Trigonometric Functions / MCR3UMinds On: 20 / Learning Goal:
· Predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function.
· Identify sine functions from real-world applications involving periodic phenomena, given various representations, and explain any restrictions that the context places on domain and range.
· Pose and solve problems based on applications involving a sine function by using a given graph or a graph generated with technology from its equation. / Materials
· Graphing calculators
· SmartBoard
· Handouts
· Chart Paper
Action: 30
Consolidate: 25
Total=75 min
Assessment
Opportunities
Minds On… / Whole Class à Discussion
Engage students in a discussion by asking them to respond to the following prompts:
· What is a periodic function? A trigonometric function?
· Compare and contrast the different sinusoidal functions / · Communication through discussion
· Group Work
Action! / Pairs à Investigation
Distribute the handout for the activity. Briefly review the key concepts about transformations and determining amplitude, period, phase shift etc. having students read and participate with answers where appropriate. Students will have further opportunity to reflect on the discussion questions as they complete the in-class activity about Ferris Wheels.
Whole Class à Discussion
Have students summarize their results from the Handout.
If students finish early, they can graph their solutions on the smartboard while others are finishing in order to check their work. Hand out calculators if necessary? Ensure that the key points of trigonometric functions are highlighted. Using the questions provided, engage the students in an exploration of the key characteristics of sinusoidal functions.
Students complete the activity in pairs, and share answers and thoughts about the activity in groups of four. In groups of four – apply Frayer Model/Placemats to get students to summarize the ideas learned.
Circulate the classroom looking for difficulties and problems.
Learning Skill (Work habits)/Observation/Anecdotal:
Observe students’ work habits and make anecdotal comments.
Consolidate Debrief / Whole Class à Teacher Leads Discussion/Note
Specific Example/Investigation
What did you find in the investigation? Does the trigonometric function in the investigation have something in common with the regular sinusoidal functions?
How can we apply what we learned in this example to a general trigonometric function? General Case: How do you find the amplitude and period of a trigonometric function in the form or ? Complete the “Key Properties” box together.
Exploration
Application / Home Activity or Further Classroom Consolidation
Students answer questions like:
- How would the graph change if passenges started at another position on the wheel (top, bottom, etc.)? What would be the same and what would be different?
- How would the graph change if the wheel rotated in the other direction?
- How would the graph change if the wheel were bigger/smaller?
Group Work/Discussion:
Ferris Wheel Activity:
A Ferris Wheel with a radius of 2.5m makes 1 revolution every 12 seconds.
It is 2m above the ground.
1. Describe the graph made by a passenger riding the Ferris Wheel. (Hint: Use some of the terminology you have learned over the last few days.)
2. Draw a graph on the chart paper provided that models the height of the Ferris Wheel with respect to time.
3. What transformations of the Cosine Function will create the graph of the Ferris Wheel?
4. Write an equation using the transformations of the Cosine Function to create a function that models the height of the Ferris Wheel with respect to time.
5. Given a diagram that is not to scale, describe another way to determine the passenger’s height when the wheel has rotated 15°. (Hint: ignore the wheel and focus on the triangle.)
6. Determine the passenger’s height for each of the following angles using the method you described in #5.
a) 15° b) 30° c) 45° d) 60°
7. What name would you give to your graph?