Determining the Equation of a Sine Function Graphically

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Submitted By: Christine Thompson
Resource Type: Lesson Plan
Subject:
- Mathematics
Topic:
- Climate Change
Level:
- Secondary

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Description

In this lesson students will be able to apply their knowledge of sinusoidal functions to determine the equation of a real-life example of cyclic phenomenon. This lesson can be used as a mathematical extension of Tread Lightly 2.1 - Where we stand.

Time Required: 1 class

Learning Objectives

By the end of the lesson, students will be able to:

- Demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions.
- Describe key properties of period functions arising from real-world applications given numeric and graphical representation
- Represent a sinusoidal function with an equation, given its graph or its properties

Teaching Process

Part A - Show video on on polar bears chatting about climate change and engage in short discussion about what students know about climate change.

Part B - Finding the equation of a sine graph graphically

Part C - Group or pairs activity where students will find the equation for a specific year, using the CO2 concentration data

Teeachers Notes

A little bit about the data….
The extracted values are for April and October of each year which approximately corresponds to the maximum and minimum CO2 concentration for each full year. The data shows oscillatory behavior each year due to natural scrubbing of CO2 from the atmosphere. Its minimum concentration each year is in the fall, resulting from high levels of photosynthesis activity all spring and summer, when trees and plants are out. In the winter, when the leaves have fallen, there is not as much photosynthesis occurring, so the CO2 remains in the atmosphere, resulting in maximum concentrations.

Part A - Video and climate change short discussion

a) Hook – show students video on climate change: http://www.youtube.com/watch?v=_Zo7wTOdc_M&feature=related
- This video is a comical video about the causes of climate change.

b) Open discussion with students about climate change.

Think/Pair/Share – ask students to think about what they know for 1 min, then talk about it with whomever is beside them for 1 min, then ask students to share with the class their ideas.

c) Introduce the concept of increasing CO2 in the atmosphere to students. Use these keys points

i) CO2 levels have been steadily rising in our atmosphere since the industrial revolution due to human activity
ii) If the demand and production of gas and oil from fossil fuels continues at the rate it is current at, the concentrations will continue to increase
iii) This is causing our planet to warm

Part B

Finding the equation of a sine function graphically

a) show students the full graph of the CO2 concentration (Graph 1, in attached documents)

b) Ask them what they notice about the graph

a. General trend? (Increasing, exponential)
b. Why do you think the data points are going up and down? What does this mean?
c. Where have you seen similar behavior like this before?

c) Show students a period of 5 years to give them a better visualization of the oscillation. (Graph 2, in attached documents)

- Explain to students why it is oscillating.

- Explain why the concentrations of CO2 are increasing.

d) Show them the graph of one particular year (1971.7-1972.7 or approximately 1972-1973). (Graph 3, in attached documents)

- Hand out each student a copy of this graph and go through the steps of finding the equation of the translated sine graph with them. A sample solution is attached.

Part C

Group Activity for formative assessment:

i. Group students in 2-3 and give each group chat paper and a graph for a specific year.

ii. Ask them to find the equation of the sine wave corresponding to their given year and provide the solution and their own drawing of the graph on chart paper(graphs in attached documents).

iii. Have a group from each year provided present their solution to the class.

iv. Compare the k values from each decade to illustrate to students how the levels of carbon dioxide are increasing.

v. Have a discussion about reducing greenhouse emissions and take the ecological footprint quiz in TL 2.1 – Where we stand and take the tread lightly challenge.