# ALEX Lesson Plan

## "Woody Sine"

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This lesson provided by:
 Author: Cathy Bennett System: Geneva City School: Geneva High School The event this resource created for: GEMS General Lesson Information
 Lesson Plan ID: 23983 Title: "Woody Sine" Overview/Annotation: The students will discover the shape of the sine function without creating a t-chart. The students will create a sine function using toothpicks. The students will then discover how the amplitude (height) and the period (number of compete waves) change when the basic graph created from the broken tooth picks was changed. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Associated Standards and Objectives
Content Standard(s):
 Mathematics MA2015 (2016) Grade: 9-12 Precalculus 16 ) For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.)* [F-IF4] (Alabama) Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry 34 ) Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3] Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry 37 ) Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [F-TF1] Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry 38 ) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. [F-TF2] Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry 40 ) Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 26 ) Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama) Mathematics MA2015 (2016) Grade: 9-12 Precalculus 29 ) (+) Use special triangles to determine geometrically the values of sine, cosine, and tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number. [F-TF3] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 30 ) (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [F-TF4]

Local/National Standards:

Primary Learning Objective(s):

Analyze the effects of parameter changes on the graphs of trigonometric functions by using the basic sine function as the beginning activity.

The students will develop the ability to predict the behavior of a graph of all six trigonometric functions based on their prior knowledge of the special angles and describe their graphs given a trigonometric equation.

Preparation Information
 Total Duration: 61 to 90 Minutes Materials and Resources: 26 toothpicks, graph paper, protractor, colored pencils, calculators for computation, If the students in this class might not be safe with toothpicks an alternative (spaghetti) may be chosen to break and form the vertical legs around the unit circle. Technology Resources Needed: Graphing calculators will be used to check the students work. Background/Preparation: Prior to this lesson, the students will need to be taught how to find the values of the trigonometric functions for all the special angles. The students will need to learn the special angles of triangles and how they form a unit circle.
Procedures/Activities:
 1.)The students will be given a blank sheet of paper and a protractor. The will construct a unit circle on a coordinate plane with a toothpick length radius. (For those students that would need assistance with this a sheet has been attached with a unit circle). 2.)The students will use a protractor to mark every 15 degrees all the way around the unit circle. 3.)The students will use their ruler to form right triangles inside the circle from each degree measure. 4.)The students will break the toothpick to match the lenghts of each vertical leg, break only one at a time and move on to step #5 5.) The students will construct an x-axis on a sheet of paper with the same degree measures listed on their unit circle as their x values. The students will transfer each leg to its appropriate degree mark on the x-axis and place a colored dot at the top of each toothpick. NOTE: Remember when you break the lengths for 180 through 360 degrees the values will point down to indicate they are negative. This activity could be recorded on a spreadsheet and then transferred to a graph. 6.)After transferring all the toothpicks form the unit cirlce to the x-axis and marking the dots at the top connect the dots with a smooth curve. 7.)The students will now make a t-chart and graph the funcions listed on the attachment to see the effect on the basic sine function that they created from the toothpicks. 8.)The students will complete the attached sheet to see how the graphs are effected by the changes in the equations. 9.)To clarify the directions see the attachment that displays student sample work. 10.)This website from NCTM may be used an extension of the activity.(cool math) 11.)The following website could be used for remediation of graphing or as an introduction to the lesson.(graph of sine funcion)

 Attachments:**Some files will display in a new window. Others will prompt you to download. Toothpick Activity.doc pictures.ppt unit.pdf
Assessment
 Assessment Strategies The students graphs will be graded for accuracy.
 Acceleration: The teacher may choose to have the students make up their own trigonometric equations and see how the amplitude and period changes. The website given as an attachment for Cool Math could be used as an extension. Intervention: The students may need to review the amplitude and period of the trigonometric functions and there location in a trigonometric equation.

 View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.