ALEX Lesson Plans
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Title: "Woody Sine"
Description:
The students will discover the shape of the sine function without creating a tchart. 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.
Standard(s): [MA2013] PRE (912) 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.)* [FIF4] (Alabama) [MA2013] ALT (912) 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.
[FBF3] [MA2013] ALT (912) 37: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [FTF1] [MA2013] ALT (912) 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. [FTF2] [MA2013] ALT (912) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [FTF5] [MA2013] PRE (912) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama) [MA2013] PRE (912) 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. [FTF3] [MA2013] PRE (912) 30: (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [FTF4]
Subject: Mathematics (9  12)
Title: "Woody Sine"
Description: The students will discover the shape of the sine function without creating a tchart. 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.
Thinkfinity Lesson Plans
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Title: Hearing Music, Seeing Waves
Description:
This reproducible preactivity sheet, from an Illuminations lesson, presents summary questions about the mathematics of music, specifically focused on sine waves and the geometric sequences of notes that are an octave apart.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] ALT (912) 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. [FTF2] [MA2013] ALT (912) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [FTF5] [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Arts,Mathematics Title: Hearing Music, Seeing Waves
Description: This reproducible preactivity sheet, from an Illuminations lesson, presents summary questions about the mathematics of music, specifically focused on sine waves and the geometric sequences of notes that are an octave apart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Lesson Plans
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Title: Rolling Into Radians
Description:
Student groups collect height versus distance data for rolling objects of different sizes. Each group produces two sinusoidal graphs of the data, one in which both axes are measured in units, and the other in which both axes are rescaled and free of units. Students note that the amplitude and period of the unitfree graph are the same for all groups, and then discuss how their measurement opens a different way of describing points on a unit circle.
Standard(s): [MA2013] ALT (912) 37: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [FTF1] [MA2013] ALT (912) 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. [FTF2]
Rolling Into Radians
http://illuminations...
Student groups collect height versus distance data for rolling objects of different sizes. Each group produces two sinusoidal graphs of the data, one in which both axes are measured in units, and the other in which both axes are rescaled and free of units. Students note that the amplitude and period of the unitfree graph are the same for all groups, and then discuss how their measurement opens a different way of describing points on a unit circle.
Interactives/Games
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Title: Interactive Unit Circle
Description:
This is an interactive model of the Unit Circle. Features include a moveable slider to change the values of central angles in radian measure.
Standard(s): [MA2013] ALT (912) 37: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [FTF1] [MA2013] ALT (912) 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. [FTF2] [MA2013] ALT (912) 39: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions. (Alabama) [MA2013] PRE (912) 30: (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [FTF4]
Interactive Unit Circle
http://www.desmos.co...
This is an interactive model of the Unit Circle. Features include a moveable slider to change the values of central angles in radian measure.

