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Title: Trigonometric Art
Description:
Students will investigate and analyze the effects of parameter changes on a trinometric function using a graphing calculator. Students will be able to create their own trigonometric art using sine, cosine, and tangent functions.
Standard(s): [MA2013] ALT (912) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [FTF5]
Subject: Mathematics (9  12)
Title: Trigonometric Art
Description: Students will investigate and analyze the effects of parameter changes on a trinometric function using a graphing calculator. Students will be able to create their own trigonometric art using sine, cosine, and tangent functions.
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Title: Traveling Around The Unit Circle
Description:
This lesson is intended to review the key ideas associated with trigonometric functions.The design of this lesson provides a collection of reproducible activities to be used in a classroom setting where students have varied backgrounds / experience with trigonometric functions.
Standard(s): [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] ALT (912) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [FTF5]
Subject: Mathematics (9  12)
Title: Traveling Around The Unit Circle
Description: This lesson is intended to review the key ideas associated with trigonometric functions.The design of this lesson provides a collection of reproducible activities to be used in a classroom setting where students have varied backgrounds / experience with trigonometric functions.
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Title: Graphing at all levels: It’s a beautiful thing!
Description:
This lesson addresses the societal issue of the arts being eliminated in many public schools be employing graphs (at any level) as an artistic media. Review of all types of graphs is included through various interactive websites.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): [AED] VA2 (712) 2: Produce works of art using a variety of techniques. [MA2013] AL1 (912) 24: Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes. [AREI12] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [FTF5] [MA2013] PRE (912) 1: (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. [NCN4] [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Subject: Arts Education (7  12), or Mathematics (9  12)
Title: Graphing at all levels: It’s a beautiful thing!
Description: This lesson addresses the societal issue of the arts being eliminated in many public schools be employing graphs (at any level) as an artistic media. Review of all types of graphs is included through various interactive websites.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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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
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Title: Do You Hear What I Hear?
Description:
In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension.
Standard(s): [S1] (8) 12: Classify waves as mechanical or electromagnetic. [S1] PHS (912) 9: Compare methods of energy transfer by mechanical and electromagnetic waves. [S1] PHY (912) 6: Describe wave behavior in terms of reflection, refraction, diffraction, constructive and destructive wave interference, and the Doppler effect. [MA2013] AL1 (912) 28: 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.* [FIF4] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL2 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (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] 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) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 31: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] ALT (912) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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) 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)
Subject: Mathematics,Science Title: Do You Hear What I Hear?
Description: In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Thinkfinity Learning Activities
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Title: Sound Wave
Description:
This student interactive, from Illuminations, helps students understand the mathematical models used to represent sound. Students come to understand the origins of the terms pitch, tone, frequency, and intensity, as well as explore the dynamics of a sound wave.
Standard(s): [S1] (8) 12: Classify waves as mechanical or electromagnetic. [S1] PHS (912) 9: Compare methods of energy transfer by mechanical and electromagnetic waves. [S1] PHY (912) 6: Describe wave behavior in terms of reflection, refraction, diffraction, constructive and destructive wave interference, and the Doppler effect. [S1] PHY (912) 7: Describe properties of reflection, refraction, and diffraction. [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [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) 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)
Subject: Mathematics,Science Title: Sound Wave
Description: This student interactive, from Illuminations, helps students understand the mathematical models used to represent sound. Students come to understand the origins of the terms pitch, tone, frequency, and intensity, as well as explore the dynamics of a sound wave. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Trigonometric Graphing
Description:
This student interactive from Illuminations allows students to graph trigonometric functions. Parameters that affect the amplitude, period, and phase shift of the function can be manipulated.
Standard(s): [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [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)
Subject: Mathematics Title: Trigonometric Graphing
Description: This student interactive from Illuminations allows students to graph trigonometric functions. Parameters that affect the amplitude, period, and phase shift of the function can be manipulated. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

