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.
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Title: Technology for Displaying Trigonometric Graph Behavior: Sine and Cosine
Description:
After interacting with a list of specified websites, students will explain the effects of various coefficients on the graphs of sine and cosine by describing these effects on a lab activity worksheet with an accuracy of 80%.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): [TC2] CA2 (912) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [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) 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) 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) 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]
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Technology for Displaying Trigonometric Graph Behavior: Sine and Cosine
Description: After interacting with a list of specified websites, students will explain the effects of various coefficients on the graphs of sine and cosine by describing these effects on a lab activity worksheet with an accuracy of 80%.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: 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
Web Resources
Lesson Plans
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Title: Graphs From the Unit Circle
Description:
In this lesson, students use uncooked spaghetti to transfer lengths from the unit circle to a function graph on large butcher paper. In the process, they discover the key features of sine and cosine graphs. The activity is presented for students working in degrees, but another version of the handouts is provided for students working in radians.
Standard(s): [MA2013] PRE (912) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama)
Graphs From the Unit Circle
http://illuminations...
In this lesson, students use uncooked spaghetti to transfer lengths from the unit circle to a function graph on large butcher paper. In the process, they discover the key features of sine and cosine graphs. The activity is presented for students working in degrees, but another version of the handouts is provided for students working in radians.
Assessments
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Title: Prerequsites for Calculus Quiz
Description:
Students will take this selfassessment to make sure they are prepared to take Calculus.
Standard(s): [MA2013] PRE (912) 13: (+) Know and apply the Binomial Theorem for the expansion of (x + y)^{n} in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal's Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) [AAPR5] [MA2013] PRE (912) 33: Prove the Pythagorean identity sin^{2}(θ) + cos^{2}(θ) = 1, and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. [FTF8] (Alabama) [MA2013] PRE (912) 3: (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. [NCN6] [MA2013] PRE (912) 14: (+) Represent a system of linear equations as a single matrix equation in a vector variable. [AREI8] [MA2013] PRE (912) 20: Determine the inverse of a function and a relation. (Alabama) [MA2013] PRE (912) 22: (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. [FBF4c] [MA2013] PRE (912) 24: (+) Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. [FBF5] [MA2013] PRE (912) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama) [MA2013] PRE (912) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama) [MA2013] PRE (912) 27: Use the sum, difference, and halfangle identities to find the exact value of a trigonometric function. (Alabama) [MA2013] PRE (912) 34: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems. [FTF9] [MA2013] PRE (912) 12: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* (Extend to infinite geometric series.) [ASSE4] (Alabama)
Prerequsites for Calculus Quiz
http://www.phschool....
Students will take this selfassessment to make sure they are prepared to take Calculus.
Interactives/Games
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Title: Sine Function (with Unit Circle)
Description:
This is an interactive model of the graph of a sine wave in the form y=sin(b). There is a slider that allows the value of "b" (in radian measure) to be changed. The unit circle is shown simultaneously with the graph of the sine function.
Standard(s): [MA2013] PRE (912) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama)
Sine Function (with Unit Circle)
http://www.desmos.co...
This is an interactive model of the graph of a sine wave in the form y=sin(b). There is a slider that allows the value of "b" (in radian measure) to be changed. The unit circle is shown simultaneously with the graph of the sine function.
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

