ALEX Lesson Plans
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Title: Conic Sections: Discovering the Degenerates
Description:
Through a mixture of online exploration, and teacher instruction, students will discover how the degenerate forms of the conic sections are formed and will be able to identify the degenerate case of each conic section.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Subject: Mathematics (9  12)
Title: Conic Sections: Discovering the Degenerates
Description: Through a mixture of online exploration, and teacher instruction, students will discover how the degenerate forms of the conic sections are formed and will be able to identify the degenerate case of each conic section.
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Title: Conic Sections: Playing With Parabolas
Description:
Through a mixture of online exploration, and teacher instruction, students will discover how parabolas are formed and will be able to use the key components from a graph (vertex, focus and directrix,) to generate the equation of a graph.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Subject: Mathematics (9  12)
Title: Conic Sections: Playing With Parabolas
Description: Through a mixture of online exploration, and teacher instruction, students will discover how parabolas are formed and will be able to use the key components from a graph (vertex, focus and directrix,) to generate the equation of a graph.
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Title: Conic Sections: Playing with Hyperbolas
Description:
Through a mixture of online exploration, and teacher instruction, students will discover how Hyberbolas are formed and will be able to use the key components (center, vertices and the asymptotes) to generate the equation of a graph.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Subject: Mathematics (9  12)
Title: Conic Sections: Playing with Hyperbolas
Description: Through a mixture of online exploration, and teacher instruction, students will discover how Hyberbolas are formed and will be able to use the key components (center, vertices and the asymptotes) to generate the equation of a graph.
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Title: Conic Sections: Playing with Ellipses
Description:
Through a mixture of online exploration, and teacher instruction, students will discover how ellipses are formed and will be able to use the key components (center, foci, directrix, vertices, major axis, minor axis) to generate the equation of a graph.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Subject: Mathematics (9  12)
Title: Conic Sections: Playing with Ellipses
Description: Through a mixture of online exploration, and teacher instruction, students will discover how ellipses are formed and will be able to use the key components (center, foci, directrix, vertices, major axis, minor axis) to generate the equation of a graph.
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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: Ellipse
Description:
This lesson is designed for an Algebra II through PreCalculus classes and introduces the conic section an ellipse. In this lesson students explore an ellipse, the set of points in a plane such that the sum of the distances from each point to two fixed points is constant. The students will investigate the construction of an ellipse and be able to recognize its major axis, semimajor axis and focal points and to be able to compute its eccentricity. 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): [S1] E&S (912) 6: Explain the length of a day and of a year in terms of the motion of Earth. [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 37: (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. [GGPE3]
Subject: Mathematics (9  12), or Science (9  12)
Title: Ellipse
Description: This lesson is designed for an Algebra II through PreCalculus classes and introduces the conic section an ellipse. In this lesson students explore an ellipse, the set of points in a plane such that the sum of the distances from each point to two fixed points is constant. The students will investigate the construction of an ellipse and be able to recognize its major axis, semimajor axis and focal points and to be able to compute its eccentricity. 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: Going the Distance for Circles
Description:
This lesson is designed for an Advanced Mathematics class and introduces the first conic section  a circle. The definition and important information related to circles is presented in a multimedia presentation. Students are then required to document what they have learned in a brochure.
Standard(s): [TC2] CA2 (912) 4: Utilize advanced features of word processing software, including outlining, tracking changes,
hyperlinking, and mail merging. [TC2] CA2 (912) 6: Utilize advanced features of multimedia software, including image, video, and audio editing. [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] GEO (912) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [GGPE1]
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Going the Distance for Circles
Description: This lesson is designed for an Advanced Mathematics class and introduces the first conic section  a circle. The definition and important information related to circles is presented in a multimedia presentation. Students are then required to document what they have learned in a brochure.
Thinkfinity Lesson Plans
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Title: Analyze the Data
Description:
In this lesson, one of a multipart unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. By analyzing a data set, students investigate and create a model for the relationship between the height of the drop and the number of drops.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 18: c. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. [FIF7d]
Subject: Mathematics,Science Title: Analyze the Data
Description: In this lesson, one of a multipart unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. By analyzing a data set, students investigate and create a model for the relationship between the height of the drop and the number of drops. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Assessments
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Title: Quick Graph
Description:
Quick Graph is a powerful, high quality, graphic calculator that has capabilities to display results in 2D or 3D. It is capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in all standard coordinate systems: Cartiesian plane, polar, spherical and cylindrical, all with amazing speed and results, which can be copied, emailed, or saved to the photo library.
Standard(s): [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) [MA2013] AL2 (912) 7: (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [NVM6] (Alabama) [MA2013] ALT (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 18: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7]
Quick Graph
http://itunes.apple....
Quick Graph is a powerful, high quality, graphic calculator that has capabilities to display results in 2D or 3D. It is capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in all standard coordinate systems: Cartiesian plane, polar, spherical and cylindrical, all with amazing speed and results, which can be copied, emailed, or saved to the photo library.
Interactives/Games
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Title: Interactive Conic Sections
Description:
This is an interactive website on cross sections. They are twodimensional representations created at the intersection of a "slicing plane" and a threedimensional object.
Standard(s): [MA2013] AL2 (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] ALT (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Interactive Conic Sections
http://www.shodor.or...
This is an interactive website on cross sections. They are twodimensional representations created at the intersection of a "slicing plane" and a threedimensional object.
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Title: Interactive Graph of an Ellipse
Description:
This is an interactive graph of an ellipse. Features include sliders which can be moved to change the coordinates of the foci to explore changes in eccentricity and the lengths of major and minor axes.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 37: (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. [GGPE3] [MA2013] ALT (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] AL2 (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Interactive Graph of an Ellipse
https://www.desmos.c...
This is an interactive graph of an ellipse. Features include sliders which can be moved to change the coordinates of the foci to explore changes in eccentricity and the lengths of major and minor axes.
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Title: Graph of a Parabola (Conic Section)
Description:
This is an interactive graph of a parabola as a conic section. The vertex, focus, and directrix of the parabola are displayed on the graph. A movable slider can change the distance between the focus and the vertex to explore the effect this distance has on the graph.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 36: (+) Derive the equations of a parabola given a focus and directrix. [GGPE2] [MA2013] ALT (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] AL2 (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama)
Graph of a Parabola (Conic Section)
http://www.desmos.co...
This is an interactive graph of a parabola as a conic section. The vertex, focus, and directrix of the parabola are displayed on the graph. A movable slider can change the distance between the focus and the vertex to explore the effect this distance has on the graph.
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Title: Graph of a Hyperbola (Conic Section)
Description:
This is an interactive graph of a hyperbola. The foci and center of the hyperbola are shown on the graph. Moveable sliders allow the coordinates of the foci to be changed to explore changes in the graph.
Standard(s): [MA2013] PRE (912) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 37: (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. [GGPE3]
Graph of a Hyperbola (Conic Section)
http://www.desmos.co...
This is an interactive graph of a hyperbola. The foci and center of the hyperbola are shown on the graph. Moveable sliders allow the coordinates of the foci to be changed to explore changes in the graph.
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Title: Quick Graph
Description:
Quick Graph is a powerful, high quality, graphic calculator that has capabilities to display results in 2D or 3D. It is capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in all standard coordinate systems: Cartiesian plane, polar, spherical and cylindrical, all with amazing speed and results, which can be copied, emailed, or saved to the photo library.
Standard(s): [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) [MA2013] AL2 (912) 7: (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [NVM6] (Alabama) [MA2013] ALT (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 18: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7]
Quick Graph
http://itunes.apple....
Quick Graph is a powerful, high quality, graphic calculator that has capabilities to display results in 2D or 3D. It is capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in all standard coordinate systems: Cartiesian plane, polar, spherical and cylindrical, all with amazing speed and results, which can be copied, emailed, or saved to the photo library.
Learning Activities
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Title: Quick Graph
Description:
Quick Graph is a powerful, high quality, graphic calculator that has capabilities to display results in 2D or 3D. It is capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in all standard coordinate systems: Cartiesian plane, polar, spherical and cylindrical, all with amazing speed and results, which can be copied, emailed, or saved to the photo library.
Standard(s): [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) [MA2013] AL2 (912) 7: (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [NVM6] (Alabama) [MA2013] ALT (912) 28: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from seconddegree equations. (Alabama) [MA2013] PRE (912) 18: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7]
Quick Graph
http://itunes.apple....
Quick Graph is a powerful, high quality, graphic calculator that has capabilities to display results in 2D or 3D. It is capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in all standard coordinate systems: Cartiesian plane, polar, spherical and cylindrical, all with amazing speed and results, which can be copied, emailed, or saved to the photo library.

