ALEX Lesson Plans
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Title: Systems of Linear Inequalities Project
Description:
The systems of linear inequalities project was designed to be used in an Algebra IB class after a preliminary lesson on systems of linear inequalities. The project is to be graded per group based on the work completed and presentation to the class. Each group is required to use a graphing calculator in its presentation.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] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6] [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 23: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11] [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]
Subject: Mathematics (9  12)
Title: Systems of Linear Inequalities Project
Description: The systems of linear inequalities project was designed to be used in an Algebra IB class after a preliminary lesson on systems of linear inequalities. The project is to be graded per group based on the work completed and presentation to the class. Each group is required to use a graphing calculator in its presentation.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: 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: Quadrilaterals
Description:
This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.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] AL1 (912) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6] [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] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] GEO (912) 9: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [GCO9] [MA2013] GEO (912) 11: Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent; the diagonals of a parallelogram bisect each other; and conversely, rectangles are parallelograms with congruent diagonals. [GCO11] [MA2013] GEO (912) 30: Use coordinates to prove simple geometric theorems algebraically. [GGPE4] [MA2013] GEO (912) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [GGPE5] [MA2013] GEO (912) 33: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [GGPE7] [MA2013] GEO (912) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama) [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1]
Subject: Mathematics (8  12)
Title: Quadrilaterals
Description: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.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: Supply and Demand
Description:
This Illuminations lesson focuses on having students create and solve a system of linear equations in a realworld setting. By solving the system, students find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or slope and yintercept.
Standard(s): [T1] ECN (12) 3: Analyze graphs to determine changes in supply and demand and their effect on equilibrium price and quality. [MA2013] AL1 (912) 19: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [AREI5] [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] AL1 (912) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Subject: Mathematics Title: Supply and Demand
Description: This Illuminations lesson focuses on having students create and solve a system of linear equations in a realworld setting. By solving the system, students find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or slope and yintercept. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Investigating Pick's Theorem
Description:
In this unit of three lessons, from Illuminations, students rediscover Pick's Theorem, which they were likely introduced to in middle school, and use algebra to determine the coefficients of the equation. They explore the concept of change as a mechanism for finding the coefficients of Pick's Theorem.
Standard(s): [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 19: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [AREI5] [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] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Subject: Mathematics Title: Investigating Pick's Theorem
Description: In this unit of three lessons, from Illuminations, students rediscover Pick's Theorem, which they were likely introduced to in middle school, and use algebra to determine the coefficients of the equation. They explore the concept of change as a mechanism for finding the coefficients of Pick's Theorem. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Web Resources
Interactives/Games
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Title: Karl's Function Plotter
Description:
Karl's Function Plotter is an interactive tool in which functions can be entered and the resulting graph displayed.
**Under the Read Me it describes the following restrictions:
"Usage Restrictions: Plotting graphs is computationally intensive. To limit the burden on the internet service provider for Karl's Calculus Tutor, you will be restricted from plotting another graph after you've plotted one for 3 minutes after plotting a small, 5 minutes after plotting a medium, 12 minutes after plotting a large, 20 minutes after plotting an extra large, and 40 minutes after plotting a huge. Tiny plots incur no delay, so you can use them to preview what the larger plot will look like. So enter your fields carefully before clicking the Plot Now button. Note that if you get an error when you attempt to plot, you will not be delayed in trying again."
**Possible alternative resource
http://www.fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ
Standard(s): [MA2013] AL1 (912) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 23: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11] [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] ALT (912) 27: Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [AREI11]
Karl's Function Plotter
http://www.karlscalc...
Karl's Function Plotter is an interactive tool in which functions can be entered and the resulting graph displayed.
**Under the Read Me it describes the following restrictions:
"Usage Restrictions: Plotting graphs is computationally intensive. To limit the burden on the internet service provider for Karl's Calculus Tutor, you will be restricted from plotting another graph after you've plotted one for 3 minutes after plotting a small, 5 minutes after plotting a medium, 12 minutes after plotting a large, 20 minutes after plotting an extra large, and 40 minutes after plotting a huge. Tiny plots incur no delay, so you can use them to preview what the larger plot will look like. So enter your fields carefully before clicking the Plot Now button. Note that if you get an error when you attempt to plot, you will not be delayed in trying again."
**Possible alternative resource
http://www.fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ

