ALEX Lesson Plans
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Title: Systems of Equations: What Method Do You Prefer?
Description:
The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of equations.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] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8EE8] [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) 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] AL2 (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] [MA2013] ALC (912) 2: Solve applicationbased problems by developing and solving systems of linear equations and inequalities. (Alabama) [MA2013] ALT (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3]
Subject: Mathematics (8  12)
Title: Systems of Equations: What Method Do You Prefer?
Description: The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of equations.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: There Has to Be a System for This Sweet Problem
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In this Illuminations lesson, students use problemsolving skills to find the solution to a multivariable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.
Standard(s): [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) 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) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [AREI7]
Subject: Mathematics Title: There Has to Be a System for This Sweet Problem
Description: In this Illuminations lesson, students use problemsolving skills to find the solution to a multivariable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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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): [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
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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
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Title: Pick's Theorem as a System of Equations
Description:
In this lesson, one of a multipart unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem.
Standard(s): [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [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) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6] [MA2013] ALT (912) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [ACED3]
Subject: Mathematics Title: Pick's Theorem as a System of Equations
Description: In this lesson, one of a multipart unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Escape from the Tomb
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In this Illuminations lesson, students solve a system of equations when presented with a problem: two bowls are suspended from the ceiling by springs and one bowl is lower than the other. Placing only marbles in one bowl and bingo chips in the other, students must work out how many items should be placed in each bowl so that the heights of the bowls are the same. There are also links to online activity sheets.
Standard(s): [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) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [AREI6] [MA2013] ALC (912) 2: Solve applicationbased problems by developing and solving systems of linear equations and inequalities. (Alabama)
Subject: Mathematics Title: Escape from the Tomb
Description: In this Illuminations lesson, students solve a system of equations when presented with a problem: two bowls are suspended from the ceiling by springs and one bowl is lower than the other. Placing only marbles in one bowl and bingo chips in the other, students must work out how many items should be placed in each bowl so that the heights of the bowls are the same. There are also links to online activity sheets. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

