ALEX Lesson Plans
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Title: Now, where did THAT come from? Deriving the Quadratic Formula
Description:
Generally, teachers expect students to memorize the quadratic formula and to know that you use it after exhausting all other means of solving a quadratic equation, i.e. as a last resort. This technologybased lesson is designed to assist students with deriving the formula on their own. Students must first be familiar with complex numbers and the process of “completing the square.”
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL1 (912) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [AREI7] [MA2013] AL2 (912) 4: Solve quadratic equations with real coefficients that have complex solutions. [NCN7] [MA2013] ALC (912) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama)
Subject: Mathematics (9  12)
Title: Now, where did THAT come from? Deriving the Quadratic Formula
Description:
Generally, teachers expect students to memorize the quadratic formula and to know that you use it after exhausting all other means of solving a quadratic equation, i.e. as a last resort. This technologybased lesson is designed to assist students with deriving the formula on their own. Students must first be familiar with complex numbers and the process of “completing the square.”
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Family Ties: Parabolas
Description:
This lesson allows students to manipulate the parameters while using the vertex form of the equation of a parabola to see the effects on the graph. The spreadsheet can be altered for other functions.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [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) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL1 (912) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [AREI7] [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] AL1 (912) 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] AL1 (912) 36: 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] AL2 (912) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [NCN9] [MA2013] AL2 (912) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9] [MA2013] ALC (912) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama) [MA2013] ALT (912) 4: Solve quadratic equations with real coefficients that have complex solutions. [NCN7] [MA2013] ALT (912) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [NCN9] [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] AM1 (912) 11: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Understand the importance of using complex numbers in graphing functions on the Cartesian or complex plane. [NCN9] (Alabama)
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Family Ties: Parabolas
Description: This lesson allows students to manipulate the parameters while using the vertex form of the equation of a parabola to see the effects on the graph. The spreadsheet can be altered for other functions.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: What's The Real Cost of That Car?
Description:
This is a Commerce and Information Technology lesson plan. A project requiring research, critical thinking and complex decisionmaking about factoring all the costs of purchasing a large ticket item... a car.
Standard(s): [BMA] BA11 (912) 4: Apply mathematical, statistical, and logical functions to solve problems using spreadsheets. [BMA] BA11 (912) 3: Design spreadsheets for personal and business use. [MA2013] AL1 (912) 10: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [AAPR1] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [MA2013] ALC (912) 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data. (Alabama) [MA2013] ALC (912) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama) [MA2013] ALC (912) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) [MA2013] DM1 (912) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the listprocessing algorithm, and studentcreated algorithms. (Alabama) [MA2013] DM1 (912) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the listprocessing algorithm, and studentcreated algorithms. (Alabama)
Subject: Business, Management, and Administration (9  12), or Mathematics (9  12)
Title: What's The Real Cost of That Car?
Description: This is a Commerce and Information Technology lesson plan. A project requiring research, critical thinking and complex decisionmaking about factoring all the costs of purchasing a large ticket item... a car.
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Title: Liquidity for Success
Description:
This lesson will input values to calculate financial ratios and intepret the information derived from the calculations. This is a Commerce and Information Technology lesson plan.
Standard(s): [FIN] FN2 (912) 8: Apply analysis ratios to evaluate solvency and earning power. [MA2013] ALC (912) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) [MA2013] ALC (912) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama) [MA2013] ALC (912) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama)
Subject: Finance (9  12), or Mathematics (9  12)
Title: Liquidity for Success
Description: This lesson will input values to calculate financial ratios and intepret the information derived from the calculations. This is a Commerce and Information Technology lesson plan.
Thinkfinity Lesson Plans
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Title: Modeling Orbital Debris Problems
Description:
In this lesson, from Illuminations, students examine the problem of space pollution caused by humanmade debris in orbit to develop an understanding of functions and modeling. The lesson gives students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities.
Standard(s): [S1] PHS (912) 7: Relate velocity, acceleration, and kinetic energy to mass, distance, force, and time. [S1] PHY (912) 1: Explain linear, uniform circular, and projectile motions using one and twodimensional vectors. [S1] PHY (912) 3: Explain planetary motion and navigation in space in terms of Kepler's and Newton's laws. [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] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] ALC (912) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama) [MA2013] AL2 (912) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [FIF9]
Subject: Mathematics,Science Title: Modeling Orbital Debris Problems
Description: In this lesson, from Illuminations, students examine the problem of space pollution caused by humanmade debris in orbit to develop an understanding of functions and modeling. The lesson gives students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

