ALEX Lesson Plans
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Title: Zero Product Property
Description:
The zero product property allows you to solve a quadratic equation by converting it into two linear equations. This is a common strategy of algebra to break down a problem into simpler parts, each solved by previously learned methods.
Standard(s): [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4]
Subject: Mathematics (9  12)
Title: Zero Product Property
Description: The zero product property allows you to solve a quadratic equation by converting it into two linear equations. This is a common strategy of algebra to break down a problem into simpler parts, each solved by previously learned methods.
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Title: Discover the Roots of a Polynomial Function
Description:
In this lesson, students will be reintroduced to the Four Step Problem  Solving Plan. The plan will be used as a 'checks and balance' tool for discovering the roots (solutions) of polynomial functions. Students will:
*Explore the problem  identify what is given and what they are asked to find.
*Develop a plan  look for a pattern, make a model, solve a simpler but related problem.
*Solve the problem  carry out the plan
*Examine the solution  check the results with the conditions in the problem, check the reasonableness of the solution
Standard(s): [MA2013] AL1 (912) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3] [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL2 (912) 17: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. [AAPR3]
Subject: Mathematics (9  12)
Title: Discover the Roots of a Polynomial Function
Description: In this lesson, students will be reintroduced to the Four Step Problem  Solving Plan. The plan will be used as a 'checks and balance' tool for discovering the roots (solutions) of polynomial functions. Students will:
*Explore the problem  identify what is given and what they are asked to find.
*Develop a plan  look for a pattern, make a model, solve a simpler but related problem.
*Solve the problem  carry out the plan
*Examine the solution  check the results with the conditions in the problem, check the reasonableness of the solution
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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: "Factoring by Mack"
Description:
This strategy for factoring trinomials will eliminate the trialanderror method used in most textbooks.The lesson will be a direct teaching lesson. With the teacher lecturing and the students taking notes and then having the students break up into groups to solve sample problems.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) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3] [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL1 (912) 8: Use the structure of an expression to identify ways to rewrite it. [ASSE2]
Subject: Mathematics (9  12)
Title: "Factoring by Mack"
Description: This strategy for factoring trinomials will eliminate the trialanderror method used in most textbooks.The lesson will be a direct teaching lesson. With the teacher lecturing and the students taking notes and then having the students break up into groups to solve sample problems.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: Classifying Complex Numbers
Description:
This lesson helps students distinguish between strictly complex numbers, strictly real numbers and strictly imaginary numbers while learning that real numbers and imaginary numbers are subsets of the set of complex numbers.
Standard(s): [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [MA2013] AL2 (912) 1: Know there is a complex number i such that i^{2} = 1, and every complex number has the form a + bi with a and b real. [NCN1] [MA2013] ALT (912) 1: Know there is a complex number i such that i^{2} = 1, and every complex number has the form a + bi with a and b real. [NCN1] [MA2013] MI1 (912) 4: Explain the development and uses of sets of numbers, including complex, real, rational, irrational, integer, whole, and natural numbers. (Alabama) [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]
Subject: Mathematics (9  12)
Title: Classifying Complex Numbers
Description: This lesson helps students distinguish between strictly complex numbers, strictly real numbers and strictly imaginary numbers while learning that real numbers and imaginary numbers are subsets of the set of complex numbers.
Web Resources
Interactives/Games
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Title: Quadratic Equation Grapher
Description:
Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms to see how they add to generate the polynomial curve.
Standard(s): [MA2013] AL1 (912) 7: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL1 (912) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [ASSE3] [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4] [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) 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]
Quadratic Equation Grapher
http://phet.colorado...
Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms to see how they add to generate the polynomial curve.
Learning Activities
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Title: Quadratic Matching
Description:
This worksheet relates functions, quadratics, factors and graphs. The students can also cut it apart for a more engaging activity if time allows.
Standard(s): [MA2013] AL1 (912) 18: Solve quadratic equations in one variable. [AREI4]
Quadratic Matching
http://mathbits.com/...
This worksheet relates functions, quadratics, factors and graphs. The students can also cut it apart for a more engaging activity if time allows.

