ALEX Lesson Plans
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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: Investigating Parabolas in Standard Form
Description:
Students explore the coefficients of a quadratic function using a graphing calculator. This is an inquiry lesson to be used as an introduction to translations and dilations of functions.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): [TC2] CA2 (912) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [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] [MA2013] AL2 (912) 34: 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] PRE (912) 16: 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. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] ALT (912) 34: 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]
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: Investigating Parabolas in Standard Form
Description: Students explore the coefficients of a quadratic function using a graphing calculator. This is an inquiry lesson to be used as an introduction to translations and dilations of functions.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: Who am I? Find A Polynomial From Its Roots
Description:
Students analyze the roots and end behavior of a polynomials and write the equation of a polynomial under given conditions. Students apply theorems concerning the multiplicity of roots, conjugates of irrational or complex imaginary roots to find a polynomial under given conditions. Students will factor polynomials to find the complex roots. Students graph polynomials and determine the local extrema. 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): [TC2] CA2 (912) 9: Practice ethical and legal use of technology systems and digital content. [TC2] CA2 (912) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [MA2013] AL2 (912) 5: (+) Extend polynomial identities to the complex numbers. [MA2013] AL2 (912) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [NCN9] [MA2013] AL2 (912) 16: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x  a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). [AAPR2] [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] [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) 5: (+) Extend polynomial identities to the complex numbers. [NCN8] [MA2013] ALT (912) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [NCN9] [MA2013] ALT (912) 16: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x  a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). [AAPR2] [MA2013] ALT (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] [MA2013] ALT (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] 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: Who am I? Find A Polynomial From Its Roots
Description: Students analyze the roots and end behavior of a polynomials and write the equation of a polynomial under given conditions. Students apply theorems concerning the multiplicity of roots, conjugates of irrational or complex imaginary roots to find a polynomial under given conditions. Students will factor polynomials to find the complex roots. Students graph polynomials and determine the local extrema. 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: Building Connections
Description:
In this lesson, from Illuminations, students make connections among different classes of polynomial functions by exploring the graphs of these functions. The questions in the activity sheets allow students to make connections between the xintercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function.
Standard(s): [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 Title: Building Connections
Description: In this lesson, from Illuminations, students make connections among different classes of polynomial functions by exploring the graphs of these functions. The questions in the activity sheets allow students to make connections between the xintercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

