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Algebra 2: Unit 3 Polynomial, Rational and Radical Functions
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last edited
by Christine Koerner 4 years, 2 months ago
Big Idea 1: The behavior, properties, and characteristics of a polynomial function can be determined by its degree.
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OAS-M: A2.A.1.4, A2.A.2.1, A2.F.1.1
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Lessons and Additional Activities
Big Idea 1 Lessons 1-3 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Discover and describe the characteristics of a polynomial function and its graph in mathematical and real-world situations.
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Using various tools, generalize characteristics of polynomial functions and their graphs.
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Use graphs, tables, and equations with the aide of technology to allow students to grapple with the differences and similarities between polynomials of varying degree, including targeting rates of change.
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Identify how the degree of the polynomial relates to end behavior, maximum number of real roots, and possible shape of the graph.
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Explain how the leading coefficient affects the end behavior and rate of change of the graph.
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Identify a polynomial function as having even or odd degree based on the graph or equation.
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Predict the degree and behavior of a polynomial given a graph, or table of values.
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Research or develop scenarios that require a polynomial function to model the situation. Use technology to model and explain.
Identify critical points and key features of the graph of a polynomial function and interpret meanings in mathematical and real-world situations.
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Identify the following features from the table or graph of a polynomial function using words, algebraic symbols, equations and inequalities, interval notation: intercepts, symmetry, maximum and minimum points, intervals of increase and decrease, intervals of positive and negative values, domain and range.
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Describe critical points and key features in the correct context of a mathematical and real world situation.
Make generalizations about how transformations affect key features of the graph of a polynomial function.
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Big Idea 2: The graph and equation of a polynomial function yields information about its roots.
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OAS-M: A2.A.1.4 A2.A.2.1 A2.N.1.1, A2.N.1.2 |
Lessons and Additional Activities
Big Idea 2 Lessons 1-3 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Recognize and explore connections between the graph of a polynomial and its zeros.
Develop, analyze and apply general characteristics of the zeros of a polynomial function based on its graph.
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Predict possible roots of a polynomial from the equation, table and/or graph.
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Calculate roots of polynomial functions algebraically and graphically.
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Choose and justify which method is most efficient to determine roots based on the characteristics of the polynomial, (ie. factoring, rational root theorem, synthetic division, long division, analyzing a graph or a table, etc.)
Solve polynomial functions in the context of real-world problems.
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Big Idea 3: Basic arithmetic operations can be performed on polynomials similar to the way they are performed on numbers.
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OAS-M: A2.F.1.5 |
Lessons and Additional Activities
Big Idea 3 Lessons 1-2 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Analyze connections between arithmetic operations on polynomials and the effect it has on the graph.
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Discover, through technology and other means, how arithmetic operations affect the shape and key characteristics of polynomials.
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Predict the shape and characteristics of the resulting graph after arithmetic operations are performed on two or more functions. (ie. degree change when multiplying two or more polynomials-how will this affect end behavior, zeros, max, mins, etc.)
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Perform arithmetic operations on polynomial functions. Justify your answers graphically. Determine key characteristics.
Discover how polynomials and operations on polynomials are modeled in real-world scenarios.
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Research and develop polynomial function models that involve various arithmetic operations, using current real-world data and scenarios. (ie, revenue, cost, sales, etc.)
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Big Idea 4: Rational functions can be described by the division of two polynomial functions.
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OAS-M: A2.A.1.3 A2.A.2.2 A2.F.1.6
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Lessons and Additional Activities
Big Idea 4 Lessons 1-3 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Discover and describe the characteristics of a rational function and its graph in mathematical and real-world situations.
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Analyze the graph of a rational function using technology. Identify critical points and key characteristics.
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Using graphs, tables and equations, find patterns, similarities, and difference between various rational functions. Form conjectures about various characteristics. (ie holes, asymptotes, oblique asymptotes, etc.)
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Calculate critical points, asymptotes, holes, and intervals of importance of a rational function using various algebraic methods (ie factoring, solving equations, etc.).
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Build a rational function when given information and/or a graph.
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Big Idea 5: Radical expressions can be written as expressions with rational exponents, and both are inverse operations of integral exponents.
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OAS-M: A2.N.1.4 A2.A.1.5 A2.F.1.7
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Lessons and Additional Activities
Big Idea 5 Lessons 1-3 Overview (includes links to teacher notes and student activities)
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Evidence of Understanding
Discover and describe the characteristics of a radical function and its graph in mathematical and real-world situations.
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Analyze, using technology, the square root and cube root function rules and graphs. Identify key characteristics. Notice similarities and differences.
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Use tables and graphs to conjecture about the domain, orientation, translations from the parent graph, critical points, etc.
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Compare and contrast the quadratic function and its inverse.
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Compare and contrast the cubic function and its inverse.
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Discover how a radical expression can be expressed using rational exponents.
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Investigate radical equations using technology.
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Algebra 2: Unit 3 Polynomial, Rational and Radical Functions
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