| Code |
Description |
| MA.912.AR.6.1: | Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems. |
| MA.912.AR.6.2: | Explain and apply the Remainder Theorem to solve mathematical and real-world problems. |
| MA.912.AR.6.3: | Explain and apply theorems for polynomials to solve mathematical and real-world problems.Clarifications:
Clarification 1: Theorems include the Factor Theorem and the Fundamental Theorem of Algebra. |
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| MA.912.AR.6.4: | Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetry; and end behavior. Clarification 2: Instruction includes representing the domain and range with inequality notation, interval notation or set-builder notation.
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| MA.912.AR.6.5: | Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior. |
| MA.912.AR.6.6: | Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features and determine constraints in terms of the context.Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetry; and end behavior.Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation.
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This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Manipulating Polynomials: | This lesson unit is intended to help you assess how well students are able to manipulate and calculate with polynomials. In particular, it aims to identify and help students who have difficulties in switching between visual and algebraic representations of polynomial expressions, performing arithmetic operations on algebraic representations of polynomials, factorizing and expanding appropriately when it helps to make the operations easier. |
| Taming the Behavior of Polynomials: | This lesson will cover sketching the graphs of polynomials while in factored form without the use of a calculator. |
| Algebra made fundamental: | This lesson introduces students to the Fundamental Theorem of Algebra. Polynomials that are not in factored form will be limited to quadratic and cubic polynomials. |
| Where did the answers go? Oh, they're imaginary!: | In this lesson, students will solve quadratic equations with imaginary (complex) solutions and be facilitated in the discovery of the Fundamental Theorem of Algebra. |
| Dancing Polynomials/Graph Me Baby: | Dancing Polynomials is designed to lead students from the understanding that the equation of a line produces a linear pattern to the realization that using an exponent greater than one will produce curvature in a graph and that further patterns emerge allowing students to predict what happens at the end of the graph. Using graphing calculators, students will examine the patterns that emerge to predict the end behavior of polynomial functions. They will experiment by manipulating equations superimposed onto landmarks in the shape of parabolas and polynomial functions. An end behavior song and dance, called "Graph Me Baby" will allow students to become graphs to physically understand the end behavior of the graph. |
Vetted resources students can use to learn the concepts and skills in this topic.
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
