Number: MA.912.AR.6
Title: Solve and graph polynomial equations and functions in one and two variables.
Type:
Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Related Benchmarks
This cluster includes the following benchmarks
| 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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Related Access Points
This cluster includes the following access points.
Access Points
| Access Point Number |
Access Point Title |
| MA.912.AR.6.AP.1: | Solve one-variable polynomial equations of degree 3 or higher in factored form, over the real number system. |
| MA.912.AR.6.AP.5: | Create a rough graph of a polynomial function of degree 3 or higher (in factored form) using zeros, multiplicity and knowledge of end behavior. |
Related Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Formative Assessments
| Name |
Description |
| Zeros of a Cubic: | Students are asked to identify the zeros of cubic polynomials, without the use of technology, and then describe what the zeros indicate about the graph. |
| Use Zeros to Graph: | Students are given the factored form of a cubic polynomial and are asked to use the zeros to sketch the graph between two given points on the coordinate plane without the use of technology. |
Lesson Plans
| Name |
Description |
| Taming the Behavior of Polynomials: | This lesson will cover sketching the graphs of polynomials while in factored form without the use of a calculator. |
| 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. |
Perspectives Video: Expert
| Name |
Description |
| Problem Solving with Project Constraints: | It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems! |
Perspectives Video: Teaching Idea
| Name |
Description |
| Multiplying Polynomials: | Unlock an effective teaching strategy for teaching multiplying polynomials in this Teacher Perspectives video for educators. |
Student Resources
Vetted resources students can use to learn the concepts and skills in this topic.
Perspectives Video: Expert
| Title |
Description |
| Problem Solving with Project Constraints: | It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems! |
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
Perspectives Video: Expert
| Title |
Description |
| Problem Solving with Project Constraints: | It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems! |
