Number: MA.912.AR.8
Title: Solve and graph rational 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.8.1: | Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.Clarifications:
Clarification 1: Within the Algebra 2 course, numerators and denominators are limited to linear and quadratic expressions. |
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| MA.912.AR.8.2: | Given a table, equation or written description of a rational function, 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; end behavior; and asymptotes.Clarification 2: Instruction includes representing the domain and range with inequality notation, interval notation or set-builder notation. Clarification 3: Within the Algebra 2 course, numerators and denominators are limited to linear and quadratic expressions.
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| MA.912.AR.8.3: | Solve and graph mathematical and real-world problems that are modeled with rational functions. 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; end behavior; and asymptotes.Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation. Clarification 3: Instruction includes using rational functions to represent inverse proportional relationships. Clarification 4: Within the Algebra 2 course, numerators and denominators are limited to linear and quadratic expressions.
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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.8.AP.1: | Solve one-variable rational equations and identify any extraneous solutions. |
| MA.912.AR.8.AP.2: | Given a table, equation or written description of a rational function, select the graph that represents the function. |
| MA.912.AR.8.AP.3: | Given a mathematical and/or real-world problem that is modeled with rational functions, solve the mathematical problem, or select the graph using key features (in terms of context) that represents this model. |
Related Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Original Student Tutorials
Formative Assessments
| Name |
Description |
| The Duplex: | Students are asked to solve a design problem in which the length of wall used in a rectangular floor plan is minimized. |
| Graphing a Rational Function: | Students are asked to graph a rational function with the use of technology and identify key features of the graph. |
Lesson Plan
| Name |
Description |
| A Rational Representation: | Students will tackle a real-world situation regarding starting a business that requires a rational equation to evaluate the plan. Students will determine a method and set of steps for solving rational equations and then revisit the original scenario and solve using the new method they have synthesized. Students will also explore, through collaborative learning structures, the concept of extraneous solutions.
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Problem-Solving Task
| Name |
Description |
| How does the solution change?: | The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them. |
Student Resources
Vetted resources students can use to learn the concepts and skills in this topic.
Original Student Tutorials
Problem-Solving Task
| Title |
Description |
| How does the solution change?: | The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them. |
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
Problem-Solving Task
| Title |
Description |
| How does the solution change?: | The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level. By asking students to reason about solutions without explicitly solving them, we get to the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally simple; the point of the task is not to test techniques in solving equations, but to encourage students to reason about them. |
