Standard 8: Solve and graph rational equations and functions in one and two variables.

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General Information
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.

Related Access Points

This cluster includes the following access points.

Access Points

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.

Formative Assessments

The Duplex:

Students are asked to solve a design problem in which the length of wall used in a rectangular floor plan is minimized.

Type: Formative Assessment

Graphing a Rational Function:

Students are asked to graph a rational function with the use of technology and identify key features of the graph.

Type: Formative Assessment

Lesson Plan

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.

 

Type: Lesson Plan

Original Student Tutorials

Solving Rational Equations: Using Common Denominators:

Learn how to solve rational functions by getting common denominators in this interactive tutorial.

Type: Original Student Tutorial

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

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.

Type: Problem-Solving Task

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Solving Rational Equations: Using Common Denominators:

Learn how to solve rational functions by getting common denominators in this interactive tutorial.

Type: Original Student Tutorial

Solving Rational Equations: Cross Multiplying:

Learn how to solve rational linear and quadratic equations using cross multiplication in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

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.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Problem-Solving Task

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.

Type: Problem-Solving Task