MA.912.AR.9.2

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Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Standard: Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1209315: Mathematics for ACT and SAT (Specifically in versions: 2022 - 2024, 2024 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.AR.9.AP.2: Solve a system consisting of a two-variable linear equation and a quadratic equation algebraically or graphically.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Using Technology:

Students are asked to use technology (e.g., spreadsheet, graphing calculator, or dynamic geometry software) to estimate the solutions of the equation f(x) = g(x) for given functions f and g.

Type: Formative Assessment

Graphs and Solutions - 2:

Students are asked to find the solution(s) of the equation f(x) = g(x) given the graphs of f and g and explain their reasoning.

Type: Formative Assessment

Using Tables:

Students are asked to find solutions of the equation f(x) = g(x) for two given functions, f and g, by constructing a table of values.

Type: Formative Assessment

Graphs and Solutions -1:

Students are asked to explain why the x-coordinate of the intersection of two functions, f and g, is a solution of the equation f(x) = g(x).

Type: Formative Assessment

Lesson Plans

Space Equations:

In this lesson, students model the orbit of a satellite and the trajectory of a missile with a system of equations. They solve the equations both graphically and algebraically.

Type: Lesson Plan

Systems of the Linear Round Table:

This lesson is a follow-up review of systems of linear equations. Students will complete a group activity called Simultaneous Round Table to solve given systems of equations. Students will solve by graphing, elimination, and substitution.  Each student will also perform error analysis on the work from their peers, which will allow them to help each other to correct those mistakes. Class will use data from error analysis to create a plan of action to decrease errors in their work.  Students will discuss the concepts and analyze problems with each other. These concepts were taught in an earlier lesson. This lesson will also help students identify common mistakes and find solutions to remedy them.

Type: Lesson Plan

Problem-Solving Tasks

The Circle and The Line:

Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

Type: Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

MFAS Formative Assessments

Graphs and Solutions - 2:

Students are asked to find the solution(s) of the equation f(x) = g(x) given the graphs of f and g and explain their reasoning.

Graphs and Solutions -1:

Students are asked to explain why the x-coordinate of the intersection of two functions, f and g, is a solution of the equation f(x) = g(x).

Using Tables:

Students are asked to find solutions of the equation f(x) = g(x) for two given functions, f and g, by constructing a table of values.

Using Technology:

Students are asked to use technology (e.g., spreadsheet, graphing calculator, or dynamic geometry software) to estimate the solutions of the equation f(x) = g(x) for given functions f and g.

Student Resources

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

Problem-Solving Tasks

The Circle and The Line:

Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

Type: Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task

Parent Resources

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

Problem-Solving Tasks

The Circle and The Line:

Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

Type: Problem-Solving Task

Introduction to Linear Functions:

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.

Type: Problem-Solving Task