MA.912.AR.3.2

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Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.

Clarifications

Clarification 1: Within this benchmark, the expectation is to solve by factoring techniques, taking square roots, the quadratic formula and completing the square.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Standard: Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
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))
1200400: Foundational Skills in Mathematics 9-12 (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.3.AP.2: Solve mathematical one-variable quadratic equations with integer coefficients over the real and complex number systems.

Related Resources

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

Formative Assessment

Complex Solutions?:

Students are asked to explain how to recognize when the quadratic formula results in complex solutions.

Type: Formative Assessment

Lesson Plans

Solving Quadratic Equations by Completing the square:

Students will model the process of completing the square (leading coefficient of 1) with algebra tiles, and then practice solving equations using the completing the square method. This lesson provides a discovery opportunity to conceptually see why the process of squaring half of the b value is considered completing the square.

Type: Lesson Plan

Solving Quadratics - Exploring Different Methods:

Students will explore how different methods find the solutions (roots) to quadratic equations including, factoring, graphing, and the quadratic formula.

Type: Lesson Plan

Radical Mathematical:

In this lesson students will solve radical equations, showing how extraneous solutions may arise. Students will solve radical equations that model real-world relationships.

Type: Lesson Plan

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.

Type: Lesson Plan

The Quadratic Quandary:

Students will sort various quadratic equations by the method they would use for solving (ie. factoring, quadratic formula). Then as a class they justify their placements and eventually discover that there are many ways to solve and that some make sense in different situations, however there is no real "correct" method for each equation type.

Type: Lesson Plan

Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

<p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>

Type: Perspectives Video: Professional/Enthusiast

MFAS Formative Assessments

Complex Solutions?:

Students are asked to explain how to recognize when the quadratic formula results in complex solutions.

Student Resources

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

Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

<p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>

Type: Perspectives Video: Professional/Enthusiast

Parent Resources

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

Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

<p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>

Type: Perspectives Video: Professional/Enthusiast