Standard 3 : Use complex numbers in polynomial identities and equations. (Algebra 2 - Additional Cluster) (Archived)



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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information

Number: MAFS.912.N-CN.3
Title: Use complex numbers in polynomial identities and equations. (Algebra 2 - Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 912
Domain-Subdomain: Number & Quantity: The Complex Number System

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions.
MAFS.912.N-CN.3.8: Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x – 2i).
MAFS.912.N-CN.3.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.912.N-CN.3.AP.7a:

Use the quadratic formula begin mathsize 12px style open parentheses x space equals space fraction numerator negative b plus-or-minus square root of b to the power of 2 space end exponent minus space 4 a c end root over denominator 2 a end fraction close parentheses end style to find solutions to quadratic equations that have complex solutions. 



Related Resources

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

Lesson Plans

Name Description
Ranking Sports Players (Quadratic Equations Practice):

In this Model Eliciting Activity, MEA, students will rank sports players by designing methods, using different indicators, and working with quadratic equations.

Model-Eliciting-Activities, MEAs, allow students to critically analyze data sets, compare information, and require students to explain their thinking and reasoning. While there is no one correct answer in an MEA, students should work to explain their thinking clearly and rationally. Therefore, teachers should ask probing questions and provide feedback to help students develop a coherent, data-as-evidence-based approach within this learning experience.

Algebra made fundamental:

This lesson introduces students to the Fundamental Theorem of Algebra. Polynomials that are not in factored form will be limited to quadratic and cubic polynomials.

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.

Perspectives Video: Professional/Enthusiast

Name Description
Quadratic Equations and Robots: <p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>


Student Resources

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

Perspectives Video: Professional/Enthusiast

Title Description
Quadratic Equations and Robots: <p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>


Parent Resources

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

Perspectives Video: Professional/Enthusiast

Title Description
Quadratic Equations and Robots: <p>Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.</p>