Cluster 3: Use polynomial identities to solve problems. (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.A-APR.3
Title: Use polynomial identities to solve problems. (Algebra 2 - Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 912
Domain-Subdomain: Algebra: Arithmetic with Polynomials & Rational Expressions

Related Standards

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MAFS.912.A-APR.3.AP.4a
Illustrate how polynomial identities are used to determine numerical relationships such as:

List of multiple formulas, for example difference of squares, sum and difference of cubes, and quadratic formula.
MAFS.912.A-APR.3.AP.4b
Prove polynomial identities by showing steps and providing reasons.
MAFS.912.A-APR.3.AP.5a
Match a binomial expression with its binomial expansion, e.g., begin mathsize 12px style left parenthesis 3 x space minus space 5 right parenthesis squared space equals space left parenthesis 3 x space minus space 5 right parenthesis left parenthesis 3 x space minus space 5 right parenthesis end style.

Related Resources

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

Lesson Plan

Binomial Expansion with Pascal's Triangle:

Pascal's Triangle will help students multiply (expand) binomials without having to use the FOIL method or the Distributive Property.

Type: Lesson Plan

Original Student Tutorial

Factoring Polynomials with Greatest Common Factor:

Learn how to factor polynomials by finding their greatest common factor in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Trina's Triangles:

In this task students investigate and ultimately prove the validity of the method of generating Pythagorean Triples that involves the polynomial identity (x2+y2)2=(x2-y2)2+(2xy)2.

Type: Problem-Solving Task

Tutorials

Binomial Theorem:

This video tutorial gives an introduction to the binomial theorem and explains how to use this theorem to expand binomial expressions.

Type: Tutorial

Pascal's Triangle for Binomial Expansion:

This tutorial shows students how to use Pascal's triangle for binomial expansion.

Type: Tutorial

Student Resources

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

Original Student Tutorial

Factoring Polynomials with Greatest Common Factor:

Learn how to factor polynomials by finding their greatest common factor in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Trina's Triangles:

In this task students investigate and ultimately prove the validity of the method of generating Pythagorean Triples that involves the polynomial identity (x2+y2)2=(x2-y2)2+(2xy)2.

Type: Problem-Solving Task

Tutorials

Binomial Theorem:

This video tutorial gives an introduction to the binomial theorem and explains how to use this theorem to expand binomial expressions.

Type: Tutorial

Pascal's Triangle for Binomial Expansion:

This tutorial shows students how to use Pascal's triangle for binomial expansion.

Type: Tutorial

Parent Resources

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

Problem-Solving Task

Trina's Triangles:

In this task students investigate and ultimately prove the validity of the method of generating Pythagorean Triples that involves the polynomial identity (x2+y2)2=(x2-y2)2+(2xy)2.

Type: Problem-Solving Task