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MAFS.912.A-SSE.1.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4- y4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Algebra: Seeing Structure in Expressions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Interpret the structure of expressions. (Algebra 1 - Major Cluster) (Algebra 2 - Major Cluster) -

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.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

Test Item Specifications

    Assessed with:
    MAFS.912.A-SSE.2.3


Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200400: Intensive Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1207310: Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206330: Analytic Geometry (Specifically in versions: 2014 - 2015 (course terminated))
1200410: Mathematics for College Success (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200700: Mathematics for College Readiness (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1200335: Algebra 2 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.A-SSE.1.AP.2a: Rewrite algebraic expressions in different equivalent forms, such as factoring or combining like terms.
MAFS.912.A-SSE.1.AP.2b: Use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely.
MAFS.912.A-SSE.1.AP.2c: Simplify expressions including combining like terms, using the distributive property, and other operations with polynomials.

Related Resources

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

Assessments

Sample 2 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 1 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 3 - High School Algebra 1 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 2 - High School Algebra 1 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Educational Game

Rewriting Expressions: Simplifying Rational Expressions With Exponents:

In this challenge game, you will be simplifying fractional expressions with exponents. Use the "Teach Me" button to review content before the challenge. During the challenge you get one free solve and two hints! After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!

Type: Educational Game

Formative Assessments

Rewriting Numerical Expressions:

Students are asked to rewrite numerical expressions to find efficient ways to calculate.

Type: Formative Assessment

Determine the Width:

Students are asked to find the width of a rectangle whose area and length are given as polynomials.

Type: Formative Assessment

Quadratic Expressions:

Students are asked to identify equivalent quadratic expressions and to name the form in which each expression is written.

Type: Formative Assessment

Finding Missing Values:

Students are asked to rewrite quadratic expressions and identify parts of the expressions.

Type: Formative Assessment

Lesson Plans

Sorting Equations and Identities:

This lesson is intended to help you assess how well students are able to:

  • Recognize the differences between equations and identities.
  • Substitute numbers into algebraic statements in order to test their validity in special cases.
  • Resist common errors when manipulating expressions such as 2(x – 3) = 2x – 3; (x + 3)2 = x2 + 32.
  • Carry out correct algebraic manipulations.
It also aims to encourage discussion on some common misconceptions about algebra.

Type: Lesson Plan

Matching Trinomials with Area Models:

Students will work in cooperative groups to explore factoring a trinomial into two binomials. Students will be given several area models and will match the correct area model to the correct trinomial.

Type: Lesson Plan

Math Is Exponetially Fun!:

The students will informally learn the rules for exponents: product of powers, powers of powers, zero and negative exponents. The activities provide the teacher with a progression of steps that help lead students to determine results without knowing the rules formally. The closing activity is hands-on to help reinforce all rules.

Type: Lesson Plan

Using algebra tiles and tables to factor trinomials (less guess and check!):

Students will use algebra tiles to visually see how to factor trinomials. In addition, they will use a 3 x 3 table. This process makes students more confident when factoring because there is less guess and check involved in solving each problem.

Type: Lesson Plan

Problem-Solving Tasks

A Cubic Identity:

Solving this problem with algebra requires factoring a particular cubic equation (the difference of two cubes) as well as a quadratic equation. An alternative solution using prime numbers and arithmetic is presented.

Type: Problem-Solving Task

Equivalent Expressions:

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. Students must understand the need to transform the factored form of the quadratic expression (a product of sums) into a sum of products in order to easily see a, the coefficient of the x2 term; k, the leading coefficient of the x term; and n, the constant term.

Type: Problem-Solving Task

Animal Populations:

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

Computations with Complex Numbers:

This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.

Type: Problem-Solving Task

Unit/Lesson Sequence

Sample Algebra 1 Curriculum Plan Using CMAP:

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

 
 
 

Using this CMAP

To view an introduction on the CMAP tool, please click here

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx 

Type: Unit/Lesson Sequence

MFAS Formative Assessments

Determine the Width:

Students are asked to find the width of a rectangle whose area and length are given as polynomials.

Finding Missing Values:

Students are asked to rewrite quadratic expressions and identify parts of the expressions.

Quadratic Expressions:

Students are asked to identify equivalent quadratic expressions and to name the form in which each expression is written.

Rewriting Numerical Expressions:

Students are asked to rewrite numerical expressions to find efficient ways to calculate.

Student Resources

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

Educational Game

Rewriting Expressions: Simplifying Rational Expressions With Exponents:

In this challenge game, you will be simplifying fractional expressions with exponents. Use the "Teach Me" button to review content before the challenge. During the challenge you get one free solve and two hints! After the challenge, review the problems as needed. Try again to get all challenge questions right! Question sets vary with each game, so feel free to play the game multiple times as needed! Good luck!

Type: Educational Game

Problem-Solving Tasks

A Cubic Identity:

Solving this problem with algebra requires factoring a particular cubic equation (the difference of two cubes) as well as a quadratic equation. An alternative solution using prime numbers and arithmetic is presented.

Type: Problem-Solving Task

Equivalent Expressions:

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. Students must understand the need to transform the factored form of the quadratic expression (a product of sums) into a sum of products in order to easily see a, the coefficient of the x2 term; k, the leading coefficient of the x term; and n, the constant term.

Type: Problem-Solving Task

Animal Populations:

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

Computations with Complex Numbers:

This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.

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

A Cubic Identity:

Solving this problem with algebra requires factoring a particular cubic equation (the difference of two cubes) as well as a quadratic equation. An alternative solution using prime numbers and arithmetic is presented.

Type: Problem-Solving Task

Equivalent Expressions:

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. Students must understand the need to transform the factored form of the quadratic expression (a product of sums) into a sum of products in order to easily see a, the coefficient of the x2 term; k, the leading coefficient of the x term; and n, the constant term.

Type: Problem-Solving Task

Animal Populations:

In this task students interpret the relative size of variable expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Type: Problem-Solving Task

Computations with Complex Numbers:

This resource involves simplifying algebraic expressions that involve complex numbers and various algebraic operations.

Type: Problem-Solving Task