# Standard 1: Interpret and rewrite algebraic expressions and equations in equivalent forms. Export Print
General Information
Number: MA.912.AR.1
Title: Interpret and rewrite algebraic expressions and equations in equivalent forms.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.912.AR.1.AP.1
Identify a part(s) of an equation or expression and explain the meaning within the context of a problem.
MA.912.AR.1.AP.2
Rearrange an equation or a formula for a specific variable.
MA.912.AR.1.AP.3
Add, subtract and multiply polynomial expressions with integer coefficients.
MA.912.AR.1.AP.4
Divide a polynomial expression by a monomial expression with integer coefficients.
MA.912.AR.1.AP.5
Divide polynomial expressions using long division, synthetic division and algebraic manipulation where the denominator is a linear expression.
MA.912.AR.1.AP.6
Solve mathematical and/or real-world problems involving addition, subtraction, multiplication or division of polynomials with integer coefficients.
MA.912.AR.1.AP.7
MA.912.AR.1.AP.8
Select a polynomial expression as a product of polynomials with integer coefficients over the real or complex number system.
MA.912.AR.1.AP.9
Apply previous understanding of rational number operations with common denominators to add and subtract rational expressions.

## Related Resources

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

## Formative Assessments

Solving Formulas for a Variable:

Students are given the slope formula and the slope-intercept equation and are asked to solve for specific variables.

Type: Formative Assessment

Solving Literal Equations:

Students are given three literal equations, each involving three variables and either addition or subtraction, and are asked to solve each equation for a specific variable.

Type: Formative Assessment

Literal Equations:

Students are given three literal equations, each involving three variables and either multiplication or division, and are asked to solve each equation for a specific variable.

Type: Formative Assessment

Solving a Literal Linear Equation:

Students are given a literal linear equation and asked to solve for a specific variable.

Type: Formative Assessment

Interpreting Basic Tax:

Students are asked to interpret the parts of an equation used to calculate the total purchase price including tax of a set of items.

Type: Formative Assessment

Subtracting Polynomials:

Students are asked to find the difference of two polynomials and explain if the difference of polynomials will always result in a polynomial.

Type: Formative Assessment

Rewriting Numerical Expressions:

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

Type: Formative Assessment

Multiplying Polynomials - 2:

Students are asked to multiply polynomials and explain if the product of two polynomials always results in a polynomial.

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

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

Multiplying Polynomials - 1:

Students are asked to multiply polynomials and explain if the product of polynomials always results in a polynomial.

Type: Formative Assessment

Students are asked to find the sum of two polynomials and explain if the sum of polynomials always results in a polynomial.

Type: Formative Assessment

Surface Area of a Cube:

Students are asked to solve the formula for the surface area of a cube for e, the length of an edge of the cube.

Type: Formative Assessment

Dot Expressions:

Students are asked to explain how parts of an algebraic expression relate to the number and type of symbols in a sequence of diagrams.

Type: Formative Assessment

What Happens?:

Students are asked to determine how the volume of a cone will change when its dimensions are changed.

Type: Formative Assessment

Rewriting Equations:

Students are given a literal equation involving four variables and are asked to solve for the variable in the quadratic term.

Type: Formative Assessment

## Lesson Plans

Free Fall Clock and Reaction Time!:

This will be a lesson designed to introduce students to the concept of 9.81 m/s2 as a sort of clock that can be used for solving all kinematics equations where a = g.

Type: Lesson Plan

Laying Tiles for Polynomial Addition and Subtraction Renovation:

In this lesson students will learn how to add and subtract polynomials.

Type: Lesson Plan

How much is your time worth?:

This lesson is designed to help students solve real-world problems involving compound and continuously compounded interest. Students will also be required to translate word problems into function models, evaluate functions for inputs in their domains, and interpret outputs in context.

Type: Lesson Plan

Efficient Storage:

The topic of this MEA is work and power. Students will be assigned the task of hiring employees to complete a given task. In order to make a decision as to which candidates to hire, the students initially must calculate the required work. The power each potential employee is capable of, the days they are available to work, the percentage of work-shifts they have missed over the past 12 months, and the hourly pay rate each worker commands will be provided to assist in the decision process. Full- and/or part-time positions are available. Through data analysis, the students will need to evaluate which factors are most significant in the hiring process. For instance, some groups may prioritize speed of work, while others prioritize cost or availability/dependability.

Type: Lesson Plan

Graphing vs. Substitution. Which would you choose?:

Students will solve multiple systems of equations using two methods: graphing and substitution. This will help students to make a connection between the two methods and realize that they will indeed get the same solution graphically and algebraically.  Students will compare the two methods and think about ways to decide which method to use for a particular problem. This lesson connects prior instruction on solving systems of equations graphically with using algebraic methods to solve systems of equations.

Type: Lesson Plan

Turning Tires Model Eliciting Activity:

The Turning Tires MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best tire material for certain situations. The main focus of the MEA is applying surface area concepts and algebra through modeling.

Type: Lesson Plan

## Original Student Tutorials

Learn how to use multistep factoring to factor quadratics in this interactive tutorial.

This is part 5 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Factoring Polynomials when "a" Does Not Equal 1, Snowflake Method:

Learn to factor quadratic trinomials when the coefficient a does not equal 1 by using the Snowflake Method in this interactive tutorial.

This is part 4 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method:

Learn how to factor quadratic polynomials when the leading coefficient (a) is not 1 by using the box method in this interactive tutorial.

This is part 3 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

The Diamond Game: Factoring Quadratics when a = 1:

Learn how to factor quadratics when the coefficient a = 1 using the diamond method in this game show-themed, interactive tutorial.

This is part 1 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Identifying Parts of Linear Expressions:

Learn to identify and interpret parts of linear expressions in terms of mathematical or real-world contexts in this original tutorial.

Type: Original Student Tutorial

Introduction to Polynomials, Part 2 - Adding and Subtracting:

Learn how to add and subtract polynomials in this online tutorial. You will learn how to combine like terms and then use the distribute property to subtract polynomials.

This is part 2 of a two-part lesson. Click below to open part 1.

Type: Original Student Tutorial

Introduction to Polynomials: Part 1:

Learn how to identify monomials and polynomials and determine their degree in this interactive tutorial.

This is part 1 in a two-part series. Click here to open Part 2.

Type: Original Student Tutorial

Long Division With Polynomials:

Use long division to rewrite a rational expression of the form a(x) divided by b(x) in the form q(x) plus the quantity r(x) divided by b(x), where a(x), b(x), q(x), and r(x) are polynomials with this interactive tutorial.

Type: Original Student Tutorial

Factoring Polynomials Using Special Cases:

Learn how to factor quadratic polynomials that follow special cases, difference of squares and perfect square trinomials, in this interactive tutorial.

This is part 2 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

Base 16 Notation in Computing:

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Type: Perspectives Video: Professional/Enthusiast

Have a need for speed? Get out your spreadsheet! Race car drivers use algebraic formulas and spreadsheets to optimize car performance.

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

Programming Mathematics: Algebra, and Variables to control Open-source Hardware:

If you are having trouble understanding variables, this video might help you see the light.

Type: Perspectives Video: Teaching Idea

## Tutorials

The golden ratio:

In this tutorial, students learn an algebraic approach to understanding Phi, one of the most amazing numbers in mathematics.

Type: Tutorial

Solving a literal equation:

Students will learn to solve a literal equation.

Type: Tutorial

Division of Polynomials:

This resource discusses dividing a polynomial by a monomial and also dividing a polynomial by a polynomial using long division.

Type: Tutorial

## Video/Audio/Animation

Solving Literal Equations:

Literal equations are formulas for calculating the value of one unknown quantity from one or more known quantities. Variables in the formula are replaced by the actual or 'literal' values corresponding to a specific instance of the relationship.

Type: Video/Audio/Animation

## Student Resources

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

## Original Student Tutorials

Learn how to use multistep factoring to factor quadratics in this interactive tutorial.

This is part 5 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Factoring Polynomials when "a" Does Not Equal 1, Snowflake Method:

Learn to factor quadratic trinomials when the coefficient a does not equal 1 by using the Snowflake Method in this interactive tutorial.

This is part 4 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Factoring Quadratics When the Coefficient a Does Not Equal 1: The Box Method:

Learn how to factor quadratic polynomials when the leading coefficient (a) is not 1 by using the box method in this interactive tutorial.

This is part 3 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

The Diamond Game: Factoring Quadratics when a = 1:

Learn how to factor quadratics when the coefficient a = 1 using the diamond method in this game show-themed, interactive tutorial.

This is part 1 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Identifying Parts of Linear Expressions:

Learn to identify and interpret parts of linear expressions in terms of mathematical or real-world contexts in this original tutorial.

Type: Original Student Tutorial

Introduction to Polynomials, Part 2 - Adding and Subtracting:

Learn how to add and subtract polynomials in this online tutorial. You will learn how to combine like terms and then use the distribute property to subtract polynomials.

This is part 2 of a two-part lesson. Click below to open part 1.

Type: Original Student Tutorial

Introduction to Polynomials: Part 1:

Learn how to identify monomials and polynomials and determine their degree in this interactive tutorial.

This is part 1 in a two-part series. Click here to open Part 2.

Type: Original Student Tutorial

Long Division With Polynomials:

Use long division to rewrite a rational expression of the form a(x) divided by b(x) in the form q(x) plus the quantity r(x) divided by b(x), where a(x), b(x), q(x), and r(x) are polynomials with this interactive tutorial.

Type: Original Student Tutorial

Factoring Polynomials Using Special Cases:

Learn how to factor quadratic polynomials that follow special cases, difference of squares and perfect square trinomials, in this interactive tutorial.

This is part 2 in a five-part series. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

Base 16 Notation in Computing:

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.

Type: Perspectives Video: Professional/Enthusiast

## Tutorials

The golden ratio:

In this tutorial, students learn an algebraic approach to understanding Phi, one of the most amazing numbers in mathematics.

Type: Tutorial

Solving a literal equation:

Students will learn to solve a literal equation.

Type: Tutorial

Division of Polynomials:

This resource discusses dividing a polynomial by a monomial and also dividing a polynomial by a polynomial using long division.

Type: Tutorial

## Video/Audio/Animation

Solving Literal Equations:

Literal equations are formulas for calculating the value of one unknown quantity from one or more known quantities. Variables in the formula are replaced by the actual or 'literal' values corresponding to a specific instance of the relationship.

Type: Video/Audio/Animation

## Parent Resources

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

## Perspectives Video: Professional/Enthusiast

Base 16 Notation in Computing:

Listen in as a computing enthusiast describes how hexadecimal notation is used to express big numbers in just a little space.