MAFS.6.EE.1.4

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
General Information
Subject Area: Mathematics
Grade: 6
Domain-Subdomain: Expressions & Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions. (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

  • Assessment Limits :
    Numbers in items must be nonnegative rational numbers. Variables must be included in the expression.
  • Calculator :

    No

  • Context :

    No context

Sample Test Items (2)

Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Grade 6 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.6.EE.1.AP.4a: Evaluate whether sides of an equation are equal using models.

Related Resources

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

Assessments

Sample 3 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 1 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Formative Assessments

Property Combinations:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Type: Formative Assessment

Equivalent Expressions:

Students are asked to determine if pairs of expressions are equivalent and to justify their responses.

Type: Formative Assessment

Equivalent Exponents:

Students are asked to identify expressions equivalent to a given exponential expression and justify their responses.

Type: Formative Assessment

Identifying Equivalent Expressions:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Type: Formative Assessment

Lesson Plans

M&Ms and Equivalent Expressions:

In this lesson, students use M&Ms and equation mats to explore the equivalency of pairs of expressions. Then they show pairs of expressions are equivalent using properties of operations. For those that are not equivalent, they provide a counterexample.

Type: Lesson Plan

Interpreting Algebraic Expressions:

This lesson unit is intended to help you assess how well students are able to translate between words, symbols, tables, and area representations of algebraic expressions. It will help you to identify and support students who have difficulty in recognizing the order of algebraic operations, recognizing equivalent expressions and understanding the distributive laws of multiplication and division over addition (expansion of parentheses).

Type: Lesson Plan

Have You Met Your Match?-Understanding Equivalent Expressions Using the Distributive Property:

In this lesson, students will use the properties of operations to generate and identify equivalent expressions. Students will apply their knowledge of the distributive property to an expression to produce equivalent expressions. The guided inquiry and hands-on memory "match" game will engage students and support student understanding of algebraic thinking.

Type: Lesson Plan

The Distributive Property:

Introductory lesson on the distributive property using word problems as context for area models.

Type: Lesson Plan

Original Student Tutorial

MacCoder's Farm Part 4: Repeat Loops:

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Problem-Solving Tasks

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

Type: Problem-Solving Task

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Type: Problem-Solving Task

Distance to School:

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Type: Problem-Solving Task

Equivalent Expressions:

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Type: Problem-Solving Task

Teaching Idea

True, False, and Open Sentences:

"Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions.

Type: Teaching Idea

Tutorials

Applying Arithmetic Properties with Negative Numbers:

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

Solving Equations with One Variable :

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

Unit/Lesson Sequence

Using the Laws of Arithmetic:

This lesson unit helps teachers assess how students perform arithmetic operations, write and evaluate numerical expression s from diagrammatic representations, apply the distributive and commutative properties, and find areas of compound rectangles. The time for the lesson is broken into a 15 minute pre-lesson task, an 80 minute lesson (or two 40 minute lessons), and a 15 minute follow up lesson or homework. Individual students will need a copy of the two tasks, a mini-whiteboard, a pen, and an eraser. Each small group will need cut-up copies of the card sets, a large sheet of poster-sized paper, and a glue stick.

Type: Unit/Lesson Sequence

Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative

MFAS Formative Assessments

Equivalent Exponents:

Students are asked to identify expressions equivalent to a given exponential expression and justify their responses.

Equivalent Expressions:

Students are asked to determine if pairs of expressions are equivalent and to justify their responses.

Identifying Equivalent Expressions:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Property Combinations:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Computer Science Original Student Tutorials

MacCoder's Farm Part 4: Repeat Loops:

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Student Resources

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

Original Student Tutorial

MacCoder's Farm Part 4: Repeat Loops:

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Problem-Solving Tasks

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

Type: Problem-Solving Task

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Type: Problem-Solving Task

Distance to School:

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Type: Problem-Solving Task

Equivalent Expressions:

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Type: Problem-Solving Task

Tutorials

Applying Arithmetic Properties with Negative Numbers:

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

Solving Equations with One Variable :

This Khan Academy presentation models solving two-step equations with one variable.

Type: Tutorial

Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative

Parent Resources

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

Problem-Solving Tasks

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

Type: Problem-Solving Task

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Type: Problem-Solving Task

Distance to School:

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Type: Problem-Solving Task

Equivalent Expressions:

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Type: Problem-Solving Task

Virtual Manipulative

Algebra Balance Scales - with Negatives:

This site provides a virtual balance on which the student can represent (and then solve) simple linear equations with integer answers. Conceptually, positive weights (unit-blocks and x-boxes) push the pans of the scale downward. Negative values are represented by balloons which can be attached to the pans of the scale. The student can then manipulate the weights to solve the equation while simultaneously seeing a visual display of these effects on the equation.

Type: Virtual Manipulative