# MAFS.6.EE.2.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
General Information
Subject Area: Mathematics
Domain-Subdomain: Expressions & Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Reason about and solve one-variable equations and inequalities. (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 of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Numbers in items must be nonnegative rational numbers. One-variable linear equations and inequalities. An equation or inequality should be given if a context is included. Inequalities are restricted to < or >. Lists of numbers should not use set notation.
• Calculator :

No

• Context :

Allowable

Sample Test Items (4)
• Test Item #: Sample Item 1
• Question:

An equation is shown.

x + 5 = 14

Which of the values can be substituted for x to make the equation true?

• Difficulty: N/A
• Type: MC: Multiple Choice

• Test Item #: Sample Item 2
• Question:

An equation is shown. What value of 3x makes the equation true?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question:

An inequality is shown. Select all the values of n that make the inequality true.

• Difficulty: N/A
• Type: MS: Multiselect

## 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.2.AP.5a: Evaluate whether both sides of an equation are equal using models.
MAFS.6.EE.2.AP.5b: Solve an equation using substitution.
MAFS.6.EE.2.AP.5c: Solve an inequality using substitution (e.g., given a budget, a student will select a number [specified set] to remain within budget).

## Related Resources

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

## Assessments

Sample 4 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 2 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## Educational Games

Solving Equations: Same Variable, Both Sides, One Solution:

In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. 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

Timed Algebra Quiz:

In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Algebra Four:

In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Educational Game

Number Puzzles:

This virtual manipulative poses problems requiring the students to position numbers in a diagram, so all numbers in a line add up to a given value.

Type: Educational Game

## Formative Assessments

Finding Solutions of Inequalities:

Students are given three inequalities and asked to determine if any numbers from a given set are solutions.

Type: Formative Assessment

Solutions of Inequalities:

Students are asked to explain what it means for a number to be a solution of an inequality.

Type: Formative Assessment

Solutions of Equations:

Students are asked to explain what it means for a number to be a solution of an equation.

Type: Formative Assessment

Finding Solutions of Equations:

Students are given three equations and asked to determine if any numbers from a given set are solutions.

Type: Formative Assessment

## Lesson Plans

Gather Data For Distribution by Programming an App:

This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet.

Type: Lesson Plan

Data Sets Represented in Computers:

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Type: Lesson Plan

How Much was Lunch?:

This lesson explores using substitution to solve one-step equations. Each real world problems involves discussion and students are expected to support their solutions.

Type: Lesson Plan

Solving One-Step Equations Using Mental Math:

In this lesson students will solve one-step equations using mental math and guess-and-check. Students will use number cubes to generate random numbers to test as solutions to the equations.

Type: Lesson Plan

Gummy vs. Gum (Number Pattern):

"In this lesson, students use gummy bears and sticks of gum to discover a number pattern and write an equation that describes it. This lesson should be conducted after students have worked with patterns and one- and two-step equations." from the Beacon Learning Center.

Type: Lesson Plan

## Original Student Tutorials

Dr. E. Quation Part 2: One Step Multiplication & Division Equations:

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials.  You'll also learn how to check your answers to make sure your answer is the solution to the equation.

Type: Original Student Tutorial

Dr. E. Quation Part 1: One Step Addition & Subtraction Equations:

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations

Type: Original Student Tutorial

## Perspectives Video: Expert

Improving Hurricane Scales:

Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale.

Type: Perspectives Video: Expert

Log Ride:

Students are asked to solve an inequality in order to answer a real-world question.

## 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

How to Test Solutions to Inequalities:

A solution to an inequality makes that inequality true. Learn how to test if a certain value of a variable makes an inequality true.

Type: Tutorial

How to Test Solutions to Equations Using Substitution:

A solution to an equation makes that equation true. Learn how to test if a certain value of a variable makes an equation true.

Type: Tutorial

Dependent and Independent Variables Exercise: The Basics:

In an equation with 2 variables, we will be able to determine which is the dependent variable, and which is the independent variable.

Type: Tutorial

How to evaluate an expression using substitution:

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

Type: Tutorial

How to evaluate an expression with variables:

Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").

Type: Tutorial

## Video/Audio/Animations

Why Do We Divide Both Sides?:

This short video provides a clear explanation why we perform the same steps on each side of an equation when solving for the variable/unknown.

Type: Video/Audio/Animation

Solving Simple Equations:

This short video provides a clear explanation about the "why" of performing the same steps on each side of an equation when solving for the variable/unknown.

Type: Video/Audio/Animation

## Virtual Manipulative

Pan Balance - Numbers:

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

Type: Virtual Manipulative

## MFAS Formative Assessments

Finding Solutions of Equations:

Students are given three equations and asked to determine if any numbers from a given set are solutions.

Finding Solutions of Inequalities:

Students are given three inequalities and asked to determine if any numbers from a given set are solutions.

Solutions of Equations:

Students are asked to explain what it means for a number to be a solution of an equation.

Solutions of Inequalities:

Students are asked to explain what it means for a number to be a solution of an inequality.

## Original Student Tutorials Mathematics - Grades 6-8

Dr. E. Quation Part 1: One Step Addition & Subtraction Equations:

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations

Dr. E. Quation Part 2: One Step Multiplication & Division Equations:

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials.  You'll also learn how to check your answers to make sure your answer is the solution to the equation.

## Student Resources

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

## Original Student Tutorials

Dr. E. Quation Part 2: One Step Multiplication & Division Equations:

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials.  You'll also learn how to check your answers to make sure your answer is the solution to the equation.

Type: Original Student Tutorial

Dr. E. Quation Part 1: One Step Addition & Subtraction Equations:

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations

Type: Original Student Tutorial

## Educational Games

Solving Equations: Same Variable, Both Sides, One Solution:

In this challenge game, you will be solving equations with variables on both sides. Each equation has a real solution. Use the "Teach Me" button to review content before the challenge. 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

Timed Algebra Quiz:

In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Algebra Four:

In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Educational Game

Number Puzzles:

This virtual manipulative poses problems requiring the students to position numbers in a diagram, so all numbers in a line add up to a given value.

Type: Educational Game

Log Ride:

Students are asked to solve an inequality in order to answer a real-world question.

## Tutorials

How to Test Solutions to Inequalities:

A solution to an inequality makes that inequality true. Learn how to test if a certain value of a variable makes an inequality true.

Type: Tutorial

How to Test Solutions to Equations Using Substitution:

A solution to an equation makes that equation true. Learn how to test if a certain value of a variable makes an equation true.

Type: Tutorial

Dependent and Independent Variables Exercise: The Basics:

In an equation with 2 variables, we will be able to determine which is the dependent variable, and which is the independent variable.

Type: Tutorial

How to evaluate an expression using substitution:

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

Type: Tutorial

How to evaluate an expression with variables:

Learn how to evaluate an expression with variables using a technique called substitution (or "plugging in").

Type: Tutorial

## Video/Audio/Animations

Why Do We Divide Both Sides?:

This short video provides a clear explanation why we perform the same steps on each side of an equation when solving for the variable/unknown.

Type: Video/Audio/Animation

Solving Simple Equations:

This short video provides a clear explanation about the "why" of performing the same steps on each side of an equation when solving for the variable/unknown.

Type: Video/Audio/Animation

## Virtual Manipulative

Pan Balance - Numbers:

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

Type: Virtual Manipulative

## Parent Resources

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

## Educational Game

Number Puzzles:

This virtual manipulative poses problems requiring the students to position numbers in a diagram, so all numbers in a line add up to a given value.

Type: Educational Game