Standard #: MAFS.6.EE.2.5 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



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
Grade: 6
Domain-Subdomain: Expressions & Equations
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 Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1

An equation is shown.

x + 5 = 14

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

 

N/A MC: Multiple Choice
Sample Item 2

An equation is shown.

begin mathsize 12px style 5 x space plus space 3 x space equals space 5 x space plus space 15 over 2 end style

What value of 3x makes the equation true?

N/A EE: Equation Editor
Sample Item 3

An inequality is shown.

begin mathsize 12px style 27 over 7 n space greater than space 4 over 3 end style

Select all the values of n that make the inequality true.

 

N/A MS: Multiselect
Sample Item 4

Select the values of x that make each equation or inequality true.

 

N/A MI: Matching Item


Related Courses

Course Number1111 Course Title222
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))


Related Resources

Educational Games

Name Description
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!

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.

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.

Formative Assessments

Name Description
Finding Solutions of Inequalities

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

Solutions of Inequalities

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

Solutions of Equations

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

Finding Solutions of Equations

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

Lesson Plans

Name Description
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.

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.

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.

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.

Original Student Tutorials

Name Description
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. 

Click here to open Part 1

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

Perspectives Video: Expert

Name Description
Improving Hurricane Scales

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

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Task

Name Description
Log Ride

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

Teaching Idea

Name Description
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.

Tutorials

Name Description
How to Test Solutions to Inequalities

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

How to Test Solutions to Equations Using Substitution

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

How to evaluate an expression with variables

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

Video/Audio/Animations

Name Description
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.

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.

Virtual Manipulative

Name Description
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.

Student Resources

Original Student Tutorials

Name Description
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. 

Click here to open Part 1

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

Educational Games

Name Description
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!

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.

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.

Problem-Solving Task

Name Description
Log Ride:

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

Tutorials

Name Description
How to Test Solutions to Inequalities:

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

How to Test Solutions to Equations Using Substitution:

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

How to evaluate an expression with variables:

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

Video/Audio/Animations

Name Description
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.

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.

Virtual Manipulative

Name Description
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.



Parent Resources

Problem-Solving Task

Name Description
Log Ride:

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



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