# MAFS.6.EE.2.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.

### Clarifications

Examples of Opportunities for In-Depth Focus

When students write equations of the form x + p = q and px = q to solve real-world and mathematical problems, they draw on meanings of operations that they are familiar with from previous grades’ work. They also begin to learn algebraic approaches to solving problems.16

16 For example, suppose Daniel went to visit his grandmother, who gave him \$5.50. Then he bought a book costing \$9.20 and had \$2.30 left. To find how much money he had before visiting his grandmother, an algebraic approach leads to the equation x + 5.50 – 9.20 = 2.30. An arithmetic approach without using variables at all would be to begin with 2.30, then add 9.20, then subtract 5.50. This yields the desired answer, but students will eventually encounter problems in which arithmetic approaches are unrealistically difficult and algebraic approaches must be used.
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 should not require students to perform operations with negative rational numbers or result in answers with negative rational numbers. Items must be one-step linear equations with one variable.
• Calculator :

No

• Context :

Allowable

Sample Test Items (3)

• Test Item #: Sample Item 2
• Question: Suzie buys a salad for \$5.12 and is given \$14.88 as change.

Which equation represents the situation if ???? is the amount Suzie had before she bought the salad?

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

• Test Item #: Sample Item 3
• Question:

This question has two parts.

Syrilla sells homemade scarves for \$4 each.

Part A. Which equation could be used to find the number of scarves, x, Syrilla needs to sell in order to earn \$200?

Part B. How many scarves does Syrilla need to sell?

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

## 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.7a: Solve problems or word problems using equations for cases in which the quantities in the problem are positive rational numbers.
MAFS.6.EE.2.AP.7b: Solve real-world, single-step linear equations involving positive rational numbers.

## 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 3 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## Formative Assessments

Equally Driven:

Students are asked to solve a real-world problem by writing and solving an equation.

Type: Formative Assessment

Center Section:

Students are asked to solve a real-world problem by writing and solving an equation.

Type: Formative Assessment

Solar Solutions:

Students are asked to solve a real-world problem by writing and solving an equation.

Type: Formative Assessment

University Parking:

Students are asked to solve a real-world problem by writing and solving an equation.

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

Going The Distance:

This lesson provides a hands-on activity where students can apply solving one-step multiplication and division equations to a real-world problem. The lesson focuses on the relationship between distance, rate, and time. The students will also represent data on graphs and draw conclusions and make interpretations based on the graphs.

Type: Lesson Plan

Writing and Solving Equations From Real World Problems:

In this lesson, students will learn to write equations for given real world problems. They will eventually write their own problem, write the equation, then solve it.

Type: Lesson Plan

Solving Equations with Beans:

Students will use dried white and black beans to solve one-step equations with integer operations.

Type: Lesson Plan

Equations with a Deck of Cards:

In this lesson, students learn about solving one- and two-step equations as well as how to use an equation to model information from a word problem. Students will play Lowest Wins, a game played with normal playing cards that challenges students to set up equations from the cards they have been dealt that will give them the lowest solution possible.

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

Bake Sale:

This lesson challenges student to develop and solve equations for mathematical and real world situations. Students will be encouraged to use the work backwards strategy using inverse operations to find a solution.

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

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

Anna in D.C.:

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

How to Solve Equations of the Form ax = b:

Here's an introduction to basic algebraic equations of the form ax = b. Remember that you can check to see if you have the right answer by substituting it for the variable!

Type: Tutorial

How to Solve One-Step Multiplication and Division Equations with Fractions and Decimals:

Learn how to solve equations in one step by multiplying or dividing a number on both sides. These problems involve decimals and fractions.

Type: Tutorial

How to Represent a Relationship with a Simple Equation:

This video demonstrates how to write and solve a one-step addition equation.

Type: Tutorial

Solving One-Step Equations Using Division:

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation.

Type: Tutorial

Why to Divide on both Sides of an Equation:

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.

Type: Tutorial

Linear Equations in One Variable:

This lesson introduces students to linear equations in one variable, shows how to solve them using addition, subtraction, multiplication, and division properties of equalities, and allows students to determine if a value is a solution, if there are infinitely many solutions, or no solution at all. The site contains an explanation of equations and linear equations, how to solve equations in general, and a strategy for solving linear equations. The lesson also explains contradiction (an equation with no solution) and identity (an equation with infinite solutions). There are five practice problems at the end for students to test their knowledge with links to answers and explanations of how those answers were found. Additional resources are also referenced.

Type: Tutorial

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

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

Algebra Balance Scales-Negatives:

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and x-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative

## MFAS Formative Assessments

Center Section:

Students are asked to solve a real-world problem by writing and solving an equation.

Equally Driven:

Students are asked to solve a real-world problem by writing and solving an equation.

Solar Solutions:

Students are asked to solve a real-world problem by writing and solving an equation.

University Parking:

Students are asked to solve a real-world problem by writing and solving an equation.

## Original Student Tutorials Science - Grades K-8

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

## 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

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

Anna in D.C.:

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

How to Solve Equations of the Form ax = b:

Here's an introduction to basic algebraic equations of the form ax = b. Remember that you can check to see if you have the right answer by substituting it for the variable!

Type: Tutorial

How to Solve One-Step Multiplication and Division Equations with Fractions and Decimals:

Learn how to solve equations in one step by multiplying or dividing a number on both sides. These problems involve decimals and fractions.

Type: Tutorial

How to Represent a Relationship with a Simple Equation:

This video demonstrates how to write and solve a one-step addition equation.

Type: Tutorial

Solving One-Step Equations Using Division:

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation.

Type: Tutorial

Why to Divide on both Sides of an Equation:

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.

Type: Tutorial

Linear Equations in One Variable:

This lesson introduces students to linear equations in one variable, shows how to solve them using addition, subtraction, multiplication, and division properties of equalities, and allows students to determine if a value is a solution, if there are infinitely many solutions, or no solution at all. The site contains an explanation of equations and linear equations, how to solve equations in general, and a strategy for solving linear equations. The lesson also explains contradiction (an equation with no solution) and identity (an equation with infinite solutions). There are five practice problems at the end for students to test their knowledge with links to answers and explanations of how those answers were found. Additional resources are also referenced.

Type: Tutorial

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

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

Algebra Balance Scales-Negatives:

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and x-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative

## Parent Resources

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

Anna in D.C.:

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

## Tutorials

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Simple Equations:

Introduction to solving one variable multiplication equations of the form px = q.

Type: Tutorial

## Virtual Manipulative

Algebra Balance Scales-Negatives:

This virtual manipulative allows the learners to solve simple linear equations through the use of a balance beam. Unit blocks and x-boxes are placed on the pans of a balance beam to balance it.

Type: Virtual Manipulative