Standard 2: Write and solve equations and inequalities in one variable.

General Information
Number: MA.7.AR.2
Title: Write and solve equations and inequalities in one variable.
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.7.AR.2.AP.1
Select a one-step inequality from a list that represents a real-world situation and given a set of three or fewer values, use substitution to solve.
MA.7.AR.2.AP.2a
Set up two-step equations in one variable based on real-world problems.
MA.7.AR.2.AP.2b
Solve two-step equations in one variable based on real-world problems, where all terms have positive integer coefficients.

Related Resources

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

Formative Assessments

Solve Equations:

Students are asked to solve two equations involving rational numbers.

Type: Formative Assessment

Write and Solve an Equation:

Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario.

Type: Formative Assessment

Squares:

Students are asked to write and solve an equation of the form p(x + q) = r in the context of a problem about the perimeter of a square.

Type: Formative Assessment

Algebra or Arithmetic?:

Students are asked to compare an arithmetic solution to an algebraic solution of a word problem.

Type: Formative Assessment

Lesson Plans

A Florida Vacation:

Students will calculate sales tax to plan a family vacation budget. Through collaborative learning activities and discussions, students will understand the concept of sales tax as a civic responsibility and recognize the importance of considering sales tax in their financial planning to contribute to their community’s public service and infrastructure in this integrated lesson plan.

Type: Lesson Plan

Debugging the Electoral College-Lesson 3:

This is the final lesson in a 3-lesson unit. In this lesson, students will review the Electoral College by debugging and improving upon a Scratch simulation of a presidential election map. Students will also apply their knowledge of variables and inequalities through the debugging process.

Type: Lesson Plan

Debugging the Electoral College-Lesson 2:

This is lesson 2 of a 3-lesson unit. In this lesson, students learn about how variables and inequalities are used in both math and computer science through the exploration of how a win/loss is calculated in an Electoral College model/simulator.

Type: Lesson Plan

How Will the Ninja Capture the Valuable Princess?:

This lesson allows students to solve two-step equations involving a mythological story line in which the princess (variable) is protected by a bodyguard (number added or subtracted in an equation) and by a protector (number multiplied or divided by the variable). The three characters live in a castle, surrounded by the moat (equal sign) and an innocent bystander that lives outside the castle (number on the opposite side of the variable). However, Ninjas are infiltrating the castle to steal the “valuable” princess. Using this story line, students must then decide who the Ninja must eliminate first to get to the princess. This lesson can also be used to solve equations with like terms on the same side and equations with the same variable on each side.

Type: Lesson Plan

Lost in Translation? Verbal and Algebraic Representations of Expressions and Equations:

This lesson is designed to assist in teacher facilitation of student understanding related to the concept of translating between verbal and algebraic two-step equations.

Type: Lesson Plan

Company Charges:

In this lesson, students will learn how to write and solve linear equations that have one solution, infinitely many solutions, and no solutions. As the students decipher word problems, they will recognize which elements of equations affect the number of possible solutions. This lesson is guided by a PowerPoint presentation.

Type: Lesson Plan

Relating Surface Area and Volume:

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Type: Lesson Plan

Original Student Tutorials

Professor E. Qual Part 2: Two-Step Equations & Rational Numbers:

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.

Type: Original Student Tutorial

Professor E. Qual Part 1: 2 Step Equations:

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.

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

Perspectives Video: Experts

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

Water Flow Modeling for Archeology Research:

<p>Submerge yourself in math as a hydrogeologist describes calculations used to investigate water flow questions related to ancient shell rings.</p>

Type: Perspectives Video: Expert

Perspectives Video: Teaching Ideas

Solving Equations using Zero Pairs:

Unlock an effective teaching strategy for teaching solving equations using zero pairs in this Teacher Perspectives video for educators.

Type: 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

Guess My Number:

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Baseball Cards:

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

Tutorials

Basic Linear Equation Word Problem:

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

Multiplying and Dividing Inequalities :

The video will solve the inequality and graph the solution.

Type: Tutorial

Video/Audio/Animations

Solving Motion Problems with Linear Equations:

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Note: This video exceeds basic expectations for the mathematical concept(s) at this grade level. The video is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extension of the mathematical concept(s). As with all materials, ensure to gauge the readiness of students or adapt according to student's needs prior to administration.

Type: Video/Audio/Animation

Solving Problems with Linear Equations:

The video explains the process of creating linear equations to solve real-world problems.

Type: Video/Audio/Animation

Student Resources

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

Original Student Tutorials

Professor E. Qual Part 2: Two-Step Equations & Rational Numbers:

Practice solving and checking two-step equations with rational numbers in this interactive tutorial.

This is part 2 of the two-part series on two-step equations. Click HERE to open Part 1.

Type: Original Student Tutorial

Professor E. Qual Part 1: 2 Step Equations:

Professor E. Qual will teach you how to solve and check two-step equations in this interactive tutorial.

This is part 1 of a two-part series about solving 2-step equations. Click HERE to open Part 2.

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

Guess My Number:

This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

Tutorials

Basic Linear Equation Word Problem:

This video shows how to construct and solve a basic linear equation to solve a word problem.

Type: Tutorial

Multiplying and Dividing Inequalities :

The video will solve the inequality and graph the solution.

Type: Tutorial

Video/Audio/Animations

Solving Motion Problems with Linear Equations:

Based upon the definition of speed, linear equations can be created which allow us to solve problems involving constant speeds, time, and distance.

Note: This video exceeds basic expectations for the mathematical concept(s) at this grade level. The video is intended for students who have demonstrated mastery within the scope of instruction who may be ready for a more rigorous extension of the mathematical concept(s). As with all materials, ensure to gauge the readiness of students or adapt according to student's needs prior to administration.

Type: Video/Audio/Animation

Solving Problems with Linear Equations:

The video explains the process of creating linear equations to solve real-world problems.

Type: Video/Audio/Animation

Parent Resources

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