# Solving One-Variable Equations

Students hone their skills of solving multi-step equations and inequalities, redefining their definition of "solution" to include cases such as infinite solutions, and interpreting solutions in context.

Math

Unit 2

## Unit Summary

In Unit 2, 8th grade students hone their skills of solving equations and inequalities. They encounter complex-looking, multi-step equations, and they discover that by using properties of operations and combining like terms, these equations boil down to simple one- and two-step equations. Students also discover that there are many different ways to approach solving a multi-step equation, and they spend time closely looking at their own work and the work of their peers. When solving an equation with variables on both sides of the equal sign, students are challenged with results such as 4=5, and they refine their definition of “solution” to take into account such examples. Throughout this unit, students use equations as models to capture real-world applications. They reason abstractly and quantitatively as they de-contextualize situations to represent them with symbols and then re-contextualize the numbers to make sense in context (MP.2).

In 6th grade, students developed the conceptual understanding of how the components of expressions and equations work. They learned how the distributive property can create equivalent forms of an expression and how combining like terms can turn an expression with three terms into an expression with one term. By the end of 7th grade, students fluently solved one- and two-step equations with rational numbers and used equations and inequalities to represent and solve word problems.

Students’ ability to manipulate and transform equations will be required again in Unit 5 and Unit 6. Furthermore, these skills will be needed throughout high school as students are introduced to new types of equations involving radicals, exponents, multiple variables, and more.

Pacing: 16 instructional days (12 lessons, 3 flex days, 1 assessment day)

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## Assessment

The following assessments accompany Unit 2.

### Pre-Unit

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

### Mid-Unit

Have students complete the Mid-Unit Assessment after lesson 7.

### Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

## Unit Prep

### Intellectual Prep

Unit Launch

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

#### Internalization of Standards via the Post-Unit Assessment

• Take the Post-Unit Assessment. Annotate for:
• Standards that each question aligns to
• Strategies and representations used in daily lessons
• Relationship to Essential Understandings of unit
• Lesson(s) that Assessment points to

#### Internalization of Trajectory of Unit

• Read and annotate the Unit Summary.
• Notice the progression of concepts through the unit using the Lesson Map.
• Essential Understandings
• Connection to Post-Unit Assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

### Essential Understandings

• Solving an equation or inequality involves changing the equation into equivalent, simpler forms in order to reveal possible values for the variable.
• Solving an equation or inequality involves using properties of operations, combining like terms, and using inverse operations.
• An equation in one-variable may have a unique solution for the variable, no possible solutions for the variable, or all possible values may be solutions for the variable.

### Vocabulary

break even

combine like terms

distribute a negative

distributive property

equation

expression

infinite solutions

inequality

no solution

properties of operations

solution

term

unique solution

To see all the vocabulary for Unit 2, view our 8th Grade Vocabulary Glossary.

### Materials

• Calculators (1 per student)

To see all the materials needed for this course, view our 8th Grade Course Material Overview.

## Lesson Map

Topic A: Simplifying Expressions and Verifying Solutions

Topic B: Analyzing and Solving Equations in One Variable

Topic C: Analyzing and Solving Inequalities in One Variable

## Common Core Standards

Key

Major Cluster

Supporting Cluster

### Core Standards

#### Expressions and Equations

• 8.EE.C.7 — Solve linear equations in one variable.
• 8.EE.C.7.A — Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
• 8.EE.C.7.B — Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

#### Reasoning with Equations and Inequalities

• A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

• 6.EE.A.2
• 6.EE.A.3
• 6.EE.B.5
• 6.EE.B.7
• 7.EE.A.1
• 7.EE.B.4
• 7.EE.B.4.A
• 7.EE.B.4.B

• A.CED.A.1
• A.CED.A.3
• A.CED.A.4

• 8.EE.C.8

• A.REI.A.1
• A.REI.B.3

### Standards for Mathematical Practice

• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

• CCSS.MATH.PRACTICE.MP6 — Attend to precision.

• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Unit 1

Exponents and Scientific Notation

Unit 3

Transformations and Angle Relationships

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