Solving One-Variable Equations

Lesson 2

Objective

Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.

Common Core Standards

Core Standards

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  • 8.EE.C.7 — Solve linear equations in one variable.

Foundational Standards

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  • 6.EE.B.5

  • 6.EE.B.7

  • 7.EE.B.4

Criteria for Success

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  1. Define and understand a solution to an equation as a number or numbers for a variable that make the equation a true statement.
  2. Use substitution to check and verify solutions to equations, simplifying first where relevant.
  3. Use inverse operations to solve 1 and 2 step equations with rational numbers.

Tips for Teachers

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  • This lesson is approaching 8.EE.7. Students should have a firm grasp on solving 1 and 2 step equations by the end of 7th grade. If needed, review concepts around solving equations in this lesson so students are prepared to solve and model with multi-step equations in upcoming lessons. 
  • The idea of “solution” is something that students will develop and build on over the course of this year. In this unit, they study solutions as they relate to single-variable equations. They will revisit solutions when they study linear equations in two variables, and then again as they relate to systems of equations.

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Anchor Problems

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Problem 1

Given the equation $${4+15x=49}$$,

a.    Is $${x=2}$$ a solution to the equation?

b.    Is $${x=3}$$ a solution to the equation?

Determine your answers without solving the equation.

Guiding Questions

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Example 1

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Determine if $${-\frac{1}{2}}$$ is a solution to the equation $${-2x+8+6x=-4(x-1)}$$.

Guiding Questions

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Problem 3

Solve each equation. Then check your solution to confirm it is correct.

a.    $${\frac{4}{3}-m= \frac{5}{3}}$$

b.    $${-(11-p)=-20}$$

c.    $${6.8=-5.4+2n}$$

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Procedural practice solving 1 and 2 step equations with rational numbers

Target Task

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Problem 1

Is $$8$$ a solution to $${\frac{1}{2}x+9=13}$$?

References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Exit Ticket

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Write 2 different equations that have $${x=5}$$ as a solution.

References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Exit Ticket

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 3

Is $${-3}$$ a solution to the equation $${3x-5=4+2x}$$? Explain.

References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Exit Ticket

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Mastery Response

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