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
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6.EE.B.7
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7.EE.B.4
Criteria for Success
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- Define and understand a solution to an equation as a number or numbers for a variable that make the equation a true statement.
- Use substitution to check and verify solutions to equations, simplifying first where relevant.
- 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.
Remote Learning Guidance
This lesson reviews concepts from 6th and 7th grades; Anchor Problems can be chosen based on what specific concept and/or skill review students need. Find more guidance on adapting our math curriculum for remote learning here.
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
References
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
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
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
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Algebra By Example 3.1 Solving 1 and 2 Step Equations
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EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3
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Exercises and Problem Set
Target Task
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Problem 1
Is $$8$$ a solution to $${\frac{1}{2}x+9=13}$$?
References
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
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
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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