Equations and Inequalities

Lesson 2

Objective

Define and identify solutions to equations.

Common Core Standards

Core Standards

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  • 6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Foundational Standards

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  • 6.EE.A.1

  • 6.EE.A.2

Criteria for Success

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  1. Define a solution to an equation as the value of the variable that, when substituted in, makes the equation a true statement.
  2. Use substitution to determine if a given value for a variable is a solution to an equation. 
  3. Make use of structure in expressions and equations to reason about the value of the variable (MP.7).

Tips for Teachers

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Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example) and Anchor Problem 2 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

Determine if the equations are true or false when the number given is used for the value of the variable. 

  1.   $${12x=84}$$; for when $${x=7}$$
  2.  $${y-10=50}$$; for when $${y=40}$$
  3.   $${{1\over2}m=16}$$; for when $${ m=32}$$
  4.   $${3(x-1)=27}$$; for when $${x=9}$$

Guiding Questions

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Problem 2

Which value of $$x$$ from the set below is the solution to the equation $$4x-14=38$$?

{6, 10, 12, 13, 15}

Guiding Questions

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Problem 3

Below are some equations that each contain a variable. A list of values is also shown. Think about what each equation means to find a solution in the list of values.

Guiding Questions

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References

Open Up Resources Grade 6 Unit 6 Lesson 22.3 “Using Structure to Find Solutions”

Grade 6 Unit 6 Lesson 2 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Feb. 27, 2018, 11:42 a.m..

Modified by The Match Foundation, Inc.

Problem Set

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Target Task

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Which equations below have a solution $${x=4}$$?

  1.   $${14-x=14}$$  
  2.   $${2x+5=9}$$
  3.   $${4x=1}$$
  4.   $${ 4x=16}$$
  5.   $${ 3x-2=10}$$
  6.   $${{1\over2}x=8}$$

Mastery Response

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