Solving One-Variable Equations

Lesson 1

Objective

Write equivalent expressions using properties of operations and verify equivalence using substitution.

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.A.1

  • 6.EE.A.2

  • 6.EE.A.3

  • 7.EE.A.1

Criteria for Success

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  1. Write equivalent expressions by combining like terms.
  2. Write equivalent expressions by applying the properties of operations.
  3. Apply the distributive property with negatives.
  4. Write expressions for verbal descriptions.
  5. Verify that two algebraic expressions are equivalent by substituting in values for the variables and showing that they evaluate to the same number.

Tips for Teachers

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  • This lesson is approaching 8.EE.7 and reviews concepts and skills from 6th and 7th grades around writing and manipulating expressions. These concepts are foundational to this 8th grade unit, and will support students in later lessons.
  • The Problem Set Guidance includes several resources; pick and choose the most appropriate activities for your students depending on their needs.

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Anchor Problems

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Problem 1

  1. Find the sum of the two expressions.

Expression A: $${12a-5b-8}$$

Expression B: $${ -b+3a-4}$$

  1. Write the expression below as a sum of two terms.

$${\frac{1}{2}(6x+18)}$$

  1. Write the expression below as a product of two factors.

$${24m-6}$$

Guiding Questions

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Problem 2

For each expression, write an equivalent simplified expression. Then verify that the expressions are equivalent by substituting a value in for $${ x}$$ and evaluating.

Original Expression Simplified Expression Equivalent?
$$2+3(x+4)$$    
$$2+3(x-4)$$    
$$2-3(x+4)$$    
$$2-3(x-4)$$    

Guiding Questions

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Problem 3

Write an expression for the sequence of operations. Then simplify each expression.

  • Add 3 to $$x$$, subtract the result from 1, then double what you have.
  • Add 3 to $$x$$, double what you have, then subtract 1 from the result.

Guiding Questions

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References

Illustrative Mathematics Writing Expressions

Writing Expressions, accessed on Aug. 30, 2017, 4:17 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

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.

Target Task

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Problem 1

Simplify each expression.

a.     $${\frac{5}{3}x-4\left ( x-\frac{1}{3} \right )}$$

 

b.    $${-\frac{1}{2}\left ( -8x+6x+10 \right )-2x}$$

Problem 2

Are the two expressions equivalent? Justify your answer using substitution.

$${-5x+15}$$   and   $${5(-x+3)}$$

Mastery Response

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