Curriculum  /  Math  /  9th Grade  /  Unit 3: Linear Expressions & Single-Variable Equations/Inequalities  /  Lesson 2

Linear Expressions & Single-Variable Equations/Inequalities

Lesson 2

Math

Unit 3

9th Grade

Lesson 2 of 12

Objective

Use properties of equations to analyze and write equivalent equations.

Common Core Standards

Core Standards

  • A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Foundational Standards

  • 7.EE.A.1
  • 8.EE.C.7.A
  • 8.EE.C.7.B

Criteria for Success

  1. Describe how the value of a term or expression will change with respect to another to maintain an equality between both sides of the equal sign. 
  2. Formalize the saying “whatever you do to one side, you do to the other” as “(operation) property of equality.”
  3. Explain how the properties of operations are different from the properties of equality.
  4. Create equivalent equations using properties of operations and equality.

Tips for Teachers

This lesson covers key concepts in this unit—culminating work students did in 6th, 7th, and 8th grade to become proficient in solving equations. Ensure that students have adequate practice and extend this lesson to two days, as necessary.

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Anchor Problems

25-30 minutes

Problem 1

In equations (a)–(d) below, the solution, $$x$$, to the equation depends on the constant, $$a$$. Assuming $$a$$ is positive, what is the effect of increasing $$a$$ on the solution? Does it increase, decrease, or remain unchanged? 

Give a reason for your answer that can be understood without solving the equation. 

a.    $$x-a=0$$

b.    $$ax=1$$

c.    $$ax=a$$

d.    $$\frac{x}{a}=1$$

Guiding Questions

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References

Illustrative Mathematics How Does the Solution Change?

How Does the Solution Change?, accessed on Sept. 12, 2017, 3:48 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 2

Which of the following equations have the same solution(s)? Give reasons for your answer that do not depend on solving the equations. 

a.    $${x+3=5x-4}$$

b.    $${x-3=5x+4}$$

c.    $${2x+8=5x-3}$$

d.    $${10x+6=2x-8}$$

e.    $${10x-8=2x+6}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Same Solutions? — Parts a-e

Same Solutions?, accessed on Sept. 12, 2017, 3:51 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

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Explain how you know that Equation A is equivalent to Equation B without solving. 

 

Equation A:    $${ 10x-8=2x+6}$$


Equation B:    $${0.3+\frac{x}{10}=\frac{1}{2} x-0.4}$$

References

Illustrative Mathematics Same Solutions? — Parts e-f

Same Solutions?, accessed on Sept. 12, 2017, 3:51 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.

Modified by Fishtank Learning, Inc.

Additional Practice

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

  • Include problems that require students to work with fractions and decimals as constants, factors, and coefficients. 
  • Include problems where students are asked to multiply or divide each side of the equation by a fraction to create an equivalent equation. Include problems where a fraction coefficient is already present and students multiply by the reciprocal to create an equivalent equation.

Next

Solve single-variable linear equations using properties of equality.

Lesson 3
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations

Topic B: Modeling with Single-Variable Linear Equations

Topic C: Properties and Solutions of Single-Variable Linear Inequalities

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