Solving One-Variable Equations

Lesson 4

Math

Unit 2

8th Grade

Lesson 4 of 12

Objective


Write and solve multi-step equations to represent situations, with variables on one side of the equation.

Common Core Standards


Core Standards

  • 8.EE.C.7.B — Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Foundational Standards

  • 7.EE.B.4

Criteria for Success


  1. Write expressions for unknowns in terms of other unknowns.
  2. Use expressions and equations to model situations with unknowns.
  3. Decontextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem (MP.2).

Tips for Teachers


  • There are various applications that can be modeled and solved with multi-step equations. This lesson covers a variety of examples including ages, money, geometry applications, consecutive integers, etc. It is more important for students to develop general strategies for tackling problems like these, rather than mastering specific examples (MP.4).
  • In terms of pacing, this lesson may be split over more than one day.

Lesson Materials

  • Calculators (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?

Guiding Questions

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Student Response

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Problem 2

After collecting coins for a month, you count them to see how much money you have. You determine that you have 12 fewer quarters than you have nickels, and you have twice as many dimes as you have quarters. Altogether, the dimes, nickels, and quarters add up to $10.60. How many of each coin do you have?

Guiding Questions

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Student Response

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Problem 3

Todd and Jason are brothers. Todd says, “I am twice as old as Jason was two years ago.” The sum of the brother’s ages is 38. How old is each brother?

Guiding Questions

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Student Response

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Problem 4

Solve the equations.

a.   $${{{2(x-4)}\over9}={{3-7}\over6}}$$

b.   $${x-0.8(3x)+14.12=0.75(8)}$$

Guiding Questions

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Student Response

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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


Problem 1

The average household uses 1400kWh of electricity per month. In one household, air conditioning uses 300kWh per month. Twice as much electricity is used to heat water as to run a refrigerator. 50% of total electricity used goes to miscellaneous uses (like lighting, dishwashers, and TVs). 

Assuming this household uses the average amount of electricity per month, how much electricity is used to heat water per month?

Student Response

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Problem 2

School uniform shirts normally cost $15 each but are on sale for 30% off the original price. You also have a coupon for $10 off the cost before you take the percent discount. If you have $150 to spend, which of the following equations will help you to determine how many shirts, $$x$$, you can buy?

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Student Response

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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.

  • Additional procedural practice with solving multi-step equations with variables on one side of the equation 
  • Include consecutive integer problems and applications with percents

Next

Model with equations using a three-act task.

Lesson 5
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Lesson Map

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

Topic A: Simplifying Expressions and Verifying Solutions

Topic B: Analyzing and Solving Equations in One Variable

Topic C: Analyzing and Solving Inequalities in One Variable

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