Curriculum / Math / 8th Grade / Unit 2: Solving One-Variable Equations / Lesson 7
Math
Unit 2
8th Grade
Lesson 7 of 12
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Write and solve multi-step equations to represent situations, including variables on both sides of the equation.
The core standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
The foundational standards covered in this lesson
7.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
You have a coupon worth $18 off the purchase of a scientific calculator. At the same time, the calculator is offered with a discount of 15%, but no further discounts may be applied. For what tag price on the calculator do you pay the same amount for each discount?
Coupon versus Discount, accessed on Aug. 31, 2017, 2:12 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.
You and your brother go to the same store to buy fruit. You purchase a large watermelon for $7.71 and 2.4 pounds of red grapes. Your brother buys a platter of pre-cut fruit for $9.95 and 1.6 pounds of red grapes. The two of you spend the same amount of money. How much do the grapes cost per pound?
Solve the equations for the variable.
a. $${-4.2x+6-8.3x={1\over2}(-9x+4)}$$
b. $${{{5-x}\over8} = {{{1\over4}x-5}\over3}}$$
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Melanie is looking for a summer job. After a few interviews, she ends up with two job offers.
a. If Melanie plans to work 10 hours per week, which job offer should she take to maximize her earnings?
b. What if Melanie works 20 hours per week?
c. How many hours would Melanie need to work in order for the pay at each job to be the same? Write and solve an equation.
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.
Lesson 6
Lesson 8
Topic A: Simplifying Expressions and Verifying Solutions
Write equivalent expressions using properties of operations and verify equivalence using substitution.
8.EE.C.7
Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.
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Topic B: Analyzing and Solving Equations in One Variable
Justify each step in solving a multi-step equation with variables on one side of the equation.
8.EE.C.7.A 8.EE.C.7.B
Write and solve multi-step equations to represent situations, with variables on one side of the equation.
8.EE.C.7.B
Model with equations using a three-act task.
Solve equations with variables on both sides of the equal sign.
Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.
8.EE.C.7.A
Solve and reason with equations with three types of solutions.
Use equations to model a business plan and determine the break-even point.
Topic C: Analyzing and Solving Inequalities in One Variable
Solve and graph inequalities with variables on one side of the inequality (optional).
A.REI.B.3
Solve and graph inequalities with variables on both sides of the inequality (optional).
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