Curriculum / Math / 8th Grade / Unit 2: Solving One-Variable Equations / Lesson 10
Math
Unit 2
8th Grade
Lesson 10 of 12
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Use equations to model a business plan and determine the break-even point.
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
Suggestions for teachers to help them teach this lesson
There is only one Anchor Problem for this lesson, however, it is longer than usual. It can be done with the whole class, or students can tackle it in small groups. The Target Task has students create their own problem similar to the Anchor Problem. The Problem Set Guidance includes a variety of resources that involve real-world applications.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Corey and Akila are making small wooden tables to sell at the school fair. They have some fixed costs and some variable costs. The fixed costs come to $160 and include things that only need to be purchased once, like an electric saw, measuring tools, and a work station. The variable costs come to $3.50 for each table and include the wood, nails, and glue needed for each table. Corey and Akila plan to sell each table for $10.
a. Fill in the chart below for different numbers of tables sold at the school fair.
b. Write an equation to represent this situation. Explain what each part of your equation represents.
c. How many tables do Corey and Akila need to sell to break even?
d. How many tables do Corey and Akila need to sell to make a profit of $150?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Create your own business model, similar to Anchor Problem 1.
Show all of your work clearly and include an equation in your answer.
An example response to the Target Task at the level of detail expected of the students.
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 9
Lesson 11
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.
Write and solve multi-step equations to represent situations, including variables on both sides of the equation.
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.
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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