Solving One-Variable Equations
Lesson 10
Objective
Use equations to model a business plan and determine the break-even point.
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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7.EE.B.4
Criteria for Success
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- De-contextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem (MP.2).
- Write and solve equations to represent a real-world business plan (MP.4).
Tips for Teachers
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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.
Remote Learning Guidance
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (can be done independently). This could be a good opportunity for students to work in small groups together. Find more guidance on adapting our math curriculum for remote learning here.
Anchor Problems
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Corey and Chloe 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 Chloe plan to sell each table for $10.
- Fill in the chart below for different numbers of tables sold at the school fair.
| # Tables Sold | Total Fixed Costs | Total Variable Costs | Total Costs | Money Earned from Sales | Total Profit or Loss |
- Write an equation to represent this situation. Explain what each part of your equation represents.
- How many tables do Corey and Chloe need to sell to break even?
- How many tables do Corey and Chloe need to sell to make a profit of $150?
Guiding Questions
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.
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EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 9
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Exercises 3-10, Problem Set 2-7
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EngageNY Mathematics Grade 8 Mathematics > Module 4
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Mid-Module Assessment (1-2)
- We Teach NYC Grade 8 Math: Expressions and Equations Unit — Performance Task (2-4)
Target Task
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Create your own business model, similar to Anchor Problem 1.
- What are you selling?
- What are your fixed costs? Your variable costs?
- How much will you sell each item for?
- How many do you need to sell to break even?
Show all of your work clearly and include an equation in your answer.
Mastery Response
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