Curriculum  /  Math  /  9th Grade  /  Unit 3: Linear Expressions & Single-Variable Equations/Inequalities  /  Lesson 8

Linear Expressions & Single-Variable Equations/Inequalities

Lesson 8

Math

Unit 3

9th Grade

Lesson 8 of 12

Objective

Write and solve equations to represent contextual situations where estimations and unit conversions are required.

Common Core Standards

Core Standards

  • F.BF.A.1 — Write a function that describes a relationship between two quantities Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • A.CED.A.1 — Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • A.CED.A.2 — Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A.CED.A.4 — Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
  • N.Q.A.1 — Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  • F.IF.B.5 — Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.F.B.4

Criteria for Success

  1. Define variables and units from a contextual situation. 
  2. Identify unit conversions and incorporate unit conversions in the definition of the variable or the algebraic model. 
  3. Write expressions and equations to model contextual situations. 
  4. Use known quantities or estimated quantities to try the algebraic model developed and determine reasonability. 
  5. Rearrange equations used to model a relationship to highlight a quantity of interest. 
  6. Solve contextual problems and interpret solution in the context of a problem.

Tips for Teachers

  • The target task is a performance task and should have a significant amount of class time devoted to modeling and solving. The problem set guidance is intentionally limited due to the nature of the target task. 
  • Guidance and feedback should be provided on the performance task “Felicia’s Drive,” as the next lesson is the beginning of a two-lesson modeling task. 
  • This lesson provides an opportunity to norm students on expectations for the modeling task that will be completed in lesson 9.
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Anchor Problems

25-30 minutes

Problem 1

Define the variables and write a model to answer the question:

"How wide do parking spaces need to be?"

Guiding Questions

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

References

Desmos Central Park

Central Park by Desmos is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed Dec. 6, 2016, 2:02 p.m..

Problem 2

Last Sunday, an accident caused a traffic jam 12 miles long on a stretch of a two-lane freeway. Define the variables and write a model that describes the number of vehicles that could have been in the traffic jam.

Guiding Questions

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

References

Illustrative Mathematics Traffic Jam

Traffic Jam, accessed on Sept. 14, 2017, 1:31 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.

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

As Felicia gets on the freeway to drive to her cousin’s house, she notices that she is a little low on gas. There is a gas station at the exit she normally takes, and she wonders if she will have to get gas before then. She normally sets her cruise control at the speed limit of 70 mph, and the freeway portion of the drive takes about an hour and 15 minutes. Her car gets about 30 miles per gallon on the freeway, and gas costs $3.50 per gallon. 

  1. Write an equation that models the number of gallons Felicia needs to make it to the gas station at the other end. 
  2. Write an equation that models the amount of money Felicia spends per mile on the freeway.

References

Illustrative Mathematics Felicia's Drive

Felicia's Drive, accessed on Sept. 14, 2017, 1:33 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.

  • Desmos Central Park — Additional parking scenarios can be found in this Desmos activity.

Next

Model a contextual situation and make an informed decision based on the model.

Lesson 9
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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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