Linear Expressions & Single-Variable Equations/Inequalities

Lesson 9

Math

Unit 3

9th Grade

Lesson 9 of 12

Objective


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

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.
  • 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.
  • 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.

Foundational Standards

  • 8.F.B.4

Criteria for Success


  1. Identify quantities, relationships, and constraints in a modeling context. 
  2. Determine and name assumptions about quantities, and use these estimations in the modeling of a contextual situation. 
  3. Assign variables and write algebraic expressions to model parts of a contextual situation. 
  4. Use expressions to model quantities of interest and substitute values to determine a reasonable solution. 
  5. Organize work and solution so thinking is transparent. 
  6. Justify model and conclusion based on relationships and assumptions from the contextual situation.

Tips for Teachers


  • In terms of pacing, this lesson can be extended for two days, with some additional practice from the unit incorporated into the daily plan.
  • This lesson is a culmination of the section on modeling that began with lesson 6.
  • The Anchor Problem also serves as the Target Task for this lesson.
  • There is no problem set for this lesson in order to allow class time to be devoted to the modeling task. Teachers may use problems or resources from prior lessons as review as needed. 
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


You are considering driving an ice cream van during the summer vacation. Your friend, who “knows everything,” tells you that “it’s easy money.” You know there is a lot to consider in doing this. Your plan is to only sell ice-cream cones, and in only one size. You also plan to rent the van. You have two choices: you can either go typical ice cream truck style and drive to several locations, park, and sell cones OR you can go food truck style and drive and park to sell cones for the day. 

Goal: Determine whether you should drive, park, and sell (option 1) or just park and sell (option 2) in order to yield a greater profit. 

  • The van costs $600/week to rent. 
  • Each ice-cream cone costs $0.50 to make (including cone and ice cream). 
  • You are planning on selling the cones for $1.50 each. 
  • You have 12 weeks during the summer that you are available to work. 
  • You cannot work more than 35 hours a week. 

There are two options for selling ice cream out of your van. 

Option 1: Typical Ice cream truck style: Drive, park, and sell… drive park sell 

  • Sell about 35 ice-cream cones per hour. 
  • Drive about 180 miles per week.
  • Cost of gas is about $0.13 per mile. 
  • Drive at an average speed of 20 miles per hour.

Option 2: Food truck style: Park and sell in one location 

  • Sell about 30 ice-cream cones per hour.
  • Seasonal permit for parking is $90. 
  • Space rental is $140 per week. 

Guiding Questions

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

References

Illustrative Mathematics Ice Cream Van

Ice Cream Van, accessed on Sept. 14, 2017, 1:50 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.
icon/arrow/right/large copy

Lesson 8

icon/arrow/right/large

Lesson 10

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

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free