Linear Functions and Applications

Lesson 6

Math

Unit 1

11th Grade

Lesson 6 of 13

Objective


Write a system of functions for contextual situations and solve algebraically. Describe the solutions in context of the problem. 

Common Core Standards


Core Standards

  • 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.
  • 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.
  • A.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Foundational Standards

  • A.REI.A.1
  • A.REI.C.5

Criteria for Success


  1. Write a system of function for a contextual situation using function notation. 
  2. Identify domain restrictions of a function based on context. 
  3. Identify ways to algebraically manipulate equations to increase solving efficiency. 
  4. Validate the solution to a system of equations algebraically.
Fishtank Plus

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

Anchor Problems


Problem 1

What is the solution to the system of linear equations below? Prove your answer algebraically.  Validate your solution using the graphs on the coordinate plane. 

$${-2y=x + 8}$$

$${\frac{1}{3}(y - 6) = x - 1}$$

Guiding Questions

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

Problem 2

A construction contractor received two deliveries of building supplies from a lumberyard. The two deliveries included 10 boxes of nails, which cost a total of $110. 

  1. Write and solve an equation to determine $$n$$, the cost in dollars of one bo{x }of nails. 

The table below shows the numbers of sheets of plywood, trim boards, and boxes of nails delivered, and the total cost of each delivery. 

  1. Using your answers from part a and the information from the table, create a system of equations that can be used to determine $${x }$$, the cost in dollars of one sheet of plywood, and $$y$$, the cost in dollars of one trim board. 
  2. Determine the cost in dollars of one sheet of plywood and the cost in dollars of one trim board. Show or explain how you got your answer. 

The contractor has an additional $200 to spend. She tells her assistant to order at least 5 trim boards and as many sheets of plywood as possible with this money. 

  1. What is the maximum number of sheets of plywood that the assistant could order following the contractor’s instructions? Show or explain how you got your answer.

Guiding Questions

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

References

Massachusetts Department of Elementary and Secondary Education Grade 10 MathematicsQuestion #36

Grade 10 Mathematics is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed July 28, 2017, 10:57 a.m..

Target Task


Jerry was recently diagnosed with celiac disease. This means that he cannot eat any food containing gluten; in particular, he cannot eat pasta made from wheat. His mom has found a gluten-free pasta that he likes a lot. It is called Ancient Harvest Quinoa Pasta. 

The pasta company is not disclosing the percentage of each ingredient in the blend, but we know that the quinoa in the blend contains 16.2% protein, and the corn in the blend contains 3.5% protein. Overall, each 57-gram serving of pasta contains 4 grams of protein. How much quinoa and how much corn is in one serving of the pasta?

References

Illustrative Mathematics Quinoa Pasta 3

Quinoa Pasta 3, accessed on July 28, 2017, 11:11 a.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.

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.

icon/arrow/right/large copy

Lesson 5

icon/arrow/right/large

Lesson 7

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Linear Functions

Topic B: Systems of Functions and Constraints

Topic C: Piecewise Functions

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