Curriculum  /  Math  /  11th Grade  /  Unit 4: Rational and Radical Functions  /  Lesson 17

Rational and Radical Functions

Lesson 17

Math

Unit 4

11th Grade

Lesson 17 of 18

Objective

Write and solve rational functions for contextual situations.

Common Core Standards

Core Standards

  • A.APR.D.6 — Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  • 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.
  • 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.

Criteria for Success

  1. Identify expressions and equations that model real-life situations. 
  2. Solve and identify extraneous solutions in real-life situations. 
  3. Describe that a rational function used to model a situation is just an example of when you would divide two polynomials.

Tips for Teachers

  • Students may need extra time to practice work problems and need to review unit rates to be proficient at these concepts. 
  • These types of problems are often referred to as “Shared Work Problems” or “Work Rate Problems.” 
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Anchor Problems

Problem 1

Working together, it takes Sam, Jenna, and Francisco 2 hours to paint one room. When Sam is working alone, he can paint one room in 6 hours. When Jenna works alone, she can paint one room in 4 hours. Describe how long it would take Francisco to paint one room on his own. 

Guiding Questions

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References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 27 — Example 1

Algebra II > Module 1 > Topic C > Lesson 27 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Jamie and Ralph take a canoe trip up a river for 1 mile and then return. The current in the river is 1 mile per hour. The total trip time is 2 hours and 24 minutes. Assuming that they are paddling at a constant rate throughout the trip, find the speed that Jamie and Ralph are paddling. When Jamie and Ralph are paddling WITH the current (one way of their trip), their speed is $${x+1}$$. When Jamie and Ralph are paddling AGAINST the current (the other way of their trip), their speed is $${x-1}$$. 

Guiding Questions

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References

Illustrative Mathematics Canoe Trip

Canoe Trip, accessed on Nov. 19, 2017, 6:23 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.

Target Task

Bob can paint a fence in 5 hours, and working with Jen, the two of them painted the fence in 2 hours. How long would it have taken Jen to paint the fence alone? 

References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 27

Algebra II > Module 1 > Topic C > Lesson 27 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

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.

  • Include problems where students are given the scenario and an expression and asked to identify the meaning of the expression, including units. 
  • Include problems where most information is given in an equation and students need to supply the missing information from the context and explain reasoning. 
  • Include problems where there is a changing rate over the course of the context of the problem and an overall rate needs to be determined. 
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Lesson 16

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Lesson 18

Lesson Map

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

Topic A: Introduction to Rational and Radical Functions and Expressions

Topic B: Features of Rational Functions and Graphing Rational Functions

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

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