Solving Rational Functions Lesson Seed
Understand solving equations as a process of reasoning and explain the reasoning.
A.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
MP1: Make sense of problems and persevere in solving them.
MP6: Attend to precision.
MP8: Look for and express regularity in repeated reasoning.
Common Core Algebra II, Unit 5
Teacher’s Notes:
This lesson seed provides potential activities to practice solving rational equations algebraically using
cross-multiplying. If time allows, introduce solving rational equations that involve addition and
subtraction.
Warm-Up:
Have students choose a partner, or assign partners. Have students watch the YouTube video on fractions
and proportions. (http://www.youtube.com/watch?v=fDty_2CjYhE) (Note: This is a review for students
but is an essential skill to be able to solve rational equations. The students should feel free to watch all of
the video or watch only the parts of the video they might need. The video should be available to the
students throughout the activity for the students to refer to as needed.)
Lesson Task/Activity:
1. Have pairs brainstorm a method to solve
x
1
 . Facilitate a class discussion on extending
x 2 4
cross-multiplying to rational functions. Discuss the importance of checking the validity of a
solution and the possibility of extraneous solutions. (Look for evidence of MP1.)
2. If students need extra reinforcement, have students watch the YouTube video on solving rational

functions (http://www.youtube.com/watch?v=F7bHF7zRwYg).
(Note: The students should feel
free to watch all of the video or watch only the parts of the video they might need. The video
should be available to the students throughout the activity for the students to refer to as needed.)
3. Have students complete the MathO practice problems. (Look for evidence of MP6 and MP8.)
4. If time allows, play one round of MathO.
Closure:
As an exit ticket, have students write a question that they would like to have answered during the next
class.
Homework:
The average hourly wage H(x) of workers in an industry is modeled by the function
H ( x) 
16.24 x
0.062 x  39.42
where 𝑥 represents the number of years since 1970.
a) In what year does the model predict that wages will be $25 per hour?
b) Is the prediction reasonable? Explain your answer.