Grade
Unit name
Lesson #
9
Factoring and
simplifying
2
Subject
Lesson
Math
Simplifying rational expressions
Teacher
John F. Mahoney
CC Standards Algebra – Seeing Structure in Expressions (page 64 )
for
A-SSE.2 - Use the structure of an expression to identify ways to rewrite it
Mathematics Algebra – Arithmetic with Polynomials and Rational Expressions (page 65)
A-APR.6 - Rewrite simple rational expressions in different forms
Mathematical Practice Standards (page 6/7)
MP3 - Construct viable arguments and critique the reasoning of others
Mathematical Practice Standards (page 8)
MP7 - Look for and make use of structure
Unit Overview
Previous
lessons
This lesson
Next lessons
Lessons during the previous two weeks focused on factoring and solving
quadratic equations by factoring.
This lesson uses factoring to simplify rational expression through canceling
common factors (both arithmetic and algebraic) in the numerator and
denominator.
Identifying errors and focus on applications of simplification of rational
expressions – through geometric probability and “work” problems.
Lesson plan: Simplifying Rational Expressions
SECTION
Introduction
TIME
2
minutes
SHIFT
Conceptual
understanding
DETAIL
Read or state the objective:
Be able to simplify rational expressions
When stating the objective – ask students what
word is within “rational.” Hopefully, they’ll say
ratio.
Make connection between ratios and fractions Ratios can be written as fractions (of integers).
Note: When you divide an integer by an integer –
you don’t always get an integer. When we’ll
divide a polynomial by a polynomial – we won’t
always get a polynomial. Integers and
polynomials have similar properties.
Group work
–
investigation
13
minutes
Conceptual
understanding
Give each group a different set of problems – on
slips of paper. These papers are the Introductory
Problems.
Students work on Introductory Problems in
groups. Instruction to students:
Work with others in your group to determine
whether, for each problem, the solution is correct
or incorrect. If it is incorrect, identify the error and
write the correct solution.
Class
discussion
5-10
minutes
Conceptual
understanding
Rotate to support groups
Lead them to see that properties true for rational
#’s are true for rational expressions.
Project the problems (via the document camera)
and have each student in the class decide whether
particular problems are correct or not.
As an option, have them transmit their results via
the TI-Navigator (to assess how well they
understand the concepts).
Consolidatio
n
5
minutes
Conceptual
understanding
Discuss that anything divided by itself equals 1.
Are there exceptions? You can’t divide 0 by 0. [0
doesn’t have a multiplicative inverse.]
Is
16 x
x3
 1? Is
 1?
16 x
x3
Always? Lead them to see that properties true for
rational #’s are true for rational expressions.
Discuss that when you multiply a number by 1, it
stays the same.
Group work
10
minutes
Conceptual
understanding
Class
discussion
3
minutes
Conceptual
understanding
close
1 minute
Distribute and have students in groups work
through a series of “leading problems” involving
factoring and cancelling.
Review the results. Emphasize the difference
between terms and factors. Emphasize the risk of
dividing by 0.
Wrap up and set homework