Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 4
Title: Rational Expressions and Equations
Subject: Algebra 2
Length of Time: 2 weeks
Unit Summary: The unit covers what a rational expression is and how to simplify it. The unit covers
adding, subtracting, multiplying, and dividing rational equations. Solving rational equations, variation and
graphing of rational equations will also be covered.
Learning Targets
Conceptual Category: Algebra Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Rewrite rational expressions
Standard#:
Standard:
A-APR.6
Rewrite simple rational expressions in different forms.
A-APR.7
Understand that rational expressions form a system analogous to the rational numbers,
closed under addition, subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.
Conceptual Category: Algebra Domain: Reasoning with Equations and Inequalities
Cluster: Understand solving equations as a process of reasoning and explain
the reasoning
Standard#:
Standard:
Explain each step in solving a simple equation as following from the equality of numbers
A-REI.1
asserted at the previous step, starting from the assumption that the original equation has a
solution. Construct a viable argument to justify a solution method.
Solve simple rational and radical equations in one variable, and give examples showing
A-REI.2
how extraneous solutions may arise.
Conceptual Category: Functions Domain: Interpreting Functions
Cluster: Analyze functions using different representations
F-IF.7
Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases
Unit Essential Question:
Unit Enduring Understandings:
 How are rational functions and their graphs similar
 Denominator cannot equal zero
to linear functions? How are they different?
 Zeros of the denominators create
discontinuities at those points for the function
at those values.
 To add or subtract rationals, need common
denominators.
 To solve a variation problem, need to find
constant of variation first.
 Solving a rational equation yields possible
solutions, substitute to check for extraneous
solutions.
Unit Objectives:
 Students will be able to simplify rational expressions.
 Students will be able to add, subtract, multiply, and divide rational expressions
 Students will be able to solve variation problems.


Students will be able to graph rational equations, identify asymptotes and removable discontinuities.
Students will be able to solve rational equations and identify solutions as feasible or extraneous.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 3 Quizzes
Summative Assessment:
 Unit Test
Lesson Plans
Topics
Timeframe (days)
Topic #1: Variation
Topic #2: Simplifying Rational Expressions
Quiz 1: Variation & Simplifying Rational
Expressions
Topic #3: Multiplying and Dividing Rational
Expressions
Topic #4: Adding and Subtracting Rational
Expressions
Quiz 2: Operations with Rational Expressions
Topic #5: Solving Rational Equations
Topic #6: Applications of Rational Equations
Topic #7: Graphing Rational Equations
Quiz 4: Solving & Graphing Rational Equations
Topic #8: Review and Unit Test
Curriculum Resources:
 www.njctl.org/courses/math/algebra2/
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