Unit 6: Rational Expressions and Functions
Algebra II
4 Weeks
Essential Questions
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Are two quantities inversely proportional if an increase in one corresponds to a decrease
in the other?
What kinds of asymptotes are possible for a rational function?
Are a rational expression and its simplified form equivalent?
Enduring Understandings
1. A rational function is a ratio of polynomial functions. If a rational function is in
simplified form and the polynomial in the denominator is not a constant, the graph of the
rational function features asymptotic behavior.
2. You can use much of what you know about multiplying and dividing fractions to multiply
and divide rational expressions.
3. To operate with rational expressions, you can use much of what you know about
operating with fractions.
4. When solving an equation involving rational expressions multiplying by the common
denominator can result in extraneous solutions.
Content
Students will know…
Topics (Pearson):
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(8-4) Rational Expressions
(8-5) Adding and Subtracting Rational Exp.
(8-6) Solving Rational Equations
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Rational expressions and complex
numbers
Expressions with like and unlike
denominators
Equations with rational coefficients
Fractional Equations
Concept of restricted value of a
variable
Extraneous solutions
Real world problems involving
fractional equations
Unit 6: Rational Expressions and Functions
Algebra II
4 Weeks
21st Learning Expectations
Students will be able to…
 Employ mathematical problem solving skills effectively.
 Make decisions and solve problems in independent and collaborative settings.
21st Century Learning Skills
Students will be able to…
 ML #1 – Make sense of problems and persevere in solving them.
 ML #2 – Reason abstractly and quantitatively.
 ML #3 – Construct viable arguments and critique the reasoning of others.
 ML #4 – Model with mathematics.
 ML #5 – Use appropriate tools strategically.
 ML #6 – Attend to precision.
Connecticut State Standards
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CC.9-12.A.REI.2 Solve simple rational and radical equations in one variable, and give
examples showing how extraneous solutions may arise.
CC.9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.*
CC.9-12.A.APR.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.
CC.9-12.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.
CC.9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve
problems. Include equations arising from linear and quadratic functions, and simple
rational and exponential functions.
CC.9-12.A.CED.3 Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a
modeling context. For example, represent inequalities describing nutritional and cost
constraints on combinations of different foods.
CC.9-12.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.*
CC.9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when
suitable factorizations are available, and showing end behavior.
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Unit 6: Rational Expressions and Functions
Algebra II
4 Weeks
Objectives
Students will be able to…
 Simplify rational expressions and complex fractions.
 Multiply and divide rational expressions.
 Add and subtract rational expressions with like and unlike denominators.
 Solve equations with rational coefficients.
 Solve fractional equations.
 Develop a concept of restricted values of a variable.
 Solve real world problems involving fractions.
Assessments
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Quiz EU1 – Simplifying Rational Expressions
Quiz EU2 – Multiplying and Dividing Rational Expressions
Quiz EU3 – Adding and Subtracting Rational Expressions
Quiz EU4 – Solving Equations Containing Rational Expressions
Unit Test – Rational Expressions and Equations
Resources
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Charles, R., Hall, B., Kennedy, D., Bass, L., Johnson, A., Murphy, S., et al. (2012).
Algebra 2: Common Core. Boston: Pearson.
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