Unit Map for Algebra 2/Trigonometry
2015 – 2016
Felisa Rincon de Gautier Institute for Law
and Public Policy
Timeframe: 7-10 days
Math Department
Mr. Balkaran
Unit 5: Rational Expressions & Equations
Number of lessons in this unit: 6
Learning Outcomes
Common Core Learning Standards addressed in this Unit: A-SSE.2, A-APR.6, A-APR.7(+), A-CED.1, A-REI.2
NYS 2005 Algebra 2 Core Curriculum standards addressed in this Unit: A2.A.5, A2.A.16, A2.A.17, A2.A.23
Standards for Mathematical Practices addressed in this Unit:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
6. Attend to precision.
7. Look for and make use of structure.
Enduring Understandings for this Unit:
Rational expressions are ratios of two polynomials, and when solving
rational equations, extraneous roots can occur as a result of variable
expressions in the denominator in the original equation. Direct and
indirect relationships can be used to model many real world situations.
Content of this Unit:
- Rational expressions
- Rational equations
- Extraneous roots
- Direct variation
- Inverse variation
Essential Questions for this Unit:
- What makes an expression or equation “rational”?
- When should a rational expression or equation?
- How are direct and inverse variations related, and how can they
be used to model real world scenarios?
Skills of this Unit:
- Manipulate and simplify rational expressions containing numbers, variables, and/or other
ratios
- Perform arithmetic operations between two rational expressions and simplify the result
- Solve rational equations and properly identify extraneous roots
- Model real world scenarios with direct and inverse variation
- Assess from a given context if direct or inverse variation, or neither, is appropriate
- Solve problems involving direct and inverse variation
Key Vocabulary & Language of this Unit:
Resources used in this Unit:
Rational expression/equation/fraction, undefined, inverse variation, direct - JMAP.org Resources for each Standard
variation, varies directly/inversely, extraneous root, constant of
- TI Smartview
proportionality
- Regents Reference table
Assessments
Formative Assessments:
- Math sprints with trade-and-grade
- Mini dry erase boards
- Daily exit slips
- Pair, group, and class discussions
- Homework assignments
- Writing prompts/journaling
- Quizzes
- Peer- and self-assessments
- Results and observations from daily learning activities
- Summaries
- Questioning
- Warm up collection and review
Summative Assessments, including Performance Tasks:
- Unit Performance Task
- Unit Exam
Instructional Pathway
Learning Activities & Teaching Strategies Used in This Unit
Standards Aim
A-SSE.2
1. What are rational
A-APR.6
expressions and how
A2.A.16
are they simplified?
Lesson Content
- Determine when a rational expression is
undefined (review)
- Simplify rational expressions to lowest
Grouping Structures
(I) = individual
(P) = with a partner
(G) = in a student group
(C) = whole class
Activities & Strategies
-
-
A-SSE.2
A-APR.6
A-APR.7
A2.A.16
2. How do we add and
subtract rational
expressions?
A-SSE.2
A-APR.6
A-APR.7
A2.A.16
3. How do we multiply
and divide rational
expressions?
A-SSE.2
A-APR.6
A2.A.17
4. What strategies exist
for simplifying more
complex rational
fractions?
-
-
-
-
A-REI.2
A2.A.23
5. How do we solve
rational equations?
-
terms and understand the process for
doing so, including mixed methods of
factoring polynomials
Assess whether a rational expression is
in its most simplified form
Include additive inverses, such as
(x – 3) and (3 – x)
Highlight vocabulary related to
simplifying, such as “in simplest form”
and “is equivalent to”
Vocabulary for graphical word wall:
rational expression/fraction, undefined
(review)
Add and subtract two or three rational
fractions that have binomials and
monomials in the denominators
Include additive inverses
Multiply and divide two or three
rational fractions that have trinomials,
binomials, and monomials in the
denominators
Include additive inverses
Simplify rational expressions that
contain one or more fractions with like
and unlike denominators in the
expression’s numerator and/or
denominator
Highlight vocabulary related to
simplifying (review)
Include real world problems in which
rational equations can be used to model
Solve rational equations that have one,
two, or no real solutions, potentially
impacted by the existence of extraneous
roots; test for extraneous roots
Include equations that have both
rational (integer and fractions) and
irrational (in simplest radical form)
solutions
-
-
-
-
-
-
A-CED.1
A2.A.5
6. How can direct and
inverse variation be
used to model and
solve real world
problems?
-
-
-
Include real world problems in which
rational equations can be used to model
Vocabulary for graphical word wall:
extraneous root
Assess whether a given graph, equation,
table, or set of points represents a direct
or inverse variation (or neither)
Determine the constant of
proportionality for a direct/inverse
variation
Given a graph, equation, table, or
situation that models a direct/inverse
variation, determine an unknown value
Given one point (x = 12 when y = 3)
and the nature of the variation (e.g. x
varies inversely as y), determine
another ordered pair
Vocabulary for graphical word wall:
inverse/direct variation, varies
directly/inversely, constant of
proportionality
-
RWC/C(physics, engineering): Direct:
Newton’s Second Law (F = ma), Ohm’s Law
(V = IR); inverse: relationship between
frequency and wavelength of sound waves (f
= k/λ)
7. Unit Exam
Differentiation strategies used in this unit & modifications embedded within this unit to provide access for all learners
-
Development of Academic & Personal Behaviors and 21st Century Skills
-
Instructional Shifts
Instructional Shift: Focus
Where in this unit is there evidence of focusing
Instructional Shift: Coherence
How does this unit build upon knowledge of
Instructional Shift: Rigor
Where is there evidence of rigor in this unit?
deeply on the concepts that are prioritized in
the standards?
prior years, and how does it support future
coursework?
This unit delves deeply into rational expressions
and equations, and equips student with several
tools for manipulating, simplifying, and solving
them. Students deepen their connection with
the content through various real world examples
of rational equations and variations.
The work in this unit build upon all previous
equation-solving skills developed to date,
through middle school and early high school, by
exposing them to variables in denominators.
This unit prepares students for work in later
courses, including physics and engineering.