Unit #: 1
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Karen Mullins
Christy Bentley, Elizabeth Smith
PREAMBLE
This unit will have students build on their knowledge of function characteristics from Math 1, and extend this knowledge to additional functions. Students also
extend their knowledge of exponents from Math 1.
STAGE 1 – DESIRED RESULTS
Unit Title: Functions, Radicals, and Exponents
Transfer Goal(s): Students will be able to independently use their learning to use the language of functions to describe, interpret and solve various functions.
Enduring Understandings:
Students will understand that…
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Functions are single-value mappings from one set-the domain of the
function-to another-its range.
 You can classify, predict and characterize various kinds of
relationships by attending to the rate at which one quantity varies with
respect to the other.
 Functions can be represented in various ways including algebraic
means, graphs, word descriptions and tables.
 Changing the way that a function is represented does not change the
function, although different representations highlight different
characteristics, and some may show only part of the function.
 Linear functions are characterized by a constant rate of change,
quadratics are characterized by a constant second difference and
exponential functions are characterized by multiple rate of change.
 Rational exponents are representations of radicals.
 Inverse variation is a relationship where one variable increases the
other one decreases.
Students will know:
 Function notation
 The structure of the constants and coefficients in linear, radical,
quadratic, absolute value and exponential functions (terms, factors,
coefficients, and parts of equations)
 Inequality and interval notation for domain and range of a function.
 Laws of Exponents
 Inverse variation formula
 Properties of rational and irrational numbers
Essential Questions:
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What defines a function?
What is the best way to represent or describe a function?
How does the rate of change distinguish different families of
functions?
How are exponents and radicals similar?
How do you solve for a variable?
Students will be able to:
 Operate with radicals
 Operate with rational exponents
 Graph equations in two variables (linear, exponential, quadratic and
absolute value, radical)
 Describe and analyze key characteristics of functions
 Solve radical equations
 Solve systems of linear-linear, linear-radical through f(x)=g(x)
 Write systems of equations given real-world problems.
 Convert between radical and rational functions.
 Create an/or graph equation and inequalities to solve problems.
 Determine which method is best to solve a given problem.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
1
Unit #: 1
NC.M2.N-RN.1
NC.M2.N-RN.2
NC.M2.N-RN.3
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Karen Mullins
Christy Bentley, Elizabeth Smith
STAGE 1– STANDARDS
Common Core State Standard(s)
Explain how expressions with rational exponents can be rewritten as
radical expressions.
Rewrite expressions with radicals and rational exponents into
equivalent expressions using the properties of exponents.
Use the properties of rational and irrational numbers to explain why:
 the sum or product of two rational numbers is rational;
 the sum of a rational number and an irrational number is
irrational;
 the product of a nonzero rational number and an irrational
number is irrational.
Create equations and inequalities in one variable that represent
quadratic, square root, inverse variation, and right triangle
trigonometric relationships and use them to solve problems
ACT Standards
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NC.M2.A-CED.1
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Create and graph equations in two variables to represent quadratic,
square root, and inverse variation relationships between quantities.
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NC.M2.A-CED.2
Create systems of linear, quadratic, square root and inverse variation
equations to model situations in context.
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NC.M2.A-CED.3
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Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Identify solutions to simple quadratic equations
Write expressions, equations, and inequalities for
common algebra settings
Solve linear inequalities that require reversal of the
inequality sign
Solve quadratic equations
Write equations and inequalities that require
planning, manipulating and/or solving
Interpret and use information from graphs in the
coordinate plane
Match number line graphs with solution sets of
simple quadratic inequalities and linear inequalities
Write expressions, equations, and inequalities for
common algebra settings
Match linear graphs with their equations
Interpret and use information from graphs in the
coordinate plane
Solve linear inequalities that require reversal of the
inequality sign
Write expressions, equations, and inequalities for
common algebra settings
Interpret and use information from graphs in the
coordinate plane
Match linear graphs with their equations
Last revision 9/8/16
2
Unit #: 1
NC.M2.A-SSE.1a
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Karen Mullins
Christy Bentley, Elizabeth Smith
Interpret expressions that represent a quantity in terms of its context.
 Perform straightforward word to symbol translations
a. Identify and interpret parts of a quadratic, square root, inverse
 Manipulate expressions and equations
variation, or right triangle trigonometric expression, including
 Solve routine two or three step arithmetic problems
terms, factors, coefficients, radicands, and exponents.
involving concepts such as rate and proportion, tax
added, percentage off, and computing with a given
average
 Solve multi step arithmetic problems that involve
planning or converting units of measure
 Write expressions, equations, and inequalities for
common algebra settings
 Combine like terms
 Factor simple quadratics (difference of squares and
perfect square trinomials)
 Manipulate expressions and equations
Interpret expressions that represent a quantity in terms of its context.
b. Interpret quadratic and square root expressions made of
multiple parts as a combination of single entities to five
meaning in terms of a context.
NC.M2.A-SSE.1b
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NC.M2.A-REI.1
NC.M2.A-REI.2
NC.M2.A-REI.11
Manipulate expressions and equations
Solve routine two or three step arithmetic problems
involving concepts such as rate and proportion, tax
added, percentage off, and computing with a given
average
Solve multi step arithmetic problems that involve
planning or converting units of measure
Write expressions, equations, and inequalities for
common algebra settings
Solve routine first degree equations
Justify a chosen solution method and each step of the solving process
for quadratic, square root and inverse variation equations using
mathematical reasoning.
Solve and interpret one variable inverse variation and square root
equations arising from a context, and explain how extraneous solutions
may be produced.
Extend the understanding that the x-coordinates of the points where the
graphs of two square root and/or inverse variation equations y = f(x)
and y = g(x) intersect are the solutions of the equation f(x) = g(x) and
approximate solutions using graphing technology or successive
approximations with ta table of values.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)

Interpret and use information from graphs in the
coordinate plane
Last revision 9/8/16
3
Unit #: 1
NC.M2.F-IF.4
NC.M2.F-IF.7
NC.M2.F-IF.9
NC.M2.F-BF.1
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Karen Mullins
Christy Bentley, Elizabeth Smith
Interpret key features of graphs, tables, and verbal descriptions in
context to describe functions that arise in applications relating two
quantities, including: domain and range, rate of change, symmetries,
and end behavior.
Analyze quadratic, square root, and inverse variation functions by
generating different representation, by hand in simple cases and using
technology for more complicated cases, to show key features,
including: domain and range; intercepts; intervals where the function is
increasing, decreasing, positive, or negative; rate of change; maximums
and minimums; symmetries; and end behavior.
Compare key features of two functions (linear, quadratic, square root,
or inverse variation functions) each with a different representation
(symbolically, graphically, numerically in tables, or by verbal
descriptions).
Write a function that describes a relationship between two quantities by
 Write expressions, equations, and inequalities for
building quadratic functions with real solution(s) and inverse variation
common algebra settings
functions given a graph, a description of a relationship, or ordered pairs
(include reading these from a table).
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
4