Algebra I – Common Core Standards
Curriculum Guide
Module 1: Relationships & Functions
Module Overview: In this module students will explore equivalent expressions through pattern tasks. Students will formalize the concept of
a function. The module will also reinforce multiple representations by using real life data represented in tables, equations and graphs.
Essential Questions:
 How can you find the terms of a sequence recursively?
 How can you represent the terms of a sequence explicitly?
 How do you determine if the function is discrete or continuous?
 How do you determine if a relation is a function?
 How do you determine if a function is linear or nonlinear?
 How do you evaluate functions for specified values?
Prerequisite Skills and Knowledge: graphing ordered pairs on a coordinate grid, completing tables from equations, completing tables given part of
the table values, evaluating expression, evaluating expressions for given input values
Tier III Vocabulary: domain and range, term, constant, step function, relation, domain, range, vertical line test, function notation, dependent
variable, independent variable, input, output, function, linear function, nonlinear function, continuous graph, discrete graph, recursively defined
sequences, explicitly defined sequences
Common Core Standards for Mathematical Practice
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Key
 ★ Modeling Standard
 *indicates a standard that appears in multiple modules
 + indicates a standard included to increase coherence
 PH Prentice Hall Algebra Two textbook 2011
 BOLD indicates TN Common Core focus standards
abc indicates a part of a standard that appears in a different module
Cumberland County Algebra One Curriculum Guide 1
Common Core Standards for Math Content
F-BF Functions-Building Functions
A. Build a function that models a relationship between
two quantities.
F-BF.A.1 Build a function that describes a relationship
between two quantities. 
a. Determine an explicit expression, a recursive
process, or steps for calculation from a context.
A-SSE Algebra-Seeing Structure in Expression
A .Interpret the structure of expressions.
A-SSE.A.1 Interpret expressions that represent a quantity
in terms of its context*.
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
Students will be able to
Activities/Resources
Using a linear pattern task:
 Given the first few figures in a sequence,
draw the next figures.
 Write an expression for the nth term in a
sequence.
 Describe the parts of the expression in
relation to the context of the pattern. (For
example, if the pattern is the perimeter of n
adjoined hexagons and a student has the
expression: 10 + 4(n-2), the student can
describe that the 10 represents the fact that 5
sides on each of 2 end hexagons are always
used while only 4 sides are used on the nonend hexagons-that number being 2 less than
the position of the term.)
Links to added material from
previous Tennessee State
Standards:
Recursive Sequences:
http://www.regentsprep.o
rg/regents/math/algtrig/A
TP3/Recursive.htm
Discrete Continuous Functions:
http://flaglerschools.com/
sites/default/files/4.2.pdf
Step Function:
http://www.icoachmath.com
/math_dictionary/step_funct
ion.html
Cumberland County Algebra One Curriculum Guide 2
F-IF Functions-Interpreting Functions
A. Understand the concept of a function and use function
notation.
F-IF.A.1 Understand that a function from one set (called the
domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If
f is a function and x is an element of its domain, then f(x)
denotes the output of f corresponding to the input x. The
graph of f is the graph of the equation y=f(x).
F-IF.A.2 Use function notation, evaluate functions for
inputs in their domains, and interpret statements that use
function notation in terms of context.
F-IF.A.3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a subset of
the integers. For example, the Fibonacci sequence is
defined recursively by f(0) = f(1)=1, f(n+1)=f(n)+f(n-1) for
n>=1
 Use the definition of a function to determine
whether a relationship is a function given a
table, graph or words.
 Given the function f(x), identify x as an
element of the domain, the input, and f(x) is
an element in the range, the output.
 Know that the graph of the function, f, is the
graph of the equation y=f(x).
 When a relation is determined to be a
function, use f(x) notation.
 Evaluate functions for inputs in their domain
(include non-linear functions).
 Interpret statements that use function notation
in terms of the context in which they are
used. (For example given f(m) = .55m + 40
as the daily cost for car rental interpret f(82)
as being the cost for driving 82 miles.
Hexagon Pattern Task
http://www.tncore.org/sites
/www/Uploads/Tab3_Alg1
_Factors_Maintenance_PA
RT.pdf
Interpreting expressions
task
http://www.illustrativem
athematics.org/illustratio
ns/389
 Recognize that sequences, sometimes defined
recursively, are functions whose domain is a
subset of the set of integers.
A-CED Algebra-Creating Equations
A. Create equations that describe numbers or
relationships.
A-CED.A.2 Create equations in two or more variables
to represent relationships between quantities; graph
equations on coordinate axes with labels and scales. *
 From contextual situations, write equations
and sketch the graph of the equation on
coordinate axes with labels and scales.
Cumberland County Algebra One Curriculum Guide 3
F-IF Functions-Interpreting Functions
B. Interpret functions that arise in applications in terms of
context.
F-IF.B.4 For a function that models a relationship
between two quantities, interpret key features of
graphs and tables in terms of the quantities, and
sketch graphs showing key features given a verbal
description of the relationship. Key features include:
intercepts; intervals where the function is increasing,
decreasing, positive, or negative; relative maximums
and minimums; symmetries; end behavior, and
periodicity. 
F-IF.5 Relate the domain of a function to its graph
and, where applicable to the quantitative relationship
that it describes. For example, if the function h(n) gives
the number of person hours it takes to assemble n
engines in the factory, then the positive integers would
be an appropriate domain of the function.
C. Analyze functions using different representations.
F-IF.C.9 Compare properties of two functions each
represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For
example, given a graph of one quadratic function and an
algebraic expression for another, say which has the larger
maximum.
Using contextual data:
Move flexibly between tables, graphs and
equations.
 Interpret graphs in terms of the data that it
represents, including identifying the meaning
of key features of the graph and domain.
 Given a graph or table which represents a
linear function, identify the key features
including intercepts.
 Given the intercepts of a linear function,
sketch the graph.
 Given the graph of a function, determine the
practical domain of the function as it relates
to the numerical relationship it describes.
 Create and graph equations, using appropriate
labels and scales.
 Create and interpret qualitative graphs.
 Compare the properties of two functions
represented in different ways.
 Given a contextual situation, graph step
functions.
Analyzing functions
http://melt-instituteresources.wikispaces.co
m/file/view/performanc
e+task.pdf
Sorting functions
http://rda.aps.edu/RDA/
Performance_Task_Ban
k/Documents/High_Sch
ool/Sorting%20Functio
ns%20-%20Task.pdf
Functions/Patterns/Create
equation
http://www.insidemathemati
cs.org/common-core-mathtasks/high-school/HS-A2003%20Number%20Tower
s.pdf
Creating Equations
http://schools.nyc.gov/NR/rd
onlyres/0D9AA86E-F6014F26-9598CF57C4FA7CAB/0/NYCD
OEHSAlgebraTheCycleSho
p_Final.pdf
F-IF.C.7 Graph functions expressed symbolically and
show key features of the graph, by hand in simple cases
and using technology for more complicated cases.
b. Graph square root, cube root and piecewise-defined
functions, including step functions and absolute value
functions.
Cumberland County Algebra One Curriculum Guide 4
Cumberland County Algebra One Curriculum Guide 5