Algebra 1
Piscataway High School
Teacher:
Ms. Your Name
Email:
Nameyourname@pway.org
Course Title: Algebra 1
Textbook:
Algebra 1 (2014), HMH (Kanold, Burger, et al.)
Course Overview
Full year course: 5.0 credits
Prerequisite: Pre-Algebra
Description: This course is designed as the first course in a traditional program for all students
who are required to take three or more years of college preparatory mathematics. Initially,
concepts mastered in the previous math course are expanded. In addition, this course covers
solving and graphing equations and inequalities, solving word problems, graphing on a
coordinate plane, solving simultaneous equations, properties of exponents, operations with
polynomial expressions, working with quadratic functions, and data analysis. Students in this
class may also be assigned to an Algebra 1 Lab class based on prior performance in mathematics.
The Algebra 1 course is structured as follows:
Unit
Topic
Length
Unit 1
Arithmetic vs. Geometric Sequences
5 Days
Unit 2
Unit 3
Unit 4
Critical Attributes of Linear Functions,
Graphs, and Tables
Critical Attributes of Exponential Functions,
Graphs, and Tables
Graph analysis of Absolute Value and
Quadratic (Vertex Form) Functions
15 Days
10 Days
20 Days
Unit 5
Polynomial and Radical Operations
10 Days
Unit 6
Relating the Roots of a
Quadratic Function to its Graph
25 Days
Unit 7
Systems of Equations
15 Days
Unit 8
Scatter Plots of all Function Types
8 Days
Unit 9
Graph Analysis of Square Root Functions
Time
permitting
Scope and Sequence – First Semester
Unit
Timing
Unit 1
5 days
Unit 2
15 days
Topic
Concepts and Skills
(1 day = 1 hour)
Assessment for Unit 1 administered by the end of Cycle 1
Arithmetic vs. Geometric  Recognize the patterns for each and complete the associated tables
 Graph each and recognize patterns effect on graph
Sequences
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Assessment for Unit 2 administered by the end of Cycle 4
Critical Attributes of
 Determine if an arithmetic sequence is a function (is the table one-to one and does
the graph pass the vertical line test?)
Linear Functions, Graphs,
 Connect the slope & y-intercept to the rate of change & initial value (identify
and Tables
Students will be able to
interchange between tables,
graphs, or equations for
any linear function and
identify the domain, range,
intercepts, and slope.
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Unit 3
10 days
slope and y-intercept from both a table and a graph)
Write a linear function in function form (𝑓(𝑥) = 𝑚𝑥 + 𝑏) from table and graph
Expand function notation to find 𝑓(𝑘), 𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘) using
the equation and the table
Transformations of Linear graphing [𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘)]
Write functions in function form (point and slope, two points, scenarios)
Review graphing linear functions using table, transformation, slope and y-int,
intercepts (intercepts are given or can be read from a table)
Graph linear functions with a restricted domain
Graph two linear functions and discuss the meaning of their intersection
Assessment for Unit 3 administered by the end of Cycle 6
Critical Attributes of
 Determine if a geometric sequence is a function (is the table one-to one and does
the graph pass the vertical line test)
Exponential Functions,
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Connect the common ratio to the growth/decay factor of an exponential function
Graphs, and Tables
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Students will be able to
interchange between tables,
graphs, or equations for any
exponential function and
identify the domain, range,
intercepts, growth/decay
factor, and asymptote(s).
Unit 4
20 days
Develop the concept of domain and range based off of table and graph.
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Make a connection between the negative exponent rule and the pattern in the table
of an exponential function
Write an exponential function in function form 𝑓(𝑥) = 𝑎𝑏 𝑥 from a table and a
graph by recognizing the pattern
Graph exponential functions with a restricted domain
Graph a linear and an exponential on the same graph and discuss the meaning of
their intersection
Model exponential function in real life scenarios throughout the unit
Throughout unit make connection between linear and exponential functions
Assessment for Unit 4 administered by the end of Cycle 10
Graph analysis of
 Determine if an absolute value graph is a function (is the table one-to one and
does the graph pass the vertical line test)
Absolute Value and
Quadratic (Vertex Form)  Expand function notation to find 𝑓(𝑘), 𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘) using
the equation and the table
Functions
Students will be able to
interchange between tables,
graphs, or equations for any
absolute value/quadratic
function and identify the
domain, range, max/min, axis
of symmetry, and intercepts.
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Transformations of absolute value graphing [𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘)]
Write an absolute value function in function form (𝑓(𝑥) = 𝑎|𝑥 − ℎ| + 𝑘) from a
table and a graph
Graph absolute value functions with a restricted domain
Graph a linear and an absolute value or two absolute value functions and discuss
the meaning of their intersections
Model absolute value functions in real life scenarios throughout the unit
Determine if a quadratic graph is a function (is the table one-to one and does the
graph pass the vertical line test)
Expand function notation to find 𝑓(𝑘), 𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘) using
the equation and the table
Transformations of quadratic graphing [𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘)]
Write a quadratic function in function form (𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘) from a table
and a graph
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Unit 5
10 days
Graph quadratic functions with a restricted domain
Graph two quadratic or a linear and a quadratic on the same graph and discuss the
meaning of their intersections
Model quadratic functions in real life scenarios throughout the unit
Throughout unit make connections between linear, exponential, absolute value,
and quadratic functions
Assessment for Unit 5 administered by the end of Cycle 13
Polynomial and Radical
 Operations with polynomials (add, subtract and multiply): multiplication is limited
to: monomial*polynomial and binomial*binomial (rules of exponents review is
Operations
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embedded within this content, but does not include negative exponents)
Simplify radicals (include Pythagorean Theorem examples)
Operations with radicals (add, subtract, multiply)
Rationalize denominators
Scope and Sequence – Second Semester
Unit
Timing
Unit 6
25 days
Topic
Concepts and Skills
(1 day = 1 hour)
Assessment for Unit 6 administered by the end of Cycle 19
Relating the Roots of a
 Factoring: GCF, 4+ terms by grouping, trinomials by grouping where 𝑎 = 1 and
𝑎 ≠ 1 (include perfect square trinomials), difference of squares
Quadratic Function to its

Finding roots/zeroes of quadratics by solving using: factoring, square roots,
Graph
Students will be able to factor
polynomials and use this
understanding to find
roots/zeroes and make the
connection to the graph.
Unit 7
15 days
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Assessment for Unit 7 administered by the end of Cycle 23
Systems of Equations
 Graph two linear equations and determine if they have 1 solution, no solution, or
Students should understand
that regardless of the number
of functions or function type
used, the solutions are
identified by their
intersection(s) on the graph as
discussed throughout the year.
Unit 8
8 days
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infinite solutions and relate to the equation
Discuss the meaning of an inequality
Substitute values into a single variable inequality to determine if it is a solution
and move to substituting an ordered pair into a two variable inequality
Graph a single linear inequality and discuss the solutions
Graph a system of linear inequalities and discuss the solutions
Solve a system of two linear equations using substitution and linear combinations
For all pairs of function types, identify number and types of solutions
Assessment for Unit 8 administered by the end of Cycle 25
 Analyze linear scatter plots, discuss correlation, find the line of best fit, and use
Scatter Plots of all
the line of best fit to make predictions
Function Types
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Unit 9
Time
permitting
quadratic formula, completing the square (with 𝑎 = 1 or GCF that creates 𝑎 = 1
with focus on perfect square trinomial)
Determine the number of solutions and connect to the equation
Connect the graph of a quadratic function to its roots
Graph quadratic functions: vertex, standard, intercept form (standard for equations
should be factorable and vertex is found using line of symmetry *no – 𝑏/2𝑎)
Convert between the three forms of a quadratic function
Modeling quadratic functions throughout the unit
Graph Analysis of Square
Root Functions
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Analyze scatter plots that are non-linear and determine the best function type to
represent the data, use technology to find the most appropriate equation
Given a scatter plot and multiple equations, determine the equation given that best
represents the data
Understand that square roots are ½ power
Transformations of square root functions [𝑓(𝑥) + 𝑘, 𝑘𝑓(𝑥), 𝑓(𝑘𝑥), 𝑓(𝑥 + 𝑘)]
Write a square root function in function form (𝑓(𝑥) = 𝑎√𝑥 − ℎ + 𝑘) from a table
and a graph
Model square root functions in real life scenarios throughout the unit
Connect graphs to linear, exponential, absolute value, and quadratic functions