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Orange School District
Algebra I
Curriculum Guide
2011 Edition
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Approved On:
BOARD OF EDUCATION
Patricia A. Arthur
President
Arthur Griffa
Vice-President
Members
Rev. Reginald T. Jackson
Stephanie Brown
Eunice Y. Mitchell
Maxine G. Johnson
David Wright
SUPERINTENDENT OF SCHOOLS
Ronald Lee
DEPUTY
SUPERINTENDENT
Dr. Paula Howard
ADMINISTRATIVE ASSISTANT TO THE
SUPERINTENDENT
Belinda Scott-Smiley
Curriculum and Instructional Services
Operations/Human Resources
BUSINESS ADMINISTRATOR
Adekunle O. James
DIRECTORS
Barbara L. Clark, Special Services
Candace Goldstein, Special Programs
Candace Wallace, Curriculum & Testing
Curriculum Contributors
Courtney Harris-Lee
Erica L. Stewart
Orange School District
Algebra I
Table of Contents
PHILOSOPHY……………………………………………………………………………………………………………………………….….4
PURPOSE & VISION ..……………………………………………………………………………………………………………………….4
STANDARDS ……………………..……………………………………………………………………………….…………………………..5
CURRICULUM GRADES 10-12 …………………………………….……………………………………………………………………..6
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Algebra I
Philosophy
Algebraic principles are the foundation of all mathematics. It is our belief that students can
apply arithmetic concepts and use reasoning to solve problems with unknown variables.
Algebra imitates life and we therefore believe that students who are successful in algebra will
be able to apply skills in everyday decision-making.
Purpose and Vision
Through Algebra, students will learn strategic reasoning and procedural skills that will lead to a
conceptual understanding of seemingly elusive context. 21st century technology requires that
students be able to make hard things seem simple. Using this guide, students will move from
the abstract to the concrete.
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Algebra I
The following standards are addressed in Algebra I.
4.1 All students will develop number sense and will perform standard numerical operations and estimations
on all types of numbers in a variety of ways
4.2 All students will develop spatial sense and the ability to use geometric properties, relationships, and
measurement to model, describe, and analyze phenomena
4.3 All students will represent and analyze relationships among variable quantities and solve problems
involving patterns, functions, and algebraic concepts and processes
4.4 All students will develop an understanding of the concepts and techniques of data analysis, probability,
and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw
appropriate references from data
4.5 All students will use mathematical processes of problem solving, communication, connections, reasoning,
representations, and technology to solve problems and communicate mathematical ideas.
3.2 All students will write in clear, concise, organized language that varies in content and form for different
audiences and purposes
8.1 All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve
problems individually and collaboratively and to create and communicate knowledge.
9.2 Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial
responsibility related to financial planning, savings, investment, and charitable giving in the global economy.
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Orange School District
Algebra I
STANDARDS:
4.1 All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of
ways
4.2 All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze
phenomena
4.3 All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic
concepts and processes
4.4 All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use
them to model situations, solve problems, and analyze and draw appropriate references from data
4.5 All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve
problems and communicate mathematical ideas.
KEY ELEMENTS
What is the variable and how can it be used to describe
patterns or represent unknowns?
1.
2.
How does a graph on paper relate to a realistic situation
encountered in everyday life?
3.
What are the measures of central tendency and how do they
help us analyze and utilize data?
What is meant by a reasonable domain and range for a
function relationship?
4.
CONTENT (What Students should know)
Understand the concept of function
Identify important features of functions and
other relations using symbolic and graphical
methods
Obtain information and draw conclusions from
graphs of functions and other relations
Describe and compare data using sets of
summary statistics including measures of center
and location including mean, mode, median,
quartile, and percentile
PERFORMANCE TARGETS
Demonstrate the understanding of a function using
problem solving.
Evaluate a function at a given point in its domain
Distinguish between functions and other relations
defined symbolically.
Assess the validity of a logical argument and give
counterexamples to disprove a statement
Describe a data set using data displays
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Algebra I
KEY ELEMENTS
How are mathematical operations performed on rational
numbers, including order of operations and distributive
property?
How can random numbers be utilized to simulate and
predict probabilities?
How can multiplication help in computing permutations
and probabilities?
CONTENT (What Students should know)
1. Generate equivalent algebraic expressions
involving polynomials and radicals; use
algebraic properties to evaluate expressions
2. Construct logical arguments based on axioms,
definitions and theorems.
3. Understand the Law of Large Numbers
PERFORMANCE TARGETS
Justify steps in generating equivalent expressions by
identifying the properties used.
Use substitution to check the equality of expressions for
some particular values of the variables
Apply Order of Operations to expressions
Calculate probabilities and apply probability concepts
to solve real-world and mathematical problems.
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Orange School District
Algebra I
KEY ELEMENTS
How can the properties of addition, subtraction,
multiplication, and division be used to simplify
expressions and solve equations?
1.
2.
How can students apply previously learned skills to
attempt increasingly complicated fractions? (e.g fractions,
radicals)
What are ratios and proportions, and how are they used
to solve problems involving percents and measurement?
3.
4.
5.
CONTENT (What Students should know)
Recognize linear, quadratic, exponential and other
common functions in real-world and mathematical
situations
Represent functions with tables, verbal
descriptions, symbols and graphs
Use substitution to check the equality of
expressions for some particular values of the
variables
Make reasonable estimates and judgments about
the accuracy of values resulting from calculations
involving measurements
Understand the roles of axioms, definitions,
undefined terms, and theorems in logical
arguments
PERFORMANCE TARGETS
Solve problems using functions and explain the results in
the original context.
Make qualitative statements about the rate of change of
a function based on its graph or table of values
Represent and solve problems in various contexts using
linear equations and quadratic functions
Justify steps in generating equivalent expressions by
identifying the properties used.
Apply the Pythagorean theorem and its converse to
solve problems and logically justify results
Apply properties of congruent and similar figures to
solve problems and logically justify results
Use Algebra to solve geometric problems unrelated to
coordinate geometry
KEY ELEMENTS
CONTENT (What Students should know)
PERFORMANCE TARGETS
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Algebra I
1.
How can addition, subtraction, multiplication, and division
be used to solve inequalities including compound
inequalities?
Represent real world and mathematical situations
using equations and inequalities involving linear,
quadratic, exponential and root functions.
Solve equations and inequalities symbolically and
graphically.
Interpret solutions in the original text
What are real-world situations that can be described and
solved by inequalities?
KEY ELEMENTS
CONTENT (What Students should know)
PERFORMANCE TARGETS
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Orange School District
Algebra I
What situations are considered direct variations or inverse
variations?
1.
2.
What is function notation and why is it used?
3.
Understand the definition of a function
Use functional notation and evaluate a
function at a given point in its domain
Distinguish between functions and other
relations defined symbolically or
graphically
Find the domain of a function
Obtain information and draw conclusions from graphs
of functions
Understand slope
Make qualitative statements about the rate of change
of a function based on its graph or table of values
KEY ELEMENTS
How are the properties of a linear equation related to its
graph and how can linear data patterns be used to
describe real data?
In what form must equations be in order to utilize a
graphing calculator?
What is the meaning of the slope of a line, especially in
real-world situations?
What if a graph doesn’t show on a calculator? What are
changes to be made on the screen of a graphing
calculator?
CONTENT (What Students should know)
1. Identify intercepts from the graph of
a function
2. Determine how translations affect
the symbolic and graphical forms of a
function
3. Know how to use graphing
technology to examine translations
4. Use scatter plots
5. Determine regression lines and
correlation coefficients.
PERFORMANCE TARGETS
Obtain information and draw conclusions from graphs
of functions.
Make qualitative statements about the rate of change
of a function based on its graph or table of values
Represent and solve problems in various contexts using
linear and quadratic functions
Sketch the graphs of common non-linear functions.
Apply properties of parallel and perpendicular lines
including properties of angles formed by a transversal
to solve problems logically and justify results
Analyze patterns and describe relationships between
two variables.
Use regression lines to make predictions and
correlation coefficients to assess the reliability of those
predictions
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Algebra I
KEY ELEMENTS
What is a system of equations/inequalities and how can
they be used to solve problems?
CONTENT (What Students should know)
Represent relationships in various contexts using
systems of linear inequalities.
PERFORMANCE TARGETS
Solve linear equations graphically
Use technology to graph
Interpret solutions
What is the significance of the intersection point of two
lines and what are ways in which this point may be
found?
KEY ELEMENTS
How can properties of exponents be used to solve real-world
problems?
CONTENT (What Students should know)
1.
2.
What are exponential growth situations?
3.
What are exponential decay situations?
4.
How are constant increase/decrease patterns different than
exponential patterns?
Recognize linear, quadratic, and exponential
functions
Represent functions with tables, verbal descriptions,
symbols, and graphs
Recognize problems that can be modeled using finite
geometric sequences and series
Estimate graphical and numerical solutions
PERFORMANCE TARGETS
Solve problems involving linear, quadratic, and
exponential functions
Explain results
Solve problems that can be modeled using finite
geometric sequences and series
Compare the solution to the appropriate graphical or
numerical estimates
Interpret solutions
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Orange School District
Algebra I
KEY ELEMENTS
What are the different number sets and how do they relate
to domain and range?
What is the difference between evaluating and solving?
How do properties of equality and inequality relate to solving
equations and inequalities?
KEY ELEMENTS
CONTENT (What Students should know)
Represent problems in various contexts using linear and
quadratic equations
Select and apply counting procedures such as multiplication
and addition principles to calculate probabilities
Describe the concepts of intersections, unions, and
complements using Venn Diagrams
PERFORMANCE TARGETS
Solve problems in various contexts using linear and
quadratic equations
Justify steps in generating equivalent expressions by
identifying the properties used
Calculate probabilities in real-world context
CONTENT (What Students should know)
PERFORMANCE TARGETS
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Orange School District
Algebra I
What are the characteristics of the different types of
functions and how can they be used?
1.
2.
What are the different forms of linear equations and how
can you determine which form is best for a given
situation?
3.
4.
How an we graph a line given each of the different forms
of a linear equation?
5.
6.
Hoe can we solve and graph inequalities and absolute
value in inequalities?
7.
Understand the definition of a function.
Distinguish between functions and other relations
defined symbolically or graphically
Define absolute value
Represent relationships in various contexts using
absolute value inequalities in two variables
Use scatter plot
Apply properties of parallel and perpendicular
lines
Use numeric, graphic and symbolic
representations of transformations in two
dimensions such as reflections, translations, scale
changes and rotations about the point of origin.
Find the domain of a function in a real world context
Display and analyze data
Use various measures associated with data to draw
Conclusions
Identify trends in data
Describe relationships within the data
Solve sample problems
Sketch graphs of linear functions and translate between
graphs, tables, and symbolic representations
What is a matrix and how can it be used?
Use graphing technology
How can matrices be used to describe transformations?
Use numeric, graphic, and symbolic re presentations of
transformations
Evaluate absolute value as specified points in their
domains
Solve absolute variable inequalities graphically
Analyze patterns and describe relationships between
variables.
Determine regression lines and correlation coefficients
Make predictions
Use a data table to graph a linear equation
Apply transformation
Describe results
KEY ELEMENTS
CONTENT (What Students should know)
PERFORMANCE TARGETS
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Orange School District
Algebra I
What is a quadratic function and its characteristics?
1.
What are the various ways to factor and when do you
know which method to use?
2.
How do you know which method is appropriate for
solving a quadratic equation?
3.
How do you graph parabolas using various quadratic
concepts such as vertex, x and y intercepts, etc?
4.
5.
How do polynomials apply to geometric concepts?
1.
How do you determine the number of roots of a
polynomial equation?
2.
What are the different ways to solve a polynomial
equation and how do you apply these methods?
Understand the concept of function and
identify important features of functions
and other relations using symbolic and
graphical methods where appropriate.
Recognize linear, quadratic, and
exponential functions in real world
situations.
Identify intercepts, zeros, maxima, minima,
and intervals of increase and decrease.
Determine how translations affect the
symbolic and graphical forms of a function
Recognize that to solve certain equations,
number systems need to be extended from
whole numbers to integers, from integers
to rational numbers, from rational
numbers to real numbers, and from real
numbers to complex numbers.
Identify the vertex, line of symmetry, and intercepts of
the parabola corresponding to a quadratic function,
using symbolic and graphical methods
Generate equivalent algebraic expressions
involving polynomials and radicals
Use algebraic properties to evaluate
expressions
Add, subtract, and multiply polynomials
Divide a polynomial by a polynomial of equal or lower
degree
Evaluate polynomial at specified points in their domains
Sketch the graphs of common non-linear functions such
as :
F(x)=X3
Represent and solve problems in various contexts using
quadratic functions
Sketch graphs of quadratic functions
Factor common monomial factors from polynomials
Factor quadratic polynomials and factor the difference of
two squares
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Orange School District
Algebra I
KEY ELEMENTS
CONTENT (What Students should know)
Recognize linear, quadratic, and exponential
functions in real world mathematical situations
2. Assess the reasonableness of a solution
3. Use graphing technology to graph functions
1.
What are radical functions and what are their
characteristics?
How are powers and radicals related?
PERFORMANCE TARGETS
Sketch the graphs of common non-linear functions
Evaluate the graph
Solve problems involving radical functions
Apply the properties of positive and negative rational
exponents to generate equivalent algebraic expressions
Solve equations that contain radical expressions
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Orange School District
Algebra I
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