ALGEBRA I
CURRICULUM GUIDE
2012-2013
Loudoun County Public Schools
Algebra
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun
County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other
statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s
teachers concerning the implementation of these standards. In many instances the local expectations for achievement exceed state
requirements. The GUIDE is the lead document for planning, assessment and curriculum work. It is a summarized reference to the entire
program. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can combine them
with the GUIDE for ease in lesson planning.
Mathematics Internet Safety Procedures
1. Teachers should review all Internet sites and links prior to using it in the classroom.
During this review, teachers need to ensure the appropriateness of the content on the site,
checking for broken links, and paying attention to any
inappropriate pop-ups or solicitation of information.
2. Teachers should circulate throughout the classroom while students are on the
internet checking to make sure the students are on the appropriate site and
are not minimizing other inappropriate sites.
3. Teachers should periodically check and update any web addresses that they have on their
LCPS web pages.
4. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
Algebra
Algebra I Nine Weeks Overview
1st Quarter
Expressions, Operations,
And Linear Equations
A.1
A.3
A.4 a, b, d
Statistics
A.10
A.9
Functions
A.7
2nd Quarter
Linear Functions, con’t
A.7
Graphing Equations
and Inequalities
A.6 a
A.6 stem
Solving Equations
and Inequalities
Solving Systems of
Equations and
Inequalities
3rd Quarter
Writing Linear
Equations
A.6 b
A.11
Polynomials
4th Quarter
Quadratic Functions A.7
A.4 b, c, f
A.11
A.2 a, b, c
A.4 a, b, e, f
A.8
A.5 a, b, c
A.4 a, b, e, f
A.5 d
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and
representations as they engage in mathematics activities throughout the year.
Algebra I page 4
Number
of Blocks
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer essential questions.)
Expressions, Operations, and Linear Equations
 Translate and evaluate expressions
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7 blocks
Translate and solve one-variable equations
Application of equations
Evaluate and simplify square and cube roots
property of multiplication and the identity property
of addition? Why are they different?
 Describe when a square root is in simplest form.
 What is the square root of a perfect square?
 Where does the square root of a nonperfect
square lie on the number line?
 Describe when a cube root is in simplest form.
 What is the cube root of a perfect cube?
 Where does the cube root of a nonperfect cube
lie on the number line?
 What is the inverse of cubing a number? What is
the inverse of squaring a number?
 Why can we take the cube root of a negative
number but not the square root of a negative
number?
 How can you tell if a square root or cube root
expression is completely simplified? Explain.
A.1 Essential Understandings

Algebra is a tool for reasoning about quantitative
situations so that relationships become apparent.
Algebra is a tool for describing and representing
Additional Instructional
Resources/Comments
Emphasize:
 Translating sentences
into equations
 Practical application
problems
Properties of the real numbers
 How do you write a function as tables and rules?
 How do you represent a function as a graph?
 What is the difference between the identity

Standard(s) of Learning
Essential Knowledge and Skills
SOL A.1 The student will represent verbal
quantitative situations algebraically and evaluate
these expressions for given replacement values of the
variables.
A.1 Essential Knowledge and Skills

Translate verbal quantitative situations into
algebraic expressions and vice versa.

Model real-world situations with
algebraic expressions in a variety of
representations (concrete, pictorial, symbolic,
verbal).

Evaluate algebraic expressions for a given
replacement set to include rational numbers.

Evaluate expressions that contain
absolute value, square roots, and cube roots.
Algebra 1 Antics Review Game
for reviewing the topics of
Algebra, Solving Equations,
Coordinate Geometry, Dealing
with Data and Patterns and
Function.
http://mathbits.com/MathBits/P
PT/Algebra.html
Emphasize:
Perfect squares and cubes
Texas Instruments – Rational
Reductionhttp://education.ti.com/educatio
nportal/activityexchange/Activity
.do?cid=US&aId=1608
Algebra I page 5
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patterns and relationships.
Mathematical modeling involves creating
algebraic representations of quantitative realworld situations.
The numerical value of an expression is
dependent upon the values of the replacement
set for the variables.
There are a variety of ways to compute the value
of a numerical expression and evaluate an
algebraic expression.
The operations and the magnitude of the
numbers in an expression impact the choice of an
appropriate computational technique.
An appropriate computational technique could be
mental mathematics, calculator, or paper and
pencil.
A.3 Essential Understandings
 A square root in simplest form is one in which the
radicand (argument) has no perfect square
factors other than one.
 A cube root in simplest form is one in which the
argument has no perfect cube factors other than
one.
 The cube root of a perfect cube is an integer.
 The cube root of a nonperfect cube lies between
two consecutive integers.
 The inverse of cubing a number is determining
the cube root.
 In the real number system, the argument of a
square root must be nonnegative while the
argument of a cube root may be any real number.
Project Graduation – lesson 5
NLVM – Algebra balance scales http://nlvm.usu.edu/en/nav/fra
mes_asid_201_g_4_t_2.html?op
en=instructions&from=category_
g_4_t_2.html
SOL A.3 The student will express the square roots
and cube roots of whole numbers and the square
root of a monomial algebraic expression in
simplest radical form.
A.3 Essential Knowledge and Skills
 Express square roots of a whole number in
simplest form.
 Express the cube root of a whole number in
simplest form.
 Express the principal square root of a
monomial algebraic expression in simplest
form where variables are assumed to have
positive values.
NLVM – Algebra Balance Scales –
negatives http://nlvm.usu.edu/en/nav/fra
mes_asid_324_g_4_t_2.html?op
en=instructions&from=category_
g_4_t_2.html
Texas Instruments – Application
of equations (TI-Nspire needed) http://education.ti.com/educatio
nportal/activityexchange/Activity
.do?cid=US&aId=13369
Algebra I page 6
A.4 a, b, d Essential Understandings
 Equations can be used as mathematical models
for real-world situations.
 Set builder notation may be used to represent
solution sets of equations.
SOL A.4 a, b, d The student will solve multistep linear
…equations in two variables, including
a. solving literal equations (formulas) for a given
variable;
b. justifying steps used in simplifying expressions
and solving equations, using field properties and
axioms of equalitiy that are valid for the set of real
numbers and its subsets;
d. solving multistep linear equations algebraically
and graphically…..
A.4 a, b, d Essential Knowledge and Skills
 Simplify expressions and solve equations,
using the field properties of the real numbers
and properties of equality to justify
simplification and solution.
 Solve a literal equation (formula) for a specified
variable.
 Solve multistep linear equations in one
variable.
Statistics
Emphasize:


Descriptive Statistics
Collect Data
Measures of Center
Box and Whisker Plots
Stem and Leaf Plots
7 blocks
A.10 Essential Questions
 How is a sample related to a population?
 How can a sample be biased?
 If a systematic sample of a population is used for
a survey containing unbiased questions, how is it
possible for the survey to be biased? Explain.
SOL A.10 The student will compare and contrast
multiple univariate data sets, using box-andwhisker plots.
Introduce sigma notation
Outlier – What does an
outlier do to your data?
Technical assistance document
Project Graduation – lesson
10
Algebra I page 7
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





Compare and contrast mean, median, and mode.
Which measure of central tendency best
describes a data set? Explain why.
Which measure of central tendency is usually the
most affected by outliers?
Write a data set that has a mean of 10, median of
10, and modes of 5 and 8
How can you identify an outlier in a data set?
What information is needed to create a Box and
Whisker plot?
Two data sets have the same mean, the same
interquartile range, and same range. Is it possible
for the box and whisker plots of such data sets to
be different? Justify your answer by creating data
sets that fit the situation.
Explain how you could translate a data set in a
stem and leaf plot to a box and whisker plot.
Compare and contrast data sets
How can you determine the best way to
represent a data set?
How are the measures of central tendency and
measures of dispersion used to compare data?
A.10 Essential Understandings


Statistical techniques can be used to organize,
display, and compare sets of data.
Box-and-whisker plots can be used to analyze
data.
Variation
Mean absolute deviation
Standard deviation
population
z-scores
Essential Questions
A.10 Essential Knowledge and Skills
Compare, contrast, and analyze data, including
data from real-world situations displayed in boxand-whisker plots.
Integrate throughout the year.
National Library of Virtual
Manipulatives – Box Plot http://nlvm.usu.edu/en/nav/fra
mes_asid_200_g_4_t_5.html?op
en=instructions&from=category_
g_4_t_5.html
Texas instruments – Box plots
and histograms (TI-Nspire)
http://education.ti.com/educatio
nportal/activityexchange/Activity
.do?cid=US&aId=9843
Texas instruments – Box plots
and histograms
http://education.ti.com/educatio
nportal/activityexchange/Activity
.do?cid=US&aId=8200
Texas instruments – Changes in
Data – (TI-Nspire)
http://education.ti.com/educatio
nportal/activityexchange/Activity
.do?cid=US&aId=12955
Emphasize:
 Absolute value
 Using calculator to assist
with the formula
 Use sigma notation
 Order of Operations
 Standard deviation as
concept of spread
Algebra I page 8
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
What are the ways to measure the dispersion of
data?
What is the sum of the deviations of data points
from the mean of a data set?
How do we express the units for standard deviation?
What does a greater value of standard deviation tell
us?
When may using the mean absolute deviation be
better than using the standard deviation or
variance?
What is a z-score?
What does a z-score tell us about a data set?
A.9 Essential Understandings
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
Descriptive statistics may include measures of
center and dispersion.
Variance, standard deviation, and mean absolute
deviation measure the dispersion of the data.
The sum of the deviations of data points from the
mean of a data set is 0.
Standard deviation is expressed in the original
units of measurement of the data.
Standard deviation addresses the dispersion of
data about the mean.
Standard deviation is calculated by taking the
square root of the variance.
The greater the value of the standard deviation,
the further the data tend to be dispersed from
the mean.
For a data distribution with outliers, the mean
absolute deviation may be a better measure of
dispersion than the standard deviation or
variance.
A z-score derived from a particular data value
tells how many standard deviations that data

SOL A.9 The student, given a set of data, will
interpret variation in real-world contexts and
calculate and interpret mean absolute deviation,
standard deviation, and z-scores.
A.9 Essential Knowledge and Skills
 Given data, including data in a real-world
context, calculate and interpret the mean
absolute deviation of a data set.
 Given data, including data in a real-world
context, calculate variance and standard
deviation of a data set and interpret the
standard deviation.
 Given data, including data in a real-world
context, calculate and interpret z-scores for a
data set.
 Explain ways in which standard deviation
addresses dispersion by examining the
formula for standard deviation.
 Compare and contrast mean absolute
deviation and standard deviation in a realworld context.
 Interpret and compare scores in their context
given standard deviation, z-scores, and
means.
Real data and context
(student driven data –
height, shoe size…)
Technical assistance document
from the VA Dept of Ed
Enhanced Scope and Sequence
2004 - Traffic Jam pp. 18-19
http://www.doe.virginia.gov/test
ing/sol/standards_docs/mathem
atics/index.shtml (suggest
opening the Algebra I document
and running a find for the title)
Algebra I page 9
value is above or below the mean of the data set.
It is positive if the data value lies above the mean
and negative if the data value lies below the
mean.
Functions
Review coordinate plane, quadrants and axes given a
table of values or ordered pairs.
 Why do we graph?
 What is the abscissa of a point of the graph of a
relation?
 What is the ordinate of a point of the graph of a
relation?
 One of the coordinates of a point is negative
while the other is positive. Can you determine
the quadrant in which the point lies? Explain.
 Explain how can you tell by looking at the
coordinates of a point whether the point is on the
x-axis or on the y-axis
 Compare and contrast relations and functions
using tables, graphs, and words.
6 blocks
(SOL A.7
continues
in Quarter
2 with
additional
time.)
A.7 Essential Understandings
 A set of data may be characterized by patterns,
and those patterns can be represented in
multiple ways.
 Graphs can be used as visual representations to
investigate relationships between quantitative
data.
 Inductive reasoning may be used to make
conjectures about characteristics of function
families.
 Each element in the domain of a relation is the
abscissa of a point of the graph of the relation.
 Each element in the range of a relation is the
ordinate of a point of the graph of the relation.
 A relation is a function if and only if each element
Recommended activities:
 Battleship to graph
points
 Graph your hand
 Plotting points to create
pictures
Emphasize vocabulary:
abscissa, domain, ordinate, range
National Library of Virtual
Manipulatives – Point plotter SOL A.7 The student will investigate and analyze http://nlvm.usu.edu/en/nav/fram
es_asid_331_g_4_t_2.html?from=
functions (linear and quadratic) families and their category_g_4_t_2.html
characteristics both algebraically and graphically,
Graphing and the Coordinate
Plan: Maze Game:
including
a)
b)
c)
d)
e)
f)
determining whether a relation is a
function;
domain and range;
zeros of a function;
x- and y-intercepts;
finding the values of a function for
elements in its domain; and
making connections between and among
multiple representations of functions
including concrete, verbal, numeric,
graphic, and algebraic.
http://www.shodor.org/interacti
vate/lessons/GraphingCoordinat
e/
Draw a Haunted House: Cool way
to Graph Coordinates and
transform the shape:
http://www.themathlab.com/Pre
Algebra/graphing/hauntedhouse.
htm
Algebra I page 10
in the domain is paired with a unique element of
the range.
 The values of f(x) are the ordinates of the points
of the graph of f.
 The object f(x) is the unique object in the range of
the function f that is associated with the object x
in the domain of f.
 For each x in the domain of f, x is a member of
the input of the function f, f(x) is a member of the
output of f, and the ordered pair [x, f(x)] is a
member of f.
 An object x in the domain of f is an x-intercept or
a zero of a function f if and only if f(x) = 0.
 Set builder notation may be used to represent
domain and range of a relation.
----------------------------------------------------What is a function?
 In the equation b=a-2, which variable is the
independent variable and which is the dependent
variable? Explain.
 Compare and contrast independent/dependent,
input/output, abscissa/ordinate, and
domain/range.
 Draw a mapping diagram for a function with 6
inputs. Then make a table to represent the
function.
 Given the graph of a function, how can you write
a rule for the function? Describe.
Identify Domain and Range
Given a table of x and y values, how do you determine
the domain and range of the function?
How can you determine whether a relation is a function?


Create a relation that is a function. Explain how
you determine this relation is function.
Are all linear graphs functions (include vertical,
A.7 Essential Knowledge and Skills
 Determine whether a relation, represented
by a set of ordered pairs, a table, or a graph is
a function.
 Identify the domain, range, zeros, and
intercepts of a function presented
algebraically or graphically.
 Represent relations and functions using
concrete, verbal, numeric, graphic, and
algebraic forms. Given one representation,
students will be able to represent the relation
in another form.
 Detect patterns in data and represent arithmetic
and geometric patterns algebraically.
 Determine whether a relation, represented by a
set of ordered pairs, a table, or a graph is a
function.
Emphasize:
 Types of graphs(absolute
value, quadratics, linear,
exponential, etc…)
 Independent and
Dependent variables
 Domain and range given
a graph
 Function and set
notation
Project Graduation – lesson 9
National Library of Virtual
Manipulatives – Function
machine http://nlvm.usu.edu/en/nav/fra
mes_asid_191_g_4_t_2.html?fro
m=category_g_4_t_2.html
National Library of Virtual
Manipulatives – Grapher http://nlvm.usu.edu/en/nav/fra
mes_asid_189_g_4_t_2.html?op
en=activities&from=category_g_
4_t_2.html
Emphasize:
Solving for y
Parent graphs
F(x)
Use set builder notation to
represent solution sets of
equations and inequalities.
Recommended activities:
Algebra I page 11
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


3 blocks
horizontal, as well as diagonal)?
Given a value of x, how do you determine f(x)?
What is an x-intercept or a zero of a function?
Why do we use set-builder notation?
In your own words describe function notation.
Assessment, Enrichment, and Remediation
Explore Learning
Think Linearly: Are these linear
situations? :
http://www.themathlab.com/Alg
ebra/linear%20functions%20regr
essions%20slope/thnklinear.htm
Algebra I page 12
Number
of Blocks
3 blocks
Topics, Essential Questions, and Essential
Understandings
(Students should be able to answer essential
questions.)
Standard(s) of Learning
Essential Knowledge and Skills
Linear Functions, continued from Quarter
1
Graphing Equations and Inequalities
8 blocks
Additional Instructional
Resources/Comments
A.6 Essential Questions
Slope/rate of change
 What does the slope of a line represent?
 How do you find the slope of a line given the
equation? Given the graph?
 Why can slope be interpreted as a rate of
change?
x and y intercepts
 How does identifying the x and y-intercepts of
a linear equation help you graph the line?
Slope intercept form
 Why is the equation y=mx+b referred to as the
slope intercept form of a linear equation?
 How do you graph linear equations given in
slope-intercept form?
Graphing inequalities
 How do we know which half-plane to shade
when we are graphing inequalities with two
variables?
 Describe the graph of solutions of a linear
inequality.
 What is a solution to an inequality?
 Explain your process used to solve an
inequality.
SOL A.6 The student will graph linear equations and
linear inequalities in two variables, including
a) determining the slope of a line when given an
equation of the line, the graph of the line, or
two points on the line. Slope will be
described as rate of change and will be
positive, negative, zero, or undefined; ….
A.6 Essential Knowledge and Skills
 Graph linear equations and inequalities in two
variables, including those that arise from a
variety of real-world situations.
 Use the parent function y = x and describe
transformations defined by changes in the
slope or y-intercept.
 Find the slope of the line, given the equation
of a linear function.
 Find the slope of a line, given the coordinates
of two points on the line.
 Find the slope of a line, given the graph of a
line.
 Recognize and describe a line with a slope that
is positive, negative, zero, or undefined.
Emphasize:
Think Linearly: Are these
linear situations? :
http://www.themathlab.com/
Algebra/linear%20functions%
20regressions%20slope/thnkl
inear.htm
Slope: Find Your Other Half:
http://www.themathlab.com
/Algebra/findyourotherhalf/sl
opecards.html
Algebra with Cockroaches
http://hotmath.com/hotmath
_help/games/kp/kp_hotmath
_sound.swf
NLVM – Function
Transformations http://nlvm.usu.edu/en/nav/f
rames_asid_329_g_4_t_2.ht
ml?open=activities&from=cat
egory_g_4_t_2.html
Algebra I page 13

Create an example using inequalities in the
real world.
Parallel and perpendicular lines
 What is the relationship between the slopes of
parallel lines?
 Explain the process you would use to find a
line parallel to the line y=-3x+2.
 What is the relationship between the slopes of
perpendicular lines?
 Explain the process you would use to find a
line perpendicular to the line y=-3x+2.
Transformations
 Come up with a set of three functions that
would be considered a family of functions.
Explain.
 How is the graph of f(x)=x related to the graph
of h(x)=-2x-3?
 How can changes in slope affect a graph?
 How can changes in the y-intercept affect a
graph?
 Compare and contrast graphing by using a
table of values,slope, x- and y- intercepts, and
transformations.
A.6 Essential Understandings
 Changes in slope may be described by
dilations or reflections or both.
 Changes in the y-intercept may be described
by translations.
 Linear equations can be graphed using slope,
x- and y-intercepts, and/or transformations of
the parent function.
 The slope of a line represents a constant rate
of change in the dependent variable when the
independent variable changes by a constant
amount.

Use transformational graphing to investigate
effects of changes in equation parameters on
the graph of the equation.
NLVM – line plotter http://nlvm.usu.edu/en/nav
/frames_asid_332_g_4_t_2.
html?from=category_g_4_t_
2.html
Texas Instruments – Algebra
Town (TI-Nspire needed) http://education.ti.com/edu
cationportal/activityexchang
e/Activity.do?cid=US&aId=1
0501
Understanding Graphing and
using a Linear Inequality:
http://www.themathlab.co
m/Algebra/linear%20functio
ns%20regressions%20slope/i
nequalities/pizzaland.htm
Texas Instruments –
Function Junction http://education.ti.com/edu
cationportal/activityexchang
e/Activity.do?cid=US&aId=9
333
Algebra I page 14

The equation of a line defines the relationship
between two variables.
 The graph of a line represents the set of points
that satisfies the equation of a line.
 A line can be represented by its graph or by an
equation.
 The graph of the solutions of a linear
inequality is a half-plane bounded by the
graph of its related linear equation. Points on
the boundary are included unless it is a strict
inequality.
 Parallel lines have equal slopes.
 The product of the slopes of perpendicular
lines is -1 unless one of the lines has an
undefined slope.
Solving Equations and Inequalities
A.4 a, b, e, f Essential Questions
5 blocks
A.4 a, b, e, f Essential Understandings
 A solution to an equation is the value or set of
values that can be substituted to make the
equation true.
 The solution of an equation in one variable can
be found by graphing the expression on each
side of the equation separately and finding the
x-coordinate of the point of intersection.
 Real-world problems can be interpreted,
represented, and solved using linear
equations.
 The process of solving linear equations can be
modeled in a variety of ways, using concrete,
pictorial, and symbolic representations.
Texas Instruments – Slope,
parallel and perpendicular
lines (TI
-Nspire) http://education.ti.com/edu
cationportal/activityexchang
e/Activity.do?cid=US&aId=1
1531
SOL A.4 a, b, e, f The student will solve multistep
linear … equations in two variables, including
a) solving literal equations (formulas) for a given
variable;
b) justifying steps used in simplifying expressions
and solving equations, using field properties
and axioms of equality that are valid for the set
of real numbers and its subsets;
d)
f)
solving multistep linear equations
algebraically and graphically;
solving real-world problems
A.4 a, b, e, f Essential Knowledge and Skills
 Solve a literal equation (formula) for a
specified variable.
 Simplify expressions and solve equations,
using the field properties of the real numbers
and properties of equality to justify
simplification and solution.
AlgeblocksTM and Equation
Solving
p. 26
Greetings pp. 27-28
AlgeblocksTM: Solving for y p.
29
AlgeblocksTM: Solving
Inequalities
p. 30
A Mystery to Solve p. 31
Solving Linear Equations pp.
32-33
Algebra I page 15


Properties of real numbers and properties of
equality can be used to justify equation
solutions and expression simplification.
Set builder notation may be used to represent
solution sets of equations.
A.8 Essential Questions
 What does the constant of proportionality
represent in a direct variation?
 What does the constant of proportionality
represent in an inverse variation?
 What is the difference between a direct
variation equation and an inverse variation
equation? Explain.
If the variables x and y vary inversely, how does
the value of y change if the value of x is
doubled? Tripled? Give examples.


Solve multistep linear equations in one
variable.
Confirm algebraic solutions to linear

equations, using a graphing calculator.
Determine if a linear equation in one
variable has one, an infinite number, or no
solutions.†
~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL A.8 The student, given a situation in a realworld context, will analyze a relation to determine
whether a direct or inverse variation exists, and
represent a direct variation algebraically and
graphically and an inverse variation algebraically.
A.5 a, b, c Essential Questions
A.5 a, b, c Essential Understandings
 A solution to an inequality is the value or set
of values that can be substituted to make the
Essential Knowledge and Skills
 Given a situation, including a real-world
situation, determine whether a direct variation
exists.
 Given a situation, including a real-world
situation, determine whether an inverse
variation exists.
 Write an equation for a direct variation, given
a set of data.
 Write an equation for an inverse variation,
Emphasize:
Function patterns
Real world context
Textbook reference: Ch 4, 12
Texas Instruments – Inverse
variation and constant of
variation http://education.ti.com/educ
ationportal/activityexchange/
Activity.do?cid=US&aId=1839
Texas Instruments – Direct,
inverse, and joint variation http://education.ti.com/educ
ationportal/activityexchange/
Activity.do?cid=US&aId=1839
Algebra I page 16



inequality true.
Real-world problems can be modeled and
solved using linear inequalities.
Properties of inequality and order can be used
to solve inequalities.
Set builder notation may be used to represent
solution sets of inequalities.
given a set of data.
Graph an equation representing a direct
variation, given a set of data.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL A.5 a, b, c The student will solve multistep linear
inequalities in two variables, including
a) solving multistep linear inequalities
algebraically and graphically;
b) justifying steps used in solving inequalities,
using axioms of inequality and properties of
order that are valid for the set of real numbers
and its subsets;
c) solving real-world problems involving
inequalities; and
A.5 a, b, c Essential Knowledge and Skills




5 blocks
Solve multistep linear inequalities in one
variable.
Justify steps used in solving inequalities,
using axioms of inequality and properties
of order that are valid for the set of real
numbers.
Solve real-world problems involving
inequalities.
Solve systems of linear inequalities
algebraically and graphically.
Solving Systems of Equations and Inequalities
A.4 a, b, e, f Essential Questions
SOL A.4 a, b, e, f The student will solve multistep
linear and quadratic equations in two variables,
including
~~~~~~~~~~~~~~~~~
Emphasize:
 the calculator to
graph and find
solution

Use Set Builder
notation to represent
solution sets of
equations and
inequalities
Project graduation – lesson 8
Texas Instruments – angles
and systems of equations http://education.ti.com/educ
ationportal/activityexchange/
Activity.do?cid=US&aId=1065
7
Algebra I page 17
a) solving literal equations (formulas) for a given
variable;
b) justifying steps used in simplifying expressions
and solving equations, using field properties and
axioms of equality that are valid for the set of
real numbers and its subsets;
e) solving systems of two linear equations in two
variables algebraically and graphically; and
f) solving real-world problems involving equations
and systems of equations.
Graphing calculators will be used both as a primary
tool in solving problems and to verify algebraic
solutions.
A.4 a, b, e, f Essential Understandings
 A system of linear equations with exactly one





solution is characterized by the graphs of two
lines whose intersection is a single point, and
the coordinates of this point satisfy both
equations.
A system of two linear equations with no
solution is characterized by the graphs of two
lines that are parallel.
A system of two linear equations having
infinite solutions is characterized by two
graphs that coincide (the graphs will appear to
be the graph of one line), and the coordinates
of all points on the line satisfy both equations.
Systems of two linear equations can be used
to model two real-world conditions that must
be satisfied simultaneously.
Equations and systems of equations can be
used as mathematical models for real-world
situations.
Set builder notation may be used to represent
solution sets of equations.
A.4 a, b, e, f Essential Knowledge and Skills
 Given a system of two linear equations in two

A.5 d Essential Questions

A.5 d Essential Understandings
 A solution to an inequality is the value or set




of values that can be substituted to make the
inequality true.
Real-world problems can be modeled and
solved using linear inequalities.
Properties of inequality and order can be used
to solve inequalities.
Set builder notation may be used to represent
solution sets of inequalities.

variables that has a unique solution, solve the
system by substitution or elimination to find
the ordered pair which satisfies both
equations.
Given a system of two linear equations in two
variables that has a unique solution, solve the
system graphically by identifying the point of
intersection.
Determine whether a system of two linear
equations has one solution, no solution, or
infinite solutions.
Write a system of two linear equations that
models a real-world situation.
Interpret and determine the reasonableness of
the algebraic or graphical solution of a system
of two linear equations that models a realworld situation.
SOL A.5 d The student will solve multistep linear
inequalities in two variables, including
Algebra I page 18
d) solving systems of inequalities.
A.5 d Essential Knowledge and Skills
 Solve real-world problems involving

3/4
blocks
Enrichment, Assessment, and Remediation
inequalities.
Solve systems of linear inequalities
algebraically and graphically.
Algebra I Quarter 3
Number
of
Blocks
Writing Linear Equations
A.6 b Essential Questions
6 blocks
Standard(s) of Learning
Topics, Essential Questions, and
Essential Understandings
( Students should be able to answer essential
questions.
Slope intercept form

State the slope-intercept form of a linear
equation and explain why this form is called slopeintercept form.

How can you find the equation of a line when
you are given two points?
Point-slope form
How do you write linear equations in point slope
form when given two points?
Standard form

How do you write an equation in standard
form if you are given the slope- intercept form?
Point-slope form?

How do you write an equation in standard
form if you are given two points?

For what form of a linear equation (slopeintercept, standard, or point – slope) would you
most likely use x and y-intercepts to graph the
line?

Given the graph of a line, write the equation
of that line in slope-intercept, point slope, and
standard form.

What does the equation of a line define?

What are two ways a line can be
represented?
Essential Knowledge and Skills
SOL A.6 b The student will graph linear equations
and linear inequalities in two variables, including
a)
determining the slope of a line when given an
equation of the line, the graph of the line, or two
points on the line. Slope will be described as rate of
change and will be positive, negative, zero, or
undefined; and
b)
writing the equation of a line when given the
graph of the line, two points on the line, or the slope
and a point on the line.
A.6 b Essential Knowledge and Skills
 Find the slope of a line, given the coordinates of




two points on the line.
Find the slope of a line, given the graph of a line.
Recognize and describe a line with a slope that is
positive, negative, zero, or undefined.
Use transformational graphing to investigate
effects of changes in equation parameters on the
graph of the equation.
Write an equation of a line when given the graph
of a line.
Additional Instructional
Resources/Comments
Algebra I Quarter 3
Parallel and perpendicular lines

Create two parallel lines and prove they are
parallel.

How could you prove that two lines are
perpendicular? Create two perpendicular lines and
prove they are perpendicular.
Horizontal and vertical lines

Use the definition of slope to explain why the
slope of a horizontal line is zero.

Use the definition of slope to determine why
the slope of a vertical line is undefined.

Relate the equation of a horizontal and
vertical line to its respective equation.
A.6 b Essential Understandings
 Changes in slope may be described by




dilations or reflections or both.
The slope of a line represents a constant rate
of change in the dependent variable when
the independent variable changes by a
constant amount.
The equation of a line defines the
relationship between two variables.
The graph of a line represents the set of
points that satisfies the equation of a line.
A line can be represented by its graph or by
an equation.
A.11 Essential Questions
Curve of best fit
Why do we want to find a curve of best fit?
 How can you tell whether a table of values
represents a quadratic function? Explain
 Create three different data sets with one
representing a linear function, one an
SOL A.11 The student will collect and analyze
data, determine the equation of the curve of
best fit in order to make predictions, and solve
real-world problems, using mathematical
models. Mathematical models will include
linear and quadratic functions.
Algebra I Quarter 3

exponential function, and one a quadratic
function.
What considerations affect experimental
design?
A.11 Essential Understandings
 The graphing calculator can be used to



16
blocks
determine the equation of a curve of best fit
for a set of data.
The curve of best fit for the relationship
among a set of data points can be used to
make predictions where appropriate.
Many problems can be solved by using a
mathematical model as an interpretation of a
real-world situation. The solution must then
refer to the original real-world situation.
Considerations such as sample size,
randomness, and bias should affect
experimental design.
A.11 Essential Knowledge and Skills




Write an equation for a curve of best fit, given a
set of no more than twenty data points in a table,
a graph, or real-world situation.
Make predictions about unknown outcomes,
using the equation of the curve of best fit.
Design experiments and collect data to address
specific, real-world questions.
Evaluate the reasonableness of a mathematical
model of a real-world situation.
Polynomials
SOL A.2 The student will perform operations on
Laws of exponents
polynomials, including
 Write three expressions involving
a) applying the laws of exponents to perform
products of powers, powers of powers,
operations on expressions;
and powers of products that are
b) adding, subtracting, multiplying, and dividing
equivalent to 12x8
polynomials; and
 Write three expressions involving
c) factoring completely first- and second-degree
quotients that are equivalent to 14x7
binomials and trinomials in one or two variables.
 Explain how an expression can be
Graphing calculators will be used as a tool for
manipulated to make negative exponents
factoring and for confirming algebraic
positive.
factorizations.
Emphasize factoring
 by Greatest
Common Factor
 with lead
coefficient of one
 with lead
coefficient other
than one
 using special
products
 Area and
perimeter
 Algebra tiles
Algebra I Quarter 3
Scientific notation
 Provide a number written in scientific
notation. Convert this number to be in
standard form as well.
Adding, subtracting,
Multiplying, dividing polynomials
 Compare and contrast the different
processes to multiply polynomials?
 Write two binomials that have the
product x2+12
 Divide polynomials by monomials
 What are the steps you would take to
divide a polynomial by a monomial? Give
an example.
 What is the unifying concept for
polynomial operations?
Factoring
 Write an equation of the form x2+bx+c=0
that has solutions -4 and 6. Explain how
you found your answer.
 Why does the difference of two squares
work? Why isn’t there a formula for the
sum of two squares?
 How do you know when a polynomial is
completely factored. Give an example.
 Which operation does factoring reverse?
 What is a prime polynomial expression?
Give an example.
 Describe the relationship between the
factors of any polynomial and the xintercepts of the graph of its relation.
 Divide polynomials by binomials
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations
to
 Simplify monomial expressions and ratios of
monomial expressions in which the
exponents are integers, using the laws of
exponents.
 Model sums, differences, products, and
quotients of polynomials with concrete
objects and their related pictorial
representations.
 Relate concrete and pictorial manipulations
that model polynomial operations to their
corresponding symbolic representations.
 Find sums and differences of polynomials.
 Find products of polynomials. Find the
quotient of polynomials, using a monomial or
binomial divisor, or a completely factored
divisor.
 Factor completely first- and second-degree
polynomials.
 Identify prime polynomials.
 Use the x-intercepts from the graphical
representation of the polynomial to
determine and confirm its factors.
Project graduation –
lesson 2
Project graduation –
lesson 3
Project graduation –
lesson 4
NLVM – Algebra Tiles http://nlvm.usu.edu/en/
nav/frames_asid_189_g_
4_t_2.html?open=activiti
es&from=category_g_4_t
_2.html
Texas Instruments –
Factored Polynomials http://education.ti.com/
educationportal/activitye
xchange/Activity.do?cid=
US&aId=6168
Algebra I Quarter 3

2/3
blocks
How is dividing a polynomial by a
binomial different than dividing a
polynomial by a monomial? Explain.
Assessment, Enrichment, and Remediation
Algebra I Quarter 4
Number
of Blocks
Topic and Essential Questions
Standard(s) of Learning
Additional Instructional
Resources/Comments
Essential Knowledge and Skills
Essential Understandings
16 blocks
Quadratic Equations and Functions
Graphing
 What steps would you take to graph a quadratic
function in standard form? Explain.
Domain and Range
 Explain how you can tell whether the graph of a
quadratic function opens up or down.
Axis of symmetry
 What is an axis of symmetry? What does it
represent?
Zeros, roots, solutions
 Compare and contrast zeros, roots, x-intercepts,
and solutions of a graph.
 Describe how you to write the factored form of a
quadratic given the roots.
Essential Knowledge and Skills
 Determine whether a relation, represented by
a set of ordered pairs, a table, or a graph is a
function.
 Identify the domain, range, zeros, and
intercepts of a function presented
Explain what the zero-product property is and
algebraically or graphically.
why it is useful. Give an example to illustrate your
 For each x in the domain of f, find f(x).
explanation.
 Represent relations and functions using
Describe two methods for solving a quadratic
concrete, verbal, numeric, graphic, and
2
equation of the form ax +c=0
algebraic forms. Given one representation,
Give values for a and c so that ax2+c=0 has (a)
students will be able to represent the relation
two solutions, (b) one solution, and (c) no real
in another form.
solution.
Solve quadratic equations by graphing, factoring,
completing the square and quadratic formula
 How can you determine the number of solutions
of a quadratic equation by looking at the graph?
Explain.



SOL A.7 The student will investigate and analyze
function (linear and quadratic) families and their
characteristics both algebraically and graphically,
including
a) determining whether a relation is a function;
b) domain and range;
c) zeros of a function;
d) x- and y-intercepts;
e) finding the values of a function for elements in
its domain; and
f) making connections between and among
multiple representations of functions including
concrete, verbal, numeric, graphic, and
algebraic.
Emphasize:
 real world
applications

calculator for
equation of curve
of best fit

Given a context, is
it linear or
quadratic?


Meaning of a zero
Use Set Builder
notation to
represent solution
sets of equations
and inequalities.
Represent relations
and functions using
concrete, verbal,
numeric, graphic, and
algebraic forms. Given
one representation,
students will be able
to represent the
relation in another
form.
Algebra I Quarter 4

Give an example of an expression that is a perfect
square trinomial. Explain why the expression is a
perfect square trinomial.
 How many solutions does x2+bx=c have if c<(b/2)2? Explain.
 What method(s) would you use to solve –
x2+8x=1? Explain your choice(s).
Discriminant
 How is the discriminant of ax2+bx+c=0 related to
the graph of y=ax2+bx+c? Explain.
 How can the discriminant be used to determine
how many solutions an equations has?
Simplifying square roots
 Describe two different sequences of steps that
you could take to simplify the expression sqrt(45)
* sqrt (5).
Curve of best fit
Why do we want to find a curve of best fit?
 How can you tell whether a table of values
represents a quadratic function? Explain
 Create three different data sets with one
representing a linear function, one an
exponential function, and one a quadratic
function.
 What considerations affect experimental design?
 How does the parent graph, y = x2, transform to
the curve of best fit?

Detect patterns in data and represent
arithmetic and geometric patterns
algebraically.
SOL A.4 b The student will solve multistep
quadratic equations in two variables, including
b) justifying steps used in simplifying expressions
and solving equations, using field properties
and axioms of equality that are valid for the set
of real numbers and its subsets;
Essential Knowledge and Skills
Simplify expressions and solve equations, using the
field properties of the real numbers and
properties of equality to justify simplification and
solution.
 Solve quadratic equations.
 Identify the roots or zeros of a quadratic
function over the real number system as the
solution(s) to the quadratic equation that is
formed by setting the given quadratic
expression equal to zero.
 Solve multistep linear equations in one
variable.
 Confirm algebraic solutions to linear and
quadratic equations, using a graphing
calculator.
SOL A.4 b, c, f The student will solve multistep
linear and quadratic equations in two variables,
including
b) justifying steps used in simplifying
expressions and solving equations, using
field properties and axioms of equality that
If short on time, move
completing the square to
post-SOL
Project Graduation Lesson 4
Texas Instruments –
The discriminanthttp://education.ti.co
m/educationportal/act
ivityexchange/Activity.
do?cid=US&aId=1608
Texas Instruments –
Quadratic Functions http://education.ti.co
m/educationportal/act
ivityexchange/Activity.
do?cid=US&aId=3512
Texas Instruments –
Introduction to
quadratic equations
(TI-Nspire) http://education.ti.co
m/educationportal/act
ivityexchange/Activity.
do?cid=US&aId=11832
Algebra I Quarter 4
are valid for the set of real numbers and its
subsets;
c) solving quadratic equations algebraically
and graphically; …
f) solving real-world problems involving
equations and systems of equations.
Graphing calculators will be used both as a
primary tool in solving problems and to
verify algebraic solutions.
Essential Knowledge and Skills
 Simplify expressions and solve equations,
using the field properties of the real numbers
and properties of equality to justify
simplification and solution.
 Solve quadratic equations.
 Identify the roots or zeros of a quadratic
function over the real number system as the
solution(s) to the quadratic equation that is
formed by setting the given quadratic
expression equal to zero.
 Confirm algebraic solutions to linear and
quadratic equations, using a graphing
calculator.
SOL A.11 The student will collect and analyze
data, determine the equation of the curve of
best fit in order to make predictions, and solve
real-world problems, using mathematical
models. Mathematical models will include
linear and quadratic functions.
Algebra I Quarter 4
Essential Knowledge and Skills
 Write an equation for a curve of best fit, given
a set of no more than twenty data points in a
table, a graph, or real-world situation.
 Make predictions about unknown outcomes,
using the equation of the curve of best fit.
 Design experiments and collect data to
address specific, real-world questions.
 Evaluate the reasonableness of a
mathematical model of a real-world situation.
6 blocks
Enrichment, Assessment, and Remediation
4 blocks
Review for Geometry and Algebra II
Algebra I Quarter 4
Prepare for geometry and/or Algebra II
Geometry Prep
Pythagorean Theorem
 If you are given the measurements of all three sides of a triangle, how can you prove that it is a right triangle? Give an example.
 What equation could be used to find side b of a right triangle if sides a and c are given?
Distance and midpoint formulas
 How is the distance formula similar to the Pythagorean Theorem?
 If you want to find the distance between two points, does it matter which point represents (x1,y1) and which point represents (x2,y2)? Explain.
Ratios and proportions
Radical expressions and equations
Algebra II prep
Radical expressions and equations
Absolute Value Equations and Inequalities in one variable
 Explain the procedure you would use to solve an absolute value equation.
 How can you solve an equation that has both an inequality and an absolute value?
Compound inequalities
 How do you solve compound inequalities?
Explain the difference between an ‘and’ inequality and an ‘or’ inequality?
Virginia Department of Education website:
http://www.doe.virginia.gov/instruction/high_school/mathematics/index.shtml
The following items can be found on the link above.
 Technical Assistance Document: 2009 Algebra I Standard of Learning A.9
 Algebra I Materials – Project Grad
 Mathematics Vocabulary - Definitions of concepts in mathematics that teachers and students should know and understand in order to learn math
content. Note: This includes vocabulary through Algebra II.
 Algebra I Formula Sheet
 Enhanced Scope and Sequence 2004
A variety of interactive games for http://www.regentsprep.org/Regents/math/ALGEBRA/games/Aquiapage.htm
Opportunities for differentiation:
Algebra I Quarter 4
Real life application on a daily basis (understanding the meaning of the data, critical thinking)
Writing out explanations in words to show understanding and processes
Gathering their own data
Unit projects on applications
Cross-curricular applications
Open-ended questions