2013 - 2014
Algebra 1
MATHEMATICS
Curriculum Map
Common Core State Standards
Common Core State Standards
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. (MACC.K12.MP.1)
Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process
which sometimes requires perseverance, flexibility, and a bit of ingenuity.
2. Reason abstractly and quantitatively. (MACC.K12.MP.2)
The concrete and the abstract can complement each other in the development of mathematical understanding:
representing a concrete situation with symbols can make the solution process more efficient, while reverting to a concrete
context can help make sense of abstract symbols.
3. Construct viable arguments and critique the reasoning of others. (MACC.K12.MP.3)
A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and
supporting evidence.
4. Model with mathematics. (MACC.K12.MP.4)
Many everyday problems can be solved by modeling the situation with mathematics.
5. Use appropriate tools strategically. (MACC.K12.MP.5)
Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen
mathematical understanding.
6. Attend to precision. (MACC.K12.MP.6)
Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical
explanations.
7. Look for and make use of structure. (MACC.K12.MP.7)
Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.
8. Look for and express regularity in repeated reasoning. (MACC.K12.MP.8)
Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results
more quickly and efficiently.
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Algebra 1: Common Core State Standards
The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The critical areas,
called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear
models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Mathematical
Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a
coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
Relationships Between Quantities and Reasoning with Equations: By the end of eighth grade students have learned to solve linear equations in
one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds
on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing,
interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the
solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential
equations. All of this work is grounded on understanding quantities and on relationships between them.
SKILLS TO MAINTAIN:
Reinforce understanding of the properties of integer exponents. The initial experience with exponential expressions, equations, and functions
involves integer exponents and builds on this understanding.
Linear and Exponential Relationships: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships
between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They explore many
examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between
representations, and understand the limitations of various representations. Students build on and informally extend their understanding of
integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between
additive and multiplicative change. Students explore systems of equations and inequalities, and they find and interpret their solutions. They
interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.
Expressions and Equations: In this unit, students build on their knowledge from the unit of Linear and Exponential Relationships, where they
extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see
structure in and create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving
quadratic expressions.
Quadratic Functions and Modeling: In this unit, students consider quadratic functions, comparing the key characteristics of quadratic functions
to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the
graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic
equation as the zeros of a related quadratic function. Students expand their experience with functions to include more specialized functions—
absolute value, step, and those that are piecewise-defined.
Descriptive Statistics: This unit builds upon students’ prior experiences with data, providing students with more formal means of assessing how
a model fits data. Students use regression techniques to describe and approximate linear relationships between quantities. They use graphical
representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at
residuals to analyze the goodness of fit.
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Algebra 1: Common Core State Standards At A Glance
First Quarter
DSA
Unit - Real Number System
MACC.912.N-RN.2.3
Unit 1- Solving Equations
and Inequalities
MACC.912.A-CED.1.1
MACC.912.A.-REI.1.1
*MA.912.A.5.4
MACC.912.A-CED.1.3
MACC.912.A-CED.1.4
MACC.912.A-REI.2.3
DIA 1 (Unit 1)
Unit 2- Linear Equations and Their
Graphs
MACC.912.F-IF.1.1
MACC.912.F-IF.1.2
MACC.912.F-IF.2.5
MACC.912.F-IF.2.4
MACC.912.F-IF.2.6
MACC.912.A-CED.1.2
*MA.912.G.1.4(Assessed with
MA.912A.A.1.4)
DIA 2 Part A
Second Quarter
Unit 2- Linear Equations and Their
Graphs (cont)
MACC.912.A-REI.4.10
MACC.912.F-IF.3.7a
MACC.912.F-LE.2.5
Unit 3- Systems of Linear
Equations and Inequalities
MACC.912.A.-REI.3.5
MACC.912.A.-REI.3.6
MACC.912.A-REI.4.11
MACC.912.A.-REI.4.12
MACC.912.A-CED.1.3
DIA 2 Part B
Unit 4-Properties of Exponents
MACC.912.N-RN.1.1
MACC.912.N-RN.1.2
MACC.912.F-IF.3.8b
SSA
N-RN: Real Number System
A-REI: Reasoning with Equations and Inequalities
F-BF: Building Functions
F-LE: Linear, Quadratic and Exponential Models
S-ID: Interpreting Data
Mathematics Department
Volusia County Schools
Third Quarter
Unit 5- Polynomials
MACC.912.A-SSE.1.1
MACC.912.A-SSE.1.2
MACC.912.A-APR.1.1
Unit 6-Factoring and Solving
Polynomials
MACC.912.A-SSE.1.1
MACC.912.A-SSE.1.2
MACC.912.A-SSE.2.3
(MA.912.A.4.3)
MACC.912.A-REI.2.4
MACC.912.A-APR.2.3
DIA 3 (Unit 6)
Unit 7- Non –Linear Functions
MACC.912.F-IF.2.4
MACC.912.F-IF.3.7a
MACC.912.F-IF.3.8a
MACC.912.F-IF.3.7b,c,e
MACC.912.F-IF.3.9
MACC.912.F-BF.2.3
MACC.912.A.-REI.4.11
Fourth Quarter
Unit 7- Non –Linear Functions(cont)
MACC.912.F-IF.1.3
MACC.912.F-LE.1.2
MACC.912.F-BF.1.1
MACC.912.A-CED.1.1
MACC.912.F-LE.1.3
MACC.912.F-LE.1.1
MACC.912.F-LE.2.5
MACC.912.A-REI.4.11
DIA 4 (Unit 7)
Unit 8-Interpreting Categorical and
Quantitative Data
*MA.912.D.7.1
*MA.912.D.7.2
Diagnostic EOC
MACC.912.S-ID.1.1
MACC.912.S-ID.1.2
MACC.912.S-ID.1.3
MACC.912.S-ID.2.6
MACC.912.S-ID.3.7
MACC.912.S-ID.3.8
MACC.912.S-ID.3.9
MACC.912.S-ID.2.5
A-CED: Create Equations that Describe Relationships
A-APR: Arithmetic with Polynomials & Rational Expressions
F-IF: Interpreting Functions
A-SSE: Seeing Structure in Expressions
Algebra 1 Curriculum Map
October 22, 2013
Fluency Recommendations
A/G- Algebra I students become fluent in solving characteristic problems involving the analytic geometry of lines, such as writing
down the equation of a line given a point and a slope. Such fluency can support them in solving less routine mathematical problems
involving linearity, as well as in modeling linear phenomena (including modeling using systems of linear inequalities in two
variables).
A-APR.1- Fluency in adding, subtracting, and multiplying polynomials supports students throughout their work in Algebra, as well as
in their symbolic work with functions. Manipulation can be more mindful when it is fluent.
A-SSE.1b- Fluency in transforming expressions and chunking (seeing parts of an expression as a single object) is essential in factoring,
completing the square, and other mindful algebraic calculations.
The following Mathematics and English Language Arts CCSS should be taught throughout the course:
MACC.912.N-Q.1.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
MACC.912.N-Q.1.2: Define appropriate quantities for the purpose of descriptive modeling.
MACC.912.N-Q.1.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
LACC.910.RST.1.3: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements or
performing tasks, attending to special cases or exceptions defined in the text.
LACC.910.RST.2.4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in
context and topics.
LACC.910.RST.3.7: Translate quantitative or technical information expressed in words in a text into visual form and translate
information expressed visually or mathematically into words.
LACC.910.SL.1.1: Initiate and participate effectively in a range of collaborative discussions with diverse partners.
LACC.910.SL.1.2: Integrate multiple sources of information presented in diverse media or formats evaluating the credibility and
accuracy of each source.
LACC.910.SL.1.3: Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning
or exaggerated or distorted evidence.
LACC.910.SL.2.4: Present information, findings and supporting evidence clearly, concisely, and logically such that listeners can follow
the line of reasoning.
LACC.910.WHST.1.1: Write arguments focused on discipline-specific content.
LACC.910.WHST.2.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task,
purpose, and audience.
LACC.910.WHST.3.9: Draw evidence from informational texts to support analysis, reflection, and research.
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
The Real Number System- Review
Essential Question(s): How does knowledge of integers help when working with rational and irrational numbers?
Standard
The students will:
MACC.912.N-RN.2.3.
Explain why the sum or product
of two rational numbers is
rational; that the sum of a rational
number and an irrational number
is irrational; and that the product
of a nonzero rational number and
an irrational number is irrational.
SMP #2, #3
Learning Goals
I can:
 classify real numbers as rational or irrational
according to their definitions.
 add, subtract, multiply and divide real
numbers.
 explain why the sum of two rational numbers
is rational.
 explain why the product of two rational
numbers is rational.
 explain why the sum of a rational and
irrational is irrational.
Remarks
Resources
This unit should be treated
as a review and be
completed within 7 days.
Algebra 1 resources for all sections:
Illustrative mathematics: provides the standards with example problems that cover the standard.
http://www.illustrativemathematics.org/standards/hs
The Math Dude: http://www.montgomeryschoolsmd.org/departments/itv/mathdude/
Algebra Nation- http://www.algebranation.com/
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 1-Solving Equations and Inequalities
Essential Question(s):
How can algebra describe the relationship between sets of numbers?
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
Learning Goals
I can:
Remarks
Resources
The students will:
MACC.912A-CED.1.1.
*AlgebraNation.com
Students may believe that solving
 identify the variables and quantities
Create equations and
an equation such as 3x + 1 = 7
represented in a real world problem.
inequalities in one variable
involves “only removing the 1,”
 write the equation or inequality that
Mini-Projects/Tasks=
and use them to solve
failing to realize that the equation 1
best models the problem.
problems.
= 1 is being subtracted to produce
http://insidemathematic
 solve linear equations and
SMP#4
the next step.
s.org/problems-of-theinequalities.
month/pom interpret the solution in the context of
onbalance.pdf
the problem.
MACC.912A.REI.1.1
 explain a process to solve equations. When using Distributive Property,
http://insidemathematic
Explain each step in solving a  apply the distributive property when
students often multiply the number
s.org/common-coresimple equation as following
(or variable) outside the
necessary to solve equations.
math-tasks/highfrom the equality of numbers
 construct a viable argument to justify parentheses by the first term in the
asserted at the previous step,
parentheses, but neglect to multiply school/HS-Aa solution method.
2003%20Number%20To
starting from the assumption
that same number by the other
wers.pdf
that the original equation has
term(s) in the parentheses.
a solution. Construct a viable
Regarding variables on both sides,
argument to justify a solution
students often will try to combine the
method.
terms as if they are on the same
SMP#4
side of the equation rather than
eliminating one of the variables.
MA.912.A.5.4
Solve algebraic proportions
Mathematics Department
Volusia County Schools

solve algebraic proportions
NGSS
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 1-Solving Equations and Inequalities (cont)
Essential Question(s):
How can algebra describe the relationship between sets of numbers?
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
Learning Goals
I can:
Remarks
Resources
The students will:
MACC.912A.CED.1.3
Students may confuse the rule of reversing Mars Tasks:
 identify the variable and
Represent constraints by
the inequality when multiplying or dividing
http://insidemathemat
quantities represented in a realequations or inequalities, and by
by a negative number, with the need to
ics.org/commonworld problem.
systems of equations and/or
reverse
the
inequality
anytime
a
negative
core-math determine the best models for a
inequalities, and interpret
sign shows up in solving the last step of
tasks/highreal-world problem.
solutions as viable or non-viable
school/HS-A write inequalities that best models the inequality. Example:
options in a modeling context.
3x > -15 or x < - 5
2003%20Number%2
a problem.
SMP #4
(Rather than correctly using the rule: -3x
0Towers.pdf
>15 or x< -5)
http://insidemathemat
MACC.912A.CED.1.4
Students may struggle to solve literal
 solve a formula for a given
ics.org/commonRearrange formulas to highlight a
equations/ formulas due to not containing
variable.
core-mathquantity of interest, using the
any numbers, so reiterating that the same
 solve problems involving literal
tasks/highsame reasoning as in solving
steps (inverse operations) are used
equations.
equations.
whether dealing with eliminating a variable school/HS-F2008%20Functions.p
SMP #4
or number may be helpful.
df
MACC.912A.REI.2.3
Solve linear equations and
inequalities in one variable,
including equations with
coefficients represented by letters.
SMP #5, #7
Mathematics Department
Volusia County Schools

solve linear equations and
inequalities in one variable.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 2 - Linear Equations and Their Graphs
Clarification: Some of the CCSS in this unit include linear and non-linear learning goals. The focus for Unit 2 are
learning goals for linear functions and inequalities. Non-linear functions will be covered in Unit 7.
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
The students will:
MACC. 912.F-IF.1.1
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, the 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).
SMP #6, #7
Learning Goals
I can:
 define relation, domain and range.
 define a function as a relation in which
each input (domain) has exactly one
output (range).
 determine if a graph, table or set of
ordered pairs represent a function.
 determine if stated rules (both numeric
and non-numeric) produce ordered pairs
that form a function.
 explain that when ‘x’ is an element of the
input of a function f(x) represents the
corresponding output.
 explain that the graph of ‘f’ is the graph of
the equation y=f(x).
Remarks
Students may believe that all
relationships having an input and an
output are functions, and therefore,
misuse the function terminology.
Students may also believe that the
notation f(x) means to multiply some
value f times another value x. The
notation alone can be confusing and
needs careful development. For
example, f(2) means the output value
of the function f when the input value
is 2.
Students may believe that it is
reasonable to input any x-value into a
function, so they will need to examine
multiple situations in which there are
various limitations to the domains.
Other letters can be used for functional
notation e.g. g(x), p(x), etc…
Mathematics Department
Volusia County Schools
Resources
Tasks & Mini-Projects
http://insidemathematics
.org/common-coremath-tasks/highschool/HS-F2008%20Functions.pdf
http://insidemathematics
.org/common-coremath-tasks/highschool/HS-F2004%20Graphs2004.p
df
http://insidemathematics
.org/common-coremath-tasks/highschool/HS-F2006%20Printing%20Ti
ckets.pdf
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 2 - Linear Equations and Their Graphs (cont)
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
The students will:
MACC. 912.F-IF.1.2
Use function notation, evaluate
functions for inputs in their
domains, and interpret statements
that use function notation in terms
of a context.
SMP #7
MACC. 912.F-IF.2.5
Relate the domain of a function to
its graph and, where applicable, to
the quantitative relationship it
describes.
SMP #4
MACC. 912.F-IF.2.4
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.
SMP #1, #7, #8
Mathematics Department
Volusia County Schools
Learning Goals
I can:
 decode function notation and explain how the output of a function is
matched to its input.
 convert a table, graph, set of ordered pairs or description into
function notation by identifying the rule used to turn inputs into
outputs and writing the rule.
 use order of operations to evaluate a function for a given domain
value.
 identify the numbers that are not in the domain of a function.
 choose and analyze inputs (and outputs) that make sense based
on the problem.
 explain how the domain of a function is represented in its graph.
 state, defend and explain the appropriate domain of a function that
represents a problem situation.





Remarks
f(x)= 2x2 +
4….squares the
input, doubles the
square and adds
four to produce the
output
Given h(x) =
the
domain has to be
positive numbers
locate the information that explains what each quantity represents.
interpret the meaning of an ordered pair.
determine if negative inputs and/or outputs make sense in the
problem.
identify and explain the x and y intercept
define intervals of increasing and decreasing of a table or graph.
Algebra 1 Curriculum Map
October 22, 2013
Resources
Course: Algebra 1
Unit 2 - Linear Equations and Their Graphs (cont)
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
The students will:
MACC. 912.F-IF.2.6
Calculate and interpret the
average rate of change of a
function (presented
symbolically or as a table)
over a specified interval.
Estimate the rate of change
from a graph.
SMP #4, #5
MACC.912.A-CED.1.2
Create equation in two or
more variables to represent
relationships between
quantities; graph equations
on coordinate axes with
labels and scales
SMP #4
MA.912.G.1.4
Use coordinate geometry to
find slopes, parallel lines,
perpendicular lines, and
equations of lines.
(Assessed with
MA.912.A.3.10)
Mathematics Department
Volusia County Schools
Learning Goals
I can:
 define and explain interval, rate of
change and average rate of change.
 calculate the average rate of change of a
function, represented either by function
notation, a graph or a table over a specific
interval.
 compare the rates of change of two or
more functions
 interpret the meaning of the average rate
of change in the context of the problem.
 set up coordinate axes using an
appropriate scale and label the axes.
 write equations of lines in various forms.
 graph equations on coordinate axes with
appropriate labels and scales.

Remarks
Students may also believe that
the slope of a linear function is
merely a number used to sketch
the graph of the line. In reality,
slopes have real-world meaning,
and the idea of a rate of change
is fundamental to understanding
major concepts from geometry to
calculus.
Resources
Get the Math http://www.thirteen.org/getthemath/files/2011/10/vidgam
esfulllesson.pdf
write equations of parallel and
perpendicular lines.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 2 - Linear Equations and Their Graphs (cont)
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
The students will:
MACC.912.A-REI.4.10.
Understand that the graph of
an equation in two variables is
the set of all its solutions
plotted in the coordinate plane,
often forming a curve (which
could be a line).
SMP #2
MACC.912.F-IF.3.7a
Graph linear functions by hand
and show intercepts.
SMP #7,#8
Learning Goals
I can:
 explain that every ordered pair on the graph of an equation
represents values that make the equation true.
 verify that any point on a graph will result in a true equation
when their coordinates are substituted into the equation.






MACC.912.F-LE.2.5
Interpret the parameters in a
linear function in terms of a
context.
SMP #2, #4



Mathematics Department
Volusia County Schools
Remarks
Resources
identify that the parent function for lines is the line f(x) = x.
identify and graph a line in the point-slope form: y-y1=m(x-x1).
identify and graph a line in slope-intercept form: f(x)=mx+b.
identify the standard form of a linear function as Ax + By = C.
use the definitions of x and y intercepts to find the intercepts of a
line in standard form and then graph the line.
relate the constants A, B, and C to the values of the x and y
intercepts and slope.
identify the names and definitions of the parameters ‘m’ and ‘b’
in a linear function f(x)=mx+b.
explain the meaning (using appropriate units) of the slope, yintercept and other points on the line when then line models a
real-world relationship.
compose an original problem situations and construct a linear
function to model it.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 3 - Systems of Linear Equations and Inequalities
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
The students will:
MACC.912A-REI.3.5
Prove that given a system of two
equations in two variables,
replacing one equation by the
sum of that equation and a
multiple of the other produces a
system with the same solutions.
SMP # 3
MACC.912.A-REI.3.6
Solve systems of linear equations
exactly and approximately (with
graphs), focusing on pairs of
linear equations in two variables.
SMP # 7
Mathematics Department
Volusia County Schools
Learning Goals
I can:
 solve a system of two linear equations by graphing and
determining the point of intersection.
 solve a system of two linear equations algebraically using
substitution.
 solve a system of two linear equations algebraically using
elimination.



Remarks
Most mistakes that
students make are
careless rather than
conceptual. Teachers
should encourage
students to learn a
certain format for solving
systems of equations
and check the answers
by substituting into all
equations in the system.
Resources
Mars Tasks:
http://insidemathe
matics.org/commo
n-core-mathtasks/highschool/HS-A2006%20Graphs2
006.pdf
Illuminations –
Supply and
Demand http://illuminations.
nctm.org/LessonD
etail.aspx?ID=L38
2
explain why some linear systems have no solutions or
infinitely many solutions.
solve a system of linear equations algebraically to find an
exact solution.
graph a system of linear equations and determine the
approximate solution to the system of linear equations by
estimating the point of intersection.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 3 - Systems of Linear Equations and Inequalities
Essential Question(s):
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
The students will:
MACC.912.A-REI.4.11
Explain why the x-coordinates of
the points where the graphs of
the equations y=f(x) and y=g(x)
intersect are the solutions of the
equations f(x)=g(x) using
technology to graph the
functions, make tables of values,
or find successive
approximations.
MACC.912.A-REI.4.12
Graph the solutions to a linear
inequality in two variables as a
half-plane (excluding the
boundary in the case of a strict
inequality), and graph the
solution set to a system of linear
inequalities in two variables as
the intersection of corresponding
half-planes.
SMP #5
MACC.912A.CED.1.3
Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret
solutions as viable or non-viable
options in a modeling context.
SMP #4
Mathematics Department
Volusia County Schools
Learning Goals
I can:
 explain that a point of intersection on the graph of a system
of equations represents a solution to both equations.
 infer that the x-coordinate of the points of intersections are
solutions for f(x) = g(x).
 use a graphing calculator to determine the approximate
solutions to a system of equations.



solve and graph linear inequalities with two variables.
solve and graph system of linear inequalities.
explain that the solution set for a system of linear
inequalities is the intersection of the shaded regions of both
inequalities and check points in the shaded region to verify
the solution.

identify the variable and quantities represented in a realworld problem.
determine the best models for a real-world problem.
write inequalities that best models a problem.


Remarks
Resources
Students will want to
give an ordered pair
answer instead of just
the x-coordinate.
Linear functions only in
this unit.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 4 – Properties of Exponents
Clarification: Radicals are now included in this sections. This will not only include the previous NGSSS standard for
radicals (adding, subtracting, multiplying, and dividing radicals) but it will also include converting between radical and
rational exponents.
Essential Question(s):
How does knowledge of integers help when working with rational and irrational numbers?
How can the relationship between quantities best be represented?
Standard
Learning Goals
I can:
Remarks
The students will:
MACC.912.N-RN.1.1.
Students sometimes misunderstand the meaning of
 evaluate and simplify
Explain how the
exponential operations, the way powers and roots relate
expressions containing zero
definition of the
to one another, and the order in which they should be
and integer exponents.
meaning of rational
performed. Attention to the base is very important.
 multiply monomials.
exponents follows from
 apply multiplication properties Consider examples: (
) and
. The position of a
extending the properties
of exponents to evaluate and
negative sign of a term with a rational exponent can
of integer exponents to
simplify expressions.
mean that the rational exponent should be either applied
those values, allowing
 divide monomials.
first to the base, 81, and then the opposite of the result is
for a notation for
 apply division properties of
taken, (
), or the rational exponent should be applied
radicals in terms of
exponents to evaluate and
to a negative term
. The answer of
will be not
rational exponents.
simplify expressions.
real
if
the
denominator
of
the
exponent
is
even.
If the root
SMP #3, #7, #8
 apply properties of rational
is odd, the answer will be a negative number.
exponents to simplify
expressions.
Students should be able to make use of estimation when
MACC.912.N-RN.1.2.
 convert between radicals and incorrectly using multiplication instead of exponentiation.
Rewrite expressions
rational exponents.
involving radicals and
Students may believe that the fractional exponent in the
rational exponents using
the properties of
expression
means the same as a factor of 1/3 in
exponents.
multiplication expression, 36 ● 1/3 and multiple the base
SMP #7
by the exponent.
Mathematics Department
Volusia County Schools
Resources
Tasks & MiniProjects
http://insidemathem
atics.org/commoncore-mathtasks/highschool/HS-A2009%20Quadratic
2009.pdf
Manipulating
Radicals http://api.ning.com/f
iles/oteyilu*j6qVWK
tAVizsGFTd*nP1b3
gsbfNN3t7yxPqAFE9x*X2Vo50q
q2gDApK8pn75oIJ
uNVQovyELA6yBV
O9Vt*yL7Ye/2mani
pulating_radicals_c
omplete.pdf
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 4 – Properties of Exponents (cont)
Essential Question(s):
How does knowledge of integers help when working with rational and irrational numbers?
How can the relationship between quantities best be represented?
Standard
Learning Goals
I can:
Remarks
Resources
The students will:
MACC.912.F-IF.3.8 b
Only part “b” of this standard
Exponential growth/decay  distinguish between exponential functions
Write a function defined by
will be covered during this
http://betterlesson.com/les
that model exponential growth and
an expression in different
unit. Part “a” will be covered
son/316881/exponentialexponential decay.
but equivalent forms to
during
the
Functions
unit.
growth-decay-an-m-m interpret the components of an exponential
reveal and explain different
study
function in the context of a problem (e.g., y =
properties of the function.
5
describes a quantity that was
b) Use the properties of
Lesson Planet –
initially 5 and increases 22.5% every three
exponents to interpret
http://www.lessonplanet.co
years.)
expressions for
Introduce
the
idea
of
classify
m/search?keywords=expo
 apply the properties of exponents to rewrite
exponential functions.
them
as
representing
nential+growth+and+decay
an exponential function to emphasize one of
SMP #2, #7
its properties (e.g., y = 5 ●
5●
, exponential growth or decay.
For example, identify percent Understanding Models
which means that increasing 22.5% in three
rate
of change in functions
growth/decay –
years is about the same as increasing 7% per
such as y =
,y=
, http://www.nsa.gov/acade
year.
mia/_files/collected_learnin
y=
,y=
,
g/high_school/modeling/un
derstanding_models.pdf
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 5 – Polynomials
Essential Question(s):
Why structure expressions in different ways?
How can the properties of the real number system be useful when working with polynomials and rational expressions?
Standard
Learning Goals
I can:
Remarks
Resources
The students will:
Students may believe that an expression cannot be factored
MACC.912.A-SSE.1.1:
Tasks &
 classify and write polynomials in
because it does not fit into a form they recognize. They need help
MiniInterpret expressions that
standard form.
with
reorganizing
the
terms
until
structures
become
evident.
Projects
represent a quantity in terms
 evaluate polynomial expressions.
Students will often combine terms that are not like terms. For
of its context.
 define expression, term, factor, and example, 2 + 3x = 5x or 3x + 2y = 5xy.
a. Interpret parts of an
http://engag
coefficient.
Students sometimes forget the coefficient of 1 when adding like
expression, such as terms,
eny.org/reso
 interpret the real-world meaning of
terms. For example, x + 2x + 3x = 5x rather than 6x.
factors and coefficients.
urce/commo
the terms, factors and coefficients of Students will change the degree of the variable when
2
b. Interpret complicated
n-corean expression in terms of their units. adding/subtracting like terms. For example, 2x + 3x = 5x rather
expressions by viewing one or  group the parts of an expression
exemplarthan 5x. Students will forget to distribute to all terms when
more of their parts as a single
multiplying.
For
example,
6(2x
+
1)
=
12x
+
1
rather
than
12x
+
6.
for-highdifferently in order to better interpret
Students may not follow the Order of Operations when simplifying
entity.
school-math
their meaning.
expressions. For example, 4x2 when x = 3 may be incorrectly
SMP #7
evaluated as 4•32 = 122 = 144, rather than 4•9 = 36.
Students fail to use the property of exponents correctly when using
the distributive property.
For example, 3x(2x – 1) = 6x – 3x = 3x instead of simplifying as
3x(2x – 1) = 6x2 – 3x.
Students fail to understand the structure of expressions. For
example, they will write 4x when x = 3 is 43 instead of 4x = 4•x so
when x = 3, 4x = 4•3 = 12. In addition, students commonly
misevaluate –32 = 9 rather than –32 = –9.
Students routinely see –32 as the same as (–3)2 = 9.
Students commonly confuse the properties of exponents,
specifically the product of powers property with the power of a
power property.
Students will incorrectly translate expressions that contain a
difference of terms. For example, 8 less than 5 times a number is
often incorrectly translated as 8 – 5n rather than 5n – 8.
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 5 – Polynomials (cont)
Essential Question(s):
Why structure expressions in different ways?
How can the properties of the real number system be useful when working with polynomials and rational expressions?
Standard
Learning Goals
I can:
Remarks
Resources
The students will:
4
4
MACC.912.A-SSE.1.2:
 multiply and divide polynomials For example, see x - y as (x²)² – (y²)², thus
Use the structure of an
recognizing it as a difference of squares that can be
by monomials.
expression to identify ways to  multiply two binomials using the factored as (x² – y²)(x² + y²).
rewrite it.
distributive property.
SMP #7
 apply models for factoring
polynomials to rewrite
expressions.
MACC.912.A-APR.1.1:
Students often forget to distribute the subtraction to
 add and subtract polynomials.
Understand that polynomials
 multiply and divide polynomials terms other than the first one. For example, students
form a system analogous to
will write (4x + 3) – (2x + 1) = 4x + 3 – 2x + 1 = 2x + 4
by monomials.
the integers, namely, they are  multiply two binomials using the rather than 4x + 3 – 2x – 1 = 2x + 2.
closed under the operations
distributive property.
of addition, subtraction, and
Students will change the degree of the variable when
multiplication; add, subtract,
adding/subtracting like terms. For example, 2x + 3x =
and multiply polynomials.
5x2 rather than 5x.
SMP #2, #7
Students may not distribute the multiplication of
polynomials correctly and only multiply like terms. For
example, they will write (x + 3)(x – 2) = x2 – 6 rather
than x2 – 2x + 3x – 6.
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 6 - Factoring and Solving Polynomials
Essential Question(s):
Why structure expressions in different ways?
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
Learning Goals
I can:
Remarks
The students will:
See remarks Unit 5
MACC.912.A-SSE.1.1:
 factor polynomials by using the greatest
Some students may believe that
Interpret expressions that represent a
common factor.
factoring and completing the square
quantity in terms of its context.
 factor polynomials using the grouping method.
are isolated techniques within a unit
a. Interpret parts of an expression, such
 factor quadratic trinomials when a=1.
of quadratic equations. Teachers
as terms, factors, and coefficients.
 factor quadratic trinomials when a>1.
should help students to see the
b. Interpret complicated expressions by
 factor perfect square trinomials.
value of these skills in the context of
viewing one or more of their parts as a
solving higher degree equations and
 factor the difference of two squares.
single entity.
examining different families of
 form a perfect-square trinomial from a given
SMP #7
functions.
quadratic binomial.
MACC.912.A-SSE.1.2:
Use the structure of an expression to
identify ways to rewrite it.
SMP #7
MACC.912.A-SSE.2.3: (MA912.A.4.3)
Choose and produce an equivalent form
of an expression to reveal and explain
properties of the quantity represented by
the expression.
a. Factor a quadratic
expression to reveal the
zeros of the function it
defines.
b. Complete the square in a quadratic
expression to reveal the maximum or
minimum value of the function it defines.
SMP #7
Mathematics Department
Volusia County Schools






look for and identify clues in the structure of
expressions in order to rewrite in another way.
apply models for factoring and multiplying
polynomials to rewrite expressions.
apply factoring methods to simplify rational
expressions.
factor a quadratic expression to find the zeroes
of the function.
predict whether a quadratic will have a minimum
or a maximum based on the value of ‘a.’
identify the maximum or minimum of a quadratic
written in the form a(x-h)2+k.
Students may think that the minimum
(the vertex) of the graph of y = (x +
2
5) is shifted to the right of the
minimum (the vertex) of the graph y
= x2 due to the addition sign.
Students should explore examples
both analytically and graphically to
overcome this misconception.
Resources
Tasks & MiniProjects
http://insidemat
hematics.org/c
ommon-coremathtasks/highschool/HS-A2006%20Quadr
atic2006.pdf
http://insidemat
hematics.org/c
ommon-coremathtasks/highschool/HS-A2007%20Two%
20Solutions.pd
f
Some students may believe that the
minimum of the graph of a quadratic
function always occur at the yintercept.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 6 - Factoring and Solving Polynomials (cont)
Essential Question(s):
Why structure expressions in different ways?
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
Learning Goals
I can:
Remarks
The students will:
MACC.912.A-REI.2.4:
 identify a quadratic expression, ax2 + bx +
Solve quadratic equations in one
c.
variable.
 identify a perfect-square trinomial by first
a. Use the method of
noticing if a and c are perfect squares and
completing the square to
if b = 2ac.
transform any quadratic
 factor a perfect-square trinomial.
equation in x into an equation
 complete the square of ax2 + bx + c to
of the form (x – p)² = q that
write the quadratic in form (x-p)2 = q.
has the same solutions. Derive  derive the quadratic formula by
the quadratic formula from this
completing the square of ax2 + bx + c.
form.
 determine the best method to solve a
b. Solve quadratic equation
quadratic equation in one variable.
by inspection (e.g., for x² = 49),  solve quadratic equations by inspection.
taking square roots,
 solve quadratic equations by finding
completing the square, the
square roots.
quadratic formula and
 solve quadratic equations by completing
factoring, as appropriate to the
the square.
initial form of the equation.
Recognize when the quadratic  solve quadratic equations using the
quadratic formula.
formula gives complex

solve quadratic equations by factoring.
solutions and write them as a ±

explain that complex solutions result when
bi for real numbers a and b.
the radicand is negative in the quadratic
SMP #7, #8
formula (b2 – 4ac < 0).
 write complex number solutions for a
quadratic equation in the form a + bi by
using i = √-1.
Mathematics Department
Volusia County Schools
Resources
http://www.purpl
emath.com/mod
ules/complex3.ht
m
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 6 - Factoring and Solving Polynomials (cont)
Essential Question(s):
Why structure expressions in different ways?
In what ways can the problem be solved, and why should one method be chosen over another?
Standard
Learning Goals
I can:
Remarks
The students will:
MACC.912.A-APR.2.3:
Tasks are limited to quadratic and
 identify the zeroes of factored polynomials.
Identify zeros of polynomials when
cubic polynomials in which linear
 identify the multiplicity of the zeroes of a
suitable factorizations are available,
and quadratic factors are
factored polynomial.
and use the zeros to construct a rough  explain how the multiplicity of zeroes provides a
available. For example, find the
graph of the function defined by the
zeros
clue as to how the graph will behave when it
polynomial.
of (x - 2)(x2 - 9).
approaches and leaves the x-intercept.
SMP #1, #8
 sketch a rough graph using the zeroes of a
polynomial and other easily identifiable points
such as the y-intercept.
Mathematics Department
Volusia County Schools
Resources
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 7 – Non-Linear Functions
Standard
The students will:
MACC. 912.F-IF.2.4
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.
SMP #1, #7, #8
Mathematics Department
Volusia County Schools
Essential Question(s):
How can the relationship between quantities best be represented?
In what ways can functions be built?
Can you determine which function best models a situation?
Learning Goals
I can:
Remarks
 locate the information that explains what each
quantity represents.
 interpret the meaning of an ordered pair.
 determine if negative inputs and/or outputs make
sense in the problem.
 identify and explain the x and y intercept
 define intervals of increasing and decreasing of a
table or graph.
 identify and explain relative maximums and
minimums.
 identify reflective and rotational symmetries in a
table or graph.
 explain why the function has symmetry in the
context of the problem.
 identify and explain positive and negative end
behavior of a function.
 define and identify a periodic function from a table
or graph.
 explain why a function is periodic.
Resources
Algebra 1 Curriculum Map
October 22, 2013
MACC.912.F-IF.3.7a
Graph quadratic functions and show
intercepts, maxima and minima.
SMP #7, #8
MACC.912.F-IF.3.8a
Write a function defined by an
expression in different but equivalent
forms to reveal and explain different
properties of the function.
a. Use the process of factoring and
completing the square in a
quadratic function to show zeros,
extreme values, and symmetry of
the graph, and interpret these in
terms of a context.
SMP #2, #7
MACC.912.F-IF.3.7b-e (excluding
“d’)
Graph function expressed symbolically
and show key features of the graph, by
hand in simple cases and using
technology for more complicated
functions.
SMP #7, #8
Mathematics Department
Volusia County Schools
 explain that the parent function for quadratic
functions is a parabola f(x) = x2 .
 explain that the minimum and maximum of a
quadratic is called the vertex.
 identify whether the vertex of a quadratic will be a
minimum or maximum by looking at the equation.
 find the y-intercept of a quadratic by substituting 0
for ‘x’ and evaluating.
 estimate the vertex of a quadratic by evaluating
different values of ‘x’.
 decide if the quadratic has x-intercepts and if so
estimate their value(s).
 graph a quadratic using evaluated points
 use technology to graph a quadratic and to find
precise values for the x-intercept(s) and maximum or
minimum.



graph using evaluated points and technology and
explain the parent function of the following: square
root, cube root, piecewise, absolute value, step, and
exponential functions.
find intercepts, maximums and minimums, end
behavior, and horizontal asymptotes (by observation)
when present.
explain how the domain of a function is represented
in its graph.
The expectation is for
F.IF.3.7a &3.7e to focus on
linear and exponential
functions in Algebra I. Include
comparisons of two functions
presented algebraically. For
example, compare the growth
of two linear functions, or two
exponential functions.
Forming
Quadratics –
http://map.maths
hell.org/material
s/download.php?
fileid=700
In Algebra I for F.IF.3.7b,
compare and contrast absolute
value, step and piecewisedefined functions with linear,
quadratic, and exponential
functions.
Highlight issues of domain,
range, and usefulness when
examining piecewise- defined
functions.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 7 – Non-Linear Functions (cont)
Standard
The students will:
MACC.912.F-IF.3.9
Compare properties of two
functions each represented in
a different way (algebraically,
graphically, numerically in
tables, or by verbal
descriptions).
MACC.912.F-BF.2.3
Identify the effect on the graph
of replacing f(x) by f(x) + k, k
f(x), f(kx), and f(x + k) for
specific values of k (both
positive and negative); find the
value of k given the graphs.
Experiment with cases and
illustrate an explanation of the
effects on the graph using
technology
SMP #5, #7
Essential Question(s):
How can the relationship between quantities best be represented?
In what ways can functions be built?
Can you determine which function best models a situation?
Learning Goals
I can:
Remarks
Key characteristics include but are not
 state the appropriate domain of a function that
limited to maxima, minima, intercepts,
represents a problem situation, defend my
symmetry, end behavior, and asymptotes.
choice, and explain why other numbers might
Students may use graphing calculators or
be excluded from the domain.
programs, spreadsheets, or computer
 identify the degree of a polynomial.
algebra systems to graph functions.
 classify exponential functions as growth or
For example, given a graph of one
decay.
quadratic function and an algebraic
 approximate the factored equation of a
expression for another, say which has the
polynomial function when looking at a graph of
larger maximum.
a function.
 determine the multiplicity of the x-intercepts of
a polynomial when looking at a graph of the
function.
‘k’ translations include: left, right, up, down,
 explain how ‘k’ translates the original graph
vertical stretch and shrink, horizontal stretch
 determine the value of ‘k’ when given the
and shrink
graph of a transformed function.
Resources
http://www.math.h
mc.edu/calculus/tu
torials/transformati
ons/
Students may believe that each family of
functions (e.g., quadratic, square root, etc.) is
independent of the others, so they may not
recognize commonalities among all functions
and their graphs.
Students may believe that the graph of y = (x –
3
3
4) is the graph of y = x shifted 4 units to the
left (due to the subtraction symbol). Examples
should be explored by hand and on a graphing
calculator to overcome this misconception.
Students often confuse the shift of a function
with the stretch of a function.
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 7 – Non-Linear Functions (cont)
Standard
The students will:
MACC.912.F-IF.1.3
Recognize that sequences are
functions, sometimes defined
recursively, whose domain is a
subset of the integers.
SMP #2, #7, #8
Essential Question(s):
How can the relationship between quantities best be represented?
In what ways can functions be built?
Can you determine which function best models a situation?
Learning Goals
I can:
Remarks





MACC.912.F-LE.1.2
Construct linear and
exponential functions,
including arithmetic and
geometric sequences, given a
graph, a description of a
relationship, or two inputoutput pairs (include reading
these from a table).
SMP #2, #7, #8
Mathematics Department
Volusia County Schools



convert a sequence into a function.
explain that a recursive formula tells
me how a sequence starts and tells
me how to use the previous value(s)
to generate the next element of the
sequence.
explain that an explicit formula
allows me to find any element of a
sequence.
distinguish between explicit and
recursive formulas for sequences.
relate arithmetic sequences to linear
functions.
relate geometric sequences to
exponential functions.
determine if a function is linear or
exponential given a sequence, a
graph, a verbal description or a table.
describe the algebraic process used
to construct the linear function and
exponential function that passes
through two points.
In F.IF.1.3 draw a connection to F.BF.2, which requires
students to write arithmetic and geometric sequences.
Emphasize arithmetic and geometric sequences as examples
of linear and exponential functions.
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.
Resources
http://www.kens
ton.k12.oh.us/k
hs/academics/
math/AA_112B_arithmetic_s
equences_recur
sive.pdf
Students should be able to explain that a recursive formula
tells how a sequence starts and how to use the previous
value(s) to generate the next element of the sequence.
Students should be able to explain that an explicit formula
allows them to find any element of a sequence without
knowing the element before it (e.g., If I want to know the 11th
number on the list, I substitute the number 11 into the explicit
formula).
Algebra 1 Assessment Limits and Clarifications
i) this standard is part of the Major work in Algebra I and will be
assessed accordingly.
ii) Tasks are limited to constructing linear and exponential
functions in simple context (not multi- step).
Prentice Hall
Textbook
Section 4.7
(arithmetic
sequences
only)
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 7 – Non-Linear Functions (cont)
Standard
The students will:
MACC.912.F-BF.1.1
Write a function that describes
the relationship between two
quantities.
SMP #4, #7
MACC.912A-CED.1.1.
Create equations and inequalities
in one variable and use them to
solve problems. Include
equations arising from linear and
quadratic functions, and simple
rational and exponential
functions.
SMP#4
MACC.912.F-LE.1.3
Observe using graphs and tables
that a quantity increasing
exponentially eventually exceeds
a quantity increasing linearly,
quadratically, or (more generally)
as a polynomial function.
Essential Question(s):
How can the relationship between quantities best be represented?
In what ways can functions be built?
Can you determine which function best models a situation?
Learning Goals
I can:
Remarks
Resources
http://www.montgom
 identify the quantities being compared in Students may believe that the process of
rewriting equations into various forms is
eryschoolsmd.org/d
a real-world problem.
simply an algebra symbol manipulation
epartments/itv/math
 write a function to describe a real-world
exercise, rather than serving a purpose of
dude/MD_Algebra1_
problem.
allowing
different
features
of
the
function
to
7-3.shtm
 compose two or more functions.
be exhibited.
Prentice Hall
Textbook Section
4.5



understand exponential functions and
how they are used.
recognize differences between graphs of
exponential functions with different bases.
apply exponential functions to model
applications that include growth and
decay in different contexts.
SMP #2, #8
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 7 – Non-Linear Functions (cont)
Standard
The students will:
MACC.912.F-LE.1.1
Distinguish between situations
that can be modeled with linear
functions and with exponential
functions.
a. Prove that linear functions
grow by equal differences
over equal intervals, and that
exponential functions grow by
equal factors over equal
intervals.
b. Recognize situations in which
one quantity changes at a
constant rate per unit interval
relative to another.
c. Recognize situations in which
a quantity grows or decays by
a constant percent rate per
unit interval relative to
another.
SMP #3, #4, #8
Mathematics Department
Volusia County Schools
Essential Question(s):
How can the relationship between quantities best be represented?
In what ways can functions be built?
Can you determine which function best models a situation?
Learning Goals
I can:
Remarks
Compare
tabular
representations
of a variety of functions to
 define a linear function and
show
that
linear
functions
have
a
first
common difference
exponential function.
(i.e.,
equal
differences
over
equal
intervals),
while
 demonstrate that an exponential
exponential functions do not (instead function values grow
function has a constant multiplier or by equal factors over equal x-intervals).
equal intervals.
 identify situations that display
Apply linear and exponential functions to real-world
equal ratios of change over equal
situations. For example, a person earning $10 per hour
intervals and can be modeled with
experiences a constant rate of change in salary given the
number of hours worked, while the number of bacteria on a
exponential functions.
dish that doubles every hour will have equal factors over
 distinguish between situations
equal intervals.
modeled with linear functions and
with exponential functions when
Provide examples of arithmetic in graphic, verbal, or tabular
presented with a real-world
forms, and have students generate formulas and equations
problem.
that describe the patterns.
Resources
http://spot.pcc.ed
u/~kkling/Mth_11
1c/SectionII_Exp
onential_and_Lo
garithmic_Functio
ns/Module3_Com
paring_Linear_an
d_Exponential/M
odule3_Comparin
g_Linear_and_Ex
ponential.pdf
Examine multiple real-world examples of exponential
functions so that students recognize that a base between 0
and 1 (such as an equation describing depreciation of an
automobile [ f(x) = 15,000(0.8)x represents the value of a
$15,000 automobile that depreciates 20% per year over the
course of x years]) results in an exponential decay, while a
base greater than 1 (such as the value of an investment
over time [ f(x) = 5,000(1.07)x represents the value of an
investment of $5,000 when increasing in value by 7% per
year for x years]) illustrates growth.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 7 – Non-Linear Functions (cont)
Standard
The students will:
MACC.912.F-LE.2.5
Interpret the parameters in an
exponential function in terms of a
context.
SMP #2, #4
MACC.912.A-REI.4.11
Explain why the x-coordinates of
the points where the graphs of
the equations y=f(x) and y=g(x)
intersect are the solutions of the
equations f(x)=g(x) using
technology to graph the
functions, make tables of values,
or find successive
approximations.
Mathematics Department
Volusia County Schools
Essential Question(s):
How can the relationship between quantities best be represented?
In what ways can functions be built?
Can you determine which function best models a situation?
Learning Goals
I can:
Remarks
 identify the names and definitions of the parameters ‘a’,
‘b’ and ‘c’ in the exponential function f(x)=a(bx)+c.
 explain the meaning (using appropriate units) of the
constant a, b, c and other points of an exponential
function when the exponential function models a realworld relationship.
 compose an original problem situation and construct an
exponential function to model it.
 explain that a point of intersection on the graph of a
system of equations represents a solution to both
equations.
 infer that the x-coordinate of the points of intersections
are solutions for f(x) = g(x).
 use a graphing calculator to determine the approximate
solutions to a system of equations.
Resources
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 8 – Interpreting Categorical and Quantitative Data
Essential Question(s):
How can the properties of data be communicated to illuminate its important features?
Standard
Learning Goals
The students will:
I can:
Remarks
MA.912.D.7.1
 find the union, intersection, and compliment of NGSS benchmark that will be
Perform set operations such
assessed on the EOC.
sets.
as union and intersection,
 determine number of elements of a set.
complement, and cross
 use tree diagrams and the Fundamental
product.
Counting Principle to count the number of
choices that can be made from sets.
MA.912.D.7.2
Use Venn diagrams to
explore relationships and
patterns and to make
arguments about
relationships between sets.

MA.912.D.7.2
Use Venn diagrams to
explore relationships and
patterns and to make
arguments about
relationships between sets.

Mathematics Department
Volusia County Schools


use VENN diagrams to organize sets of data
and to make predictions about the given data.
Identify the cross product of two sets.
NGSS benchmark that will be
assessed on the EOC.
use VENN diagrams to organize sets of data
and to make predictions about the given data.
identify the cross product of two sets.
NGSS benchmark that will be
assessed on the EOC.
Resources
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 8 – Interpreting Categorical and Quantitative Data (cont)
Essential Question(s):
How can the properties of data be communicated to illuminate its important features?
Standard
Learning Goals
The students will:
I can:
Remarks
MACC.912.S-ID.1.1
 choose the appropriate scale to represent data on
Represent data with plots on
a number line.
the real number line (dot
 construct a dot plot, histogram and box plot.
plots, histograms and box
 calculate the 5-number summary for a set of data.
plots).
SMP #1, #5
MACC.912.S-ID.1.2
Mean or Median (not
 describe the center and spread of the data
Use statistics appropriate to
mode)
distribution.
the shape of the data
Interquartile Range (IQR)
 choose histogram with the largest mean and
distribution to compare center
and Standard Deviation
standard deviation.
(median, mean) and spread
 choose the box plot with the greatest IQR.
(interquartile range, standard  compare two or more data sets by examining
deviation) of two or more
their shapes, center, and spreads.
sets.
SMP #1, #5
MACC.912.S-ID.1.3
Shape included: Skewed
 interpret the differences in shape, center, and
Interpret differences in shape,
Right (positive), Skewed
spread in the context of the problem.
center and spread in the
Left (negative),
 identify outliers.
context of data sets,
Symmetrical Normal,
 predict the effect an outlier will have on the
accounting for possible
Symmetrical Non-Normal
shape, center and spread.
effects of extreme data points  decide whether to include the outliers as part of
and Uniform
(outliers).
the data set or to remove them.
SMP #1, #5
Mathematics Department
Volusia County Schools
Resources
Interactive – Aligned
Resources – lessons
for stats
http://www.shodor.org/i
nteractivate/standards/
organization/objective/2
331/
Interpreting Statistics http://map.mathshell.or
g/materials/download.p
hp?fileid=686
Representing Data:
Using Box Plots
http://map.mathshell.or
g/materials/download.p
hp?fileid=1243
Get the Math –
http://www.thirteen.org/
get-themath/files/2012/04/Mat
h-in-Restaurants-FullLesson-Final4.17.12.pdf
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 8 – Interpreting Categorical and Quantitative Data (cont)
Essential Question(s):
How can the properties of data be communicated to illuminate its important features?
Standard
The students will:
Learning Goals
I can:
MACC.912.S-ID.1.4
Use the mean and standard
deviation of a data set to fit it to a
normal distribution and to estimate
population percentages.
Recognize that there are data sets
for which such a procedure is not
appropriate. Use calculators,
spreadsheets, and tables to
estimate areas under the normal
curve.
SMP #2, #5, #7

MACC.912.S-ID.2.6
Represent data on two quantitative
variables on a scatter plot, and
describe how the variables are
related.
a. Fit a function to the data; use
functions fitted to data to solve
problems in the context of the data.
Use given functions or choose a
function suggested by the context.
Emphasize linear, quadratic, and
exponential models.
a.
Informally assess the fit of a
function by plotting and analyzing
residuals.
b.
Fit a linear function for a scatter
plot that suggests a linear association
SMP #2, #4
Mathematics Department
Volusia County Schools














use the mean and standard deviation of a set of data
to fit the data to a normal curve
use the 68-95-99.7 Rule to estimate the percent of a
normal population that falls within 1,2 or 3 standard
deviations of the mean
recognize that normal distributions are only
appropriate for unimodal and symmetric shapes
estimate the area under a normal curve using a
calculator, table or spreadsheet
explain that scatter plots can only be used to represent
quantitative variables.
identify the independent and dependent variable.
describe the relationship of the variables.
construct a scatter plot and identify any outliers.
determine when linear, quadratic and exponential models
should be used to represent a data set.
determine whether linear and exponential models are
increasing or decreasing.
use technology to find the function of best fit, sketch the
function and use it to make predictions.
compute residuals.
construct and analyze a residual plot to determine
whether the function is an appropriate fit.
sketch a line of best fit on a scatter plot.
write the equation of the line of best fit (y=mx+b) using
technology or by using two points on the best fit line.
Remarks
Resources
The 68-95-99.7 Rule is
also known as the
Empirical Rule.
Statistics
Education Web
(STEW) – lesson
plans
http://www.amsta
t.org/education/st
ew/
Residual = observed
value – predicted value
A residual plot is a
scatter plot of the
independent variable
and the residuals.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 8 – Interpreting Categorical and Quantitative Data (cont)
Essential Question(s):
How can the properties of data be communicated to illuminate its important features?
Standard
The students will:
MACC.912.S-ID.3.7
Interpret the slope (rate of
change) and the intercept
(constant term) of a linear model
in the context of the data.
SMP #2, #4, #5
MACC.912.S-ID.3.8
Compute (using technology) and
interpret the correlation
coefficient of a linear fit.
SMP #4, #5
Learning Goals
I can:

interpret the meaning of the slope and y-intercept in terms of
the units stated in the data.




MACC.912.S-ID.3.9
Distinguish between correlation
and causation.
SMP #2, #3, #4




Mathematics Department
Volusia County Schools
Remarks
Resources
explain that correlation coefficient applies only to quantitative
variables and measures the “goodness of a linear fit”.
explain that correlation must be between -1 and 1 inclusive
and explain what each of these values mean.
compute correlation (r) using a graphing calculator or other
appropriate technology.
apply correlation to interpret the direction and strength of a
linear model and determine if it is a good fit for the data.
recognize that correlation does not imply causation and that
causation is not illustrated on a scatter plot.
choose two variables that could be correlated because one is
the cause of the other and defend my selection.
choose two variables that could be correlated even though
neither variable could be the cause of the other and defend my
selection.
determine if statements of causation seem reasonable or
unreasonable and defend my opinion.
Algebra 1 Curriculum Map
October 22, 2013
Course: Algebra 1
Unit 8 – Interpreting Categorical and Quantitative Data (cont)
Essential Question(s):
How can the properties of data be communicated to illuminate its important features?
Standard
The students will:
MACC.912.S-ID.2.5
Summarize categorical data for
two categories in two-way
frequency tables. Interpret
relative frequencies in the
context of the data (including
joint, marginal, and conditional
relative frequencies). Recognize
possible associations and trends
in the data.
SMP #2
Learning Goals
I can:

read and interpret data displayed in a two-way
frequency table.

write clear summaries of data displayed in a twoway frequency table.

calculate percentages using ratios to yield relative
frequencies.

calculate joint, marginal and conditional relative
frequencies.

interpret and explain the meaning of relative
frequencies in the context of a problem.

draw bar charts or pie charts to represent the
relative frequencies.

describe patterns observed in the data
recognize the association between two variables
by comparing conditional and marginal percentages.
Remarks
Resources
Representing Data 1:
Using Frequency Graphs
http://map.mathshell.org/
materials/download.php?
fileid=1230
Algebra 1 resources for all sections:
Illustrative mathematics: provides the standards with example problems that cover the standard.
http://www.illustrativemathematics.org/standards/hs
The Math Dude: http://www.montgomeryschoolsmd.org/departments/itv/mathdude/
Algebra Nation- http://www.algebranation.com/
Mathematics Department
Volusia County Schools
Algebra 1 Curriculum Map
October 22, 2013