Lynn Public Schools
Algebra 1
Curriculum Map
SY 2013-2014
LYNN PUBLIC SCHOOLS
Administrative Offices – 90 Commercial Street, Lynn, MA 01905
Tel. (781) 477-7220 ~ Fax. (781) 477-7487
Dr. Catherine Latham
Superintendent of Schools
Dr. Jaye Warry
Deputy Superintendent of Schools
Mrs. Susan Rowe
Deputy Superintendent of Schools
Mrs. Kimberlee Powers
Executive Director of Curriculum and Instruction
Lynn School Committee
Mrs. Judith Kennedy, Chairman
Mrs. Patricia M. Capano, Vice-Chairman
Mrs. Maria O. Carrasco
Mrs. Donna M. Coppola
Mr. Charles Gallo
Mr. John E. Ford, Jr.
Mr. Richard Starbard
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
LYNN PUBLIC SCHOOLS
Administrative Offices – 90 Commercial Street, Lynn, MA 01905
Tel. (781) 477-7220 ~ Fax. (781) 477-7487
Shirley A. Albert
Assistant Director of Curriculum and Instruction
Mathematics K-12
Algebra 1 Mathematics Curriculum Committee
Kathleen Bonnevie
William Cammett
Barbara Funicella
Matthew Kane
Donna Jalbert
Edward Johns
Mark Johnston
Jennifer Mack
Josh Mower
Timothy Phelps
Steven Picariello
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Algebra 1 Curriculum Map SY 2013-2014
This curriculum map is divided among 10 units. The units are sequenced in a way that we believe best develops
and connects the mathematical content described in the 2011 Massachusetts Curriculum Frameworks for
Mathematics. However, the order of the standards included in any unit does not imply a sequence of content
within that unit. Some standards may be revisited several times during the year; others may be only partially
addressed in different units, depending on the mathematical focus of the unit. The standards are meant to be
viewed as connected ideas that build understanding of key mathematical concepts. Please note that this is an
evolving document and may be revised throughout the school year.
Quarter 1
Unit 1: Connecting Patterns and Functions
Unit 2: Introduction to Linear Functions
Quarter 2
Unit 3: Modeling Linear Data
Unit 4: Solving Linear Equations and Inequalities
Unit 5: Systems of Linear Equations and Inequalities
Quarter 3
Unit 6: Exponential Functions
Unit 7: Linear and Exponential Models
Unit 8: Arithmetic and Geometric Sequences
Unit 9: Operations on Polynomials
Quarter 4
Unit 10: Quadratics
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Introduction
The fundamental purpose of the Model Algebra I course is to formalize and extend the mathematics that students learned
in the middle grades. This course is comprised of standards selected from the high school conceptual categories, which
were written to encompass the scope of content and skills to be addressed throughout grades 9–12 rather than through
any single course. Therefore, the complete standard is presented in the model course, with clarifying footnotes as needed
to limit the scope of the standard and indicate what is appropriate for study in this particular course. For example, the
scope of Model Algebra I is limited to linear, quadratic, and exponential expressions and functions as well as some work
with absolute value, step, and functions that are piecewise-defined. Therefore, although a standard may include
references to logarithms or trigonometry, those functions are not to be included in coursework for Model Algebra I; they
will be addressed later in Model Algebra II. Reminders of this limitation are included as footnotes where appropriate in the
Model Algebra I standards.
For the high school Model Algebra I course, 1 instructional time should focus on four critical areas: (1) deepen and extend
understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and
engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and
cube roots; and (4) apply linear models to data that exhibit a linear trend.
(1) 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. In Algebra
I, students analyze and explain the process of solving an equation and justify the process used in solving a
system of equations. Students develop fluency writing, interpreting, and translating among various forms of
linear equations and inequalities, and use 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.
(2) In earlier grades, students define, evaluate, and compare functions, and use them to model relationships
between quantities. In Algebra I, students learn function notation and develop the concepts of domain and
range. They focus on linear, quadratic, and exponential functions, including sequences, and also explore
absolute value, step, and piecewise-defined functions; they interpret functions given graphically, numerically,
symbolically, and verbally; translate between representations; and understand the limitations of various
representations. Students build on and 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.
(3) Students extend the laws of exponents to rational exponents involving square and cube roots and apply this
new understanding of number; they 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. Students become facile with algebraic manipulation, including rearranging and
collecting terms, and factoring, identifying, and canceling common factors in rational expressions. 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.
1
Adapted from the Common Core State Standards for Mathematics and Appendix A: Designing High School Courses based on the
Common Core State Standards for Mathematics.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Students expand their experience with functions to include more specialized functions—absolute value, step,
and those that are piecewise-defined.
(4) Building upon their prior experiences with data, students explore a more formal means of assessing how a
model fits data. Students use regression techniques to describe approximately linear relationships between
quantities. They use graphical representations and knowledge of context to make judgments about the
appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.
The Standards for Mathematical Practice complement the content standards so that students increasingly engage with the
subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school
years.
Throughout Algebra 1, students should continue to develop proficiency with the eight Standards for Mathematical
Practice. These practices should become the natural way in which students come to understand and do mathematics.
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and preserve in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
The Standards for Mathematical Practice complement the content standards at each grade level so that students
increasingly engage with the subject matter as they grow in mathematical maturity and expertise.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 1: Algebra 1 Unit 1A
Unit 1A: Constructing Graphs
Duration: 4 days
Overview of Unit 1A
This unit focuses on critical area 4. The focus of this unit is to introduce the principles for creating neutral, well-designed
graphs. Choosing appropriate values and scales for both axes to present meaningful displays of data is highlighted.
Students also review the distinction between independent and dependent variables in functional relationship and learn
graphing conventions related to this distinction. Students also begin to distinguish between discrete and continuous
functions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
N.Q.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. 
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. 
N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 
MA.3.a. Describe the effects of approximate error in measurement and rounding on measurements and on computed
values from measurements. Identify significant figures in recorded measures and computed values based on the context
given and the precision of the tools used to measure. 
S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 
S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread
(interquartile range, standard deviation) of two or more different data sets. 
S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of
extreme data points (outliers). 
S.ID.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. *
S.ID.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. 

Indicates Modeling Standard
* Note: Introduce in Algebra I; expand in Algebra II
Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
4. Model with mathematics
6. Attend to precision.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Essential Question:
1. What kind of information can we get from different types of graphs?
2. How can we use the mean, median, mode and range to describe a set of data?
3. Why do we need three different measures of central tendency?
Vocabulary:
Units, Graphs, Data Displays, Independent, Dependent, Histogram, Discrete, Continuous, Scale, Origin, Function, Axes,
Ordered Pair, Outlier, Measures of Central Tendency
Student Outcomes:
By the end of unit 1A, through assessment, students will demonstrate that they are able to:




Properly label and scale a graph
Identify the independent and dependent variables
Determine the appropriate graph for the given data
Find measures of central tendency
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 1: Algebra 1 Unit 1B
Unit 1B: Multiple Representations in the Real World
Duration: 6 days
Overview of Unit 1B
This unit focuses on critical areas 2 and 4. This topic connects the various representations of a problem—words, concrete
elements, numbers, graphs, and algebraic expression--as students explore linear relationships. Building on previous work
with independent and dependent variables, students are introduced to the concept of the domain and range of a function.
Students also learn how the same situation can be represented by different but equivalent algebraic expressions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.CED.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. 
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales. 
A.CED.3 Represent constraints by equations or inequalities,1 and by systems of equations and/or inequalities, and
interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing
nutritional and cost constraints on combinations of different foods. 
A.REI.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).
F.IF.MA.8.c. Translate among different representations of functions and relations: graphs, equations, point sets, and
tables
1
Equations and inequalities in this standard should be linear
Indicates Modeling Standard
Standards for Mathematical Practice:

2. Reason abstractly and quantitatively.
4. Model with mathematics
6. Attend to precision.
Essential Question:
1. How can we use mathematics to provide models that help us interpret data, make predictions and better understand the
world in which we live?
2. What are the limitations of these models?
Vocabulary:
Units, Graphs, Domain, Range, Independent, Dependent, Discrete, Continuous, Scale, Origin, Function, Axes, Algebraic
Expressions, Equations and Inequalities, Solutions
Student Outcomes:
By the end of unit 1B, through assessment, students will demonstrate that they are able to:
 Describe the domain and range of the function
 Create equations and inequalities to solve problems
 Graph equations on coordinate axes with labels and scales
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 1: Algebra 1 Unit 1C
Unit 1C: Functions
Duration: 6 days
Overview of Unit 1C
This unit focuses on critical area 2. This topic introduces how to recognize and represent a dependency relationship
between two variables, in which one depends on the other in a systematic way. This relationship is called a function.
Students learn how to identify, represent, and evaluate functions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x)
denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function
notation in terms of a context.
Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
4. Model with mathematics
6. Attend to precision.
Essential Question:
1. How do you represent functions?
2. What is the purpose of function notation?
Vocabulary:
Function, Function Notation, Domain, Range, Relation, Input, Output, Element, Evaluate
Student Outcomes:
By the end of unit 1C, through assessment, students will demonstrate that they are able to:
 Identify, represent, and evaluate functions
 Write an equation in function notation and evaluate a function for given input values
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 1: Algebra 1 Unit 1D
Unit 1D: Analyzing Graphs
Duration: 4 days
Overview of Unit 1D
This unit focuses on critical area 2. This topic is designed to enable students to understand clearly what is happening on a
graph and to develop their ability to interpret information from axis labels and axis scales and, depending on the
information desired, a graph's direction or graph intersections.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity. 

Indicates Modeling Standard
Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
4. Model with mathematics
6. Attend to precision.
Essential Question:
How can you represent a function symbolically from a graph, a verbal description, or a table of values?
Vocabulary:
Interpret, Intercepts, Intervals, Increasing/Decreasing Functions, Relative Minimums/Maximums, Symmetries
Student Outcomes:
By the end of unit 1D, through assessment, students will demonstrate that they are able to:
 Identify the key features of a graph of a function, or its table of values, including minimums and maximums,
increasing and decreasing intervals, symmetry and end behavior.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 1: Algebra 1 Unit 2A
Unit 2A: Exploring Rate of Change
Duration: 6 Days
Overview of Unit 2A
Critical area 2 is the primary focus for this unit, and in this sub-unit the standards covered will be limited to their linear
portions primarily and will be revisited throughout the year and further courses. The focus will be directed to the general
concepts of a linear function and its attributes.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity. 
F.IF.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. 

Indicates Modeling Standard
Standards for Mathematical Practice:
4. Model with mathematics.
8. Look for and express regularity in repeated reasoning.
Essential Question:
What is a rate of change?
Vocabulary:
Rate of Change, Tables, Functions, Linear Functions, Linear Equations, Graphs, Variables, Data, Interval
Student Outcomes:
By the end of unit 2A, through assessment, students will demonstrate that they are able to:


Calculate and interpret rate of change (slope) from a graph and from tabular data.
Identify linear models and that other data sets require nonlinear models.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 1: Algebra 1 Unit 2B
Unit 2B: Understanding Slope, Intercepts and Various Linear Functions
Duration: 9 Days
Overview of Unit 2B
Critical area 2 is the primary focus for this unit, and in this sub-unit the standards covered will be limited to their linear
portions primarily and will be revisited throughout the year and further courses. The focus will be directed to the general
concepts of a linear function, including the x- y- intercepts, various linear equation forms and further increased
understanding of slope.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F.BF. 3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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. Include recognizing even and odd functions from their graphs and
algebraic expressions for them.
F. IF.7a Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. 
F. IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically
in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic
expression for another, say which has the larger maximum.
F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs (include reading these from a table). 
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. 

Indicates Modeling Standard
Standards for Mathematical Practice:
4. Model with mathematics.
8. Look for and express regularity in repeated reasoning.
Essential Question:
What does the slope of a line indicate about the line?
What information does the equation of a line give you?
How are equations and graphs related?
Vocabulary:
Rate of Change, Tables, Functions, Linear Functions, Linear Equations, Graphs, Variables, Standard Form, SlopeIntercept Form, Point-Slope Form, Constant, X-intercept, Y-intercept
Student Outcomes:
By the end of unit 2B, through assessment, students will demonstrate that they are able to:



Graph linear equations in the various forms
Identify and plot points from the various functions.
Create linear equations using graphs, tables, input output pairs, and slope and a point.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 2: Algebra 1 Unit 3
Unit 3: Modeling Linear Data
Duration: 8 days
Overview of Unit 3
This unit focuses on critical area 4. This topic revisits analyzing rate of change to determine whether using a linear model
to represent data is appropriate. It also introduces the use of residuals to informally assess the fit of a linear function.
Students learn that correlation does not imply causation. They also explore transformations of functions by transforming the
parent function y = x to create linear models for data.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 
S.ID.6a 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. 
S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals. 
S.ID.6c Fit a linear function for a scatter plot that suggests a linear association. 
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 
S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. 
S.ID.9 Distinguish between correlation and causation. 

Indicates Modeling Standard
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
Essential Question:
How do you use a graphing calculator to determine the line of best fit based on the given data?
How can you decide whether a correlation exists between paired numerical data?
How do you find a linear model for a set of paired numerical data and how do you evaluate the accuracy of the fit?
Vocabulary:
Scatter Plot, Positive Correlation, Negative Correlation, No Correlation, Causation, Slope, Rate of Change, Y-Intercept,
Line of Best Fit, Linear Model, Data, and Function, Residuals, Trend Line
Student Outcomes:
By the end of unit 3, through assessment, students will demonstrate that they are able to:






Create and interpret scatter plots
Properly label and scale a graph
Use trend lines to make predictions
Interpret the slope and y-intercept of a linear model in the context of the data
Compute using technology and interpret the correlation coefficient of a linear fit
Distinguish between correlation and causation
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 2: Algebra 1 Unit 4A
Unit 4A: Solving Linear Equations
Duration: 8 days
Overview of Unit 4A
This unit focuses on critical areas 1 and 2. In this unit, students learn how linear equations are related to functions. The
topic explores how different representations of a function lead to techniques to solve linear equations, including tables,
graphs, concrete models, algebraic operations, and "undoing" (reasoning backwards).
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.CED.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. 
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes
with labels and scales. 
A.CED.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. For example, represent inequalities describing nutritional and cost
constraints on combinations of different foods. 
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example,
rearrange Ohm’s law V = IR to highlight resistance R. 
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step,
starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
MA.3.a. Solve linear equations and inequalities in one variable involving absolute value.
A.REI.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 equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of
values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.* 
F.IF.7b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 
*Note: In Algebra 1, functions are limited to linear, absolute value and exponential functions for this cluster.

Indicates Modeling Standard
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
6. Attend to precision.
Essential Question:
How can you use the properties of equality to support your solution to a linear equation?

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Vocabulary:
Formula, one-step equations, multi-step equations, solution, function notation, absolute value function, exponential function,
approximate, coefficient, and table of values.
Student Outcomes:
By the end of unit 4A, through assessment, students will demonstrate that they are able to:




Solve one-step equations in one variable
Solve multi-step equations
Solve a formula for a given variable
Be able to distinguish between the graphs of linear, absolute value and exponential functions
 Approximate the solution for any two of the functions listed above using technology
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 2: Algebra 1 Unit 4B
Unit 4B: Solving Linear Inequalities
Duration: 6 days
Overview of Unit 4B
This unit focuses on critical areas 1and 2. This topic introduces students to solution techniques for linear inequalities in
one and two variables. Students learn to solve with graphs, tables, and algebraic operations.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.CED.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. 
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales. 
A.CED.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. For example, represent inequalities describing
nutritional and cost constraints on combinations of different foods. 
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous
step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a
solution method.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by
letters. MA.3.a.Solve linear equations and inequalities in one variable involving absolute value.
A.REI.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 equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic functions. 
*Note: In Algebra 1, functions are limited to linear, absolute value and exponential functions for this cluster.

Indicates Modeling Standard
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
6. Attend to precision.
Essential Question:
How does solving a linear equation compare to solving a linear inequality?
What are the properties needed to solve linear inequalities?

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Vocabulary:
Greater Than or Equal To, Less Than or Equal To, Formula, One-Step Inequalities, Multi-Step Inequalities, Absolute
Value Inequality, Conjunction, Disjunction, Solution, Function Notation, Exponential Function, Approximate, Coefficient,
and Table of Values.
Student Outcomes:
By the end of this unit 4B, through assessment, students will demonstrate that they are able to:
 Solve and graph one-step inequalities in one variable
 Solve and graph multi-step inequalities with two variables
 Solve and graph absolute value inequalities
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 2: Algebra 1 Unit 5
Unit 5 Systems of Linear Equations and Inequalities
Duration: 10 Days
Overview of Unit 5
Critical area 2 is the primary focus for this unit. The focus will be directed to systems of linear equations and inequalities.
Specifically, the initial focus will be on graphical solutions (estimations). The further exploration will introduce and
expand the substitution and combination/elimination methods. Technology methods are also highly encouraged after the
mastery of the foregoing concepts.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.CED.1; A.CED.3
A.REI.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.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
A.REI.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 equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the
functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 
A.REI.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 the corresponding half-planes.

Indicates Modeling Standard
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
6. Attend to precision.
Essential Question:
What are the three types of solutions to a system of linear equations and what do they represent?
How can you use a system of linear equations or inequalities to model and solve real-world problems?
Vocabulary:
Systems of Linear Equations, Systems of Linear Inequalities, Substitution Method, Linear Combination Method,
Intersection, Variable, Solution(s), Feasible Area, Half-Plane, Identity, No Solution, Independent Equations, Dependent
Equations
Student Outcomes:
By the end of unit 5, through assessment, students will demonstrate that they are able to:
 Graph the intersection of two lines to determine the solutions to systems of linear equations and inequalities.
 Solve systems of equations by using both the linear combination method and the substitution method.
 Use technology to determine the solutions to linear systems of equations and inequalities.
19
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 3: Algebra 1 Unit 6A
Unit 6A: Laws of Exponents
Duration: 5 days
Overview of Unit 6A
This unit focuses on critical area 3. This topic is a refresher on laws of exponents. It reviews principles for multiplying
and dividing exponential expressions with common bases. It also uses explorations of number patterns to develop the
meanings of positive and negative exponents, as well as zero as an exponent. The topic also introduces students to
fractional exponents.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A-SSE.1 Interpret expressions that represent a quantity in terms of its context. 
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret
P(1 + r)n as the product of P and a factor not depending on P.
A-SSE.3
c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression
1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.
N-RN.1Explain how the definition of the meaning of rational exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we
define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
N-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Indicates Modeling Standard
Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
4. Model with mathematics.
6. Attend to precision
Essential Question:
What are the laws of exponents and how do they simplify mathematical operations?
Vocabulary:
Exponential Function, Exponent, Base, Power, Radical, and Rational Exponent.
Student Outcomes:
By the end of this unit 6A, through assessment, students will demonstrate that they are able to:
 Multiply and divide exponential expressions with a common base.
 Simplify positive, negative, zero and rational exponents.
20
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 3: Algebra 1 Unit 6B
Unit 6B: Evaluating and Graphing Exponential Functions
Duration: 6 days
Overview of Unit 6B
This unit focuses on critical areas 2, 3 and 4. This unit introduces students to exponential functions. Students will learn to
evaluate, identify, and graph exponential functions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude. 
*Note: In Algebra 1 it is sufficient to graph exponential functions showing intercepts. Showing end behavior of
exponential functions and graphing logarithmic and trigonometric functions is not part of Algebra 1.
F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent
rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify them as
representing exponential growth or decay.
MA.8.c. Translate among different representations of functions and relations: graphs, equations, point sets, and tables.
F-BF.1.b Combine standard function types using arithmetic operations. For example, build a function that models the
temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the
model. 

Indicates Modeling Standard
Standards for Mathematical Practice:
2. Reason abstractly and quantitatively.
4. Model with mathematics
6. Attend to precision.
Essential Question:
How do exponential functions model real world problems?
How do you write, graph, and interpret an exponential function?
Vocabulary:
Exponential decay, Exponential growth, Intercepts, Coefficient, and Base.
Student Outcomes:
By the end of unit 6B, through assessment, students will demonstrate that they are able to:




Evaluate exponential functions
Identify and graph exponential functions in standard form.
Identify intercepts
Distinguish between growth and decay based on functional and graphical notation.
21
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 3: Algebra 1 Unit 7
Unit 7 Linear and Exponential Models
Duration: 5 Days
Overview of Unit 7
Critical areas 1, 2, and 4 are the primary foci for this unit. The lessons will be directed to working with and modeling
linear and exponential relations of linear equations and inequalities. Specifically, the initial direction will be on graphical
modeling (estimations) and comparing exponential function with linear functions graphically, numerically and
analytically. Technological methods are highly encouraged to foster mastery of the core concepts.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F.BF.1 Write a function that describes a relationship between two quantities.
F.BF.1b Combine standard function types using arithmetic operations. For example, build a function that
models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate
these functions to the model. 
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model
situations, and translate between the two forms. 
F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals. 
F.LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to
another. 
F.LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval
relative to another. 
F.LE.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. 
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. 

Indicates Modeling Standard
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
22
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Essential Question:
How do linear functions compare with exponential functions graphically, numerically, and analytically?
Vocabulary:
Linear Equations, Exponential Functions, Exponential Growth, Exponential Decay, Exponent, Coefficient, Base,
Compound Interest, Rate
Student Outcomes:
By the end of unit 7, through assessment, students will demonstrate that they are able to:
 Describe, compare, and contrast linear and exponential functions.
 Graph exponential growth and decay functions from data displays and equations.
 Use technology as part of deriving the outcomes.
23
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 3: Algebra 1 Unit 8
Unit 8: Arithmetic and Geometric Sequences
Duration: 7 days
Overview of Unit 8
This unit focuses on critical area 2. In this topic students explore the basic characteristics of arithmetic and geometric
sequences and connect them to linear and exponential functions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element
of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the
output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n  1) for n ≥ 1.
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model
situations, and translate between the two forms. 
F-LE.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. 
F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a
description of a relationship, or two input-output pairs (include reading these from a table). 
Note: In Algebra I, identify linear and exponential sequences that are defined recursively; continue the study of
sequences in Algebra II.

Indicates Modeling Standard
Standards for Mathematical Practice:
7. Look for and make use of structure
8. Look for express regularity in repeated reasoning
Essential Question:
What is the difference between an Arithmetic and Geometric sequence?
How do you find the nth term in a sequence?
Vocabulary:
Sequence, Term, Arithmetic, Geometric, Common Difference, Common Ratio, Recursive, Explicit Formula, Nth Term,
Growth, Decay
24
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Student Outcomes:
By the end of unit 8, through assessment, students will demonstrate that they are able to:
 Recognize and extend arithmetic and geometric sequence
 Find an explicit or recursive formula for an arithmetic or geometric sequence
25
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 3: Algebra 1 Unit 9
Unit 9: Operations on Polynomials
Duration: 10 days
Overview of Unit 9
This unit focuses on critical area 3. This topic explores polynomial operations through a construction scenario. Students
learn how to multiply, add, and subtract polynomials using concrete models and analytic techniques. They also learn how
to factor trinomials using concrete models and analytic techniques. Students apply their new skills in working with
rational expressions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
N-RN.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.
A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. *
A.SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus
recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
A.SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
* Note: For Algebra I, focus on adding and multiplying polynomial expressions, factoring or expanding polynomial
expressions to identify and collect like terms, applying the distributive property.
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Essential Question:
How are operations on polynomial expressions performed?
How are polynomial expressions in various forms factored?
What is the purpose of factoring polynomials?
Vocabulary:
Polynomials, Terms, Rational, Irrational, Integers, Closure, Factoring, Trinomials, Difference of Squares, Coefficients,
Constant, Degree, Standard Form of a Polynomial, Distributive Property
Student Outcomes:
By the end of unit 9, through assessment, students will demonstrate that they are able to:




Determine the parts of a polynomial expression
Add, subtract and multiply polynomials
Use distributive property on polynomials
Factor polynomials
26
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 4: Algebra 1 Unit 10A
Unit 10A Graphing and Factoring Quadratic Functions
Duration: 10 Days
Overview of Unit 10A
Critical areas 2 and 3 are the primary foci for this unit. The lessons will be directed to factoring and graphing quadratic functions and
relations. Specifically, the initial direction will be on graphical modeling (estimations) and comparing quadratic functions with linear
and exponential functions graphically, numerically and analytically. Technological methods are highly encouraged to foster mastery of
the core concepts.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.SSE.1 Interpret expressions that represent a quantity in terms of its context. 
a.Interpret parts of an expression, such as terms, factors, and coefficients.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes
with labels and scales. 
A.REI.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).
F.LE.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. 
F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the
domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms
of a context.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the
quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end
behavior; and periodicity. 
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if
the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function
F.IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for
more complicated cases. 
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. 
F.IF.8 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.
F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by

indicates Modeling standard.
27
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
F.IF.MA.10 Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial, rational,
logarithmic, exponential, or trigonometric.
F.BF.1 Write a function that describes a relationship between two quantities. 
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of
a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
F.BF.4. Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
For example, f(x) =2x3 or f(x) = (x + 1)/(x  1) for x ≠ 1.

Indicates Modeling Standard
Standards for Mathematical Practice:
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
Essential Question:
How are quadratic functions used to model, analyze, and interpret mathematical relationships?
How does factoring further the analysis of quadratic functions?
Vocabulary:
Quadratic (Functions, Equations, Factors), Parabola, Vertex, Axis of Symmetry, Maximum, Minimum, Monomial, Binomial, Trinomial,
Coefficients, Constant, Perfect Square Trinomial, Difference of Two Squares, Factoring, Roots, Quadratic Equation Form (Standard,
Vertex, and Factored)
Student Outcomes:
By the end of Unit 10A, through assessment, students will demonstrate that they are able to:



Describe, compare, and contrast quadratic functions with linear and exponential functions.
Graph quadratic functions from data displays and equations.
Factor quadratic functions to determine zeros (roots), vertex, and axis of symmetry.
 Use tables and graphs on a graphing calculator (or appropriate technology) to explore the relationships between roots, zeros,
and x-intercepts.

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
28
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 4: Algebra 1 Unit 10B
Unit 10B Completing the Square
Duration: 5 days
Overview of Unit 10B
Critical areas 2 and 3 are the primary foci for this unit. This topic focuses on solving quadratic functions by completing the square in order to
graph the function.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.SSE.1. Interpret expressions that represent a quantity in terms of its context. 
a. Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with
labels and scales. 
A.REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form
(x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
A.REI.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).
F.LE.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. 
F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain
exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the
input x. The graph of f is the graph of the equation y = f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a
context.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities,
and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For
example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the
positive integers would be an appropriate domain for the function. 
F.IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more
complicated cases. 
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. 
F.IF.8 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.

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
29
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal
descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger
maximum.
F.BF.1 Write a function that describes a relationship between two quantities. 
a. Determine an explicit expression, a recursive process, or steps for calculation from a context. 
b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a
cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
F.BF.4 Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For
example, f(x) =2x3 or f(x) = (x + 1)/(x  1) for x ≠ 1.

Indicates Modeling Standard
Standards for Mathematical Practice:
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
Essential Question:
What does “completing the square” mean in the context of solving quadratic functions?
Vocabulary:
Quadratic (Functions, Equations, Factors), Parabola, Vertex, Axis of Symmetry, Maximum, Minimum, Trinomial, Coefficients, Constant,
Perfect Square Trinomial, Factoring, Roots, Completing the Square, Quadratic Equation Form (Standard, Vertex, and Factored), Irrational
solutions, No real solution
Student Outcomes:
By the end of unit 10B, through assessment, students will demonstrate that they are able to:

Complete the square of a quadratic equation and determine zeros (roots), vertex, and axis of symmetry.
 Use technology as part of validating the solutions.

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
30
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 4: Algebra 1 Unit 10C
Unit 10C: The Quadratic Formula
Duration: 5 days
Overview of Unit 10C
This unit focuses on critical area 3. This topic extends the work of the previous topic by introducing students to the
quadratic formula as a method for solving quadratic equations. As using this formula sometimes requires students to
simplify expressions containing square roots, the connection between the algebra and the geometry of square roots is
explored. Students also learn how the value of the discriminant indicates the nature of the solutions.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form
(x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
A.REI.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a ± bi for real numbers a and b.
MA.4.c. Demonstrate an understanding of the equivalence of factoring, completing the square, or using the quadratic
formula to solve quadratic equations.
Note: It is sufficient in Algebra 1 to recognize when roots are not real; writing complex roots is included in Algebra
2.
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
Essential Question:
How do you solve quadratic equations?
What are the considerations for choosing a specific method for solving quadratic functions?
Vocabulary:
Quadratic formula, Discriminant, Roots, Zeros, Solutions, Distinct Roots
Student Outcomes:
By the end of unit 10C, through assessment, students will demonstrate that they are able to:
 Use the quadratic formula to find roots of quadratic functions
 Use the discriminant to determine the nature of the roots
 Solve quadratic equations by inspection
31
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
Quarter 4: Algebra 1 Unit 10D
Unit 10D: Modeling with Quadratic Functions
Duration: 5 days
Overview of Unit 10D
This unit focuses on critical area 2. This topic continues the exploration of quadratic functions, focusing on how to build quadratic
functions that model real-world situations. Students learn how to use the method of completing the square to transform quadratic
function rules to understand the behavior of the function. Best fit and the quadratic regression feature of graphic calculators are used to
find a quadratic function rule in the form y = ax² + bx + c to fit data.
Content Standards:
The order of the standards shown below does not imply the sequence in which they should be taught.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes
with labels and scales. 
A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the
quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end
behavior; and periodicity. 
F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for
more complicated cases. 
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. 
F.IF.8 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.

Indicates Modeling Standard
Note: Algebra I does not include the study of conic equations; include quadratic equations typically included in Algebra I.
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
5. Use appropriate tools strategically.
Essential Question:
How do you model data using a quadratic function?
How can you know if your model is accurate?
Vocabulary:
Quadratic regression, Non-Linear System
Student Outcomes:
By the end of unit 10D, through assessment, students will demonstrate that they are able to:
 Use technology to find a quadratic regression
 Build quadratic functions that model real-world situations
 Solve a simple system involving linear equations and a quadratic equation

indicates Modeling standard.
(+) indicates standard beyond College and Career Ready.
32
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
33
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Overview
Number and Quantity
The Real Number System

Extend the properties of exponents to
rational exponents.

Use properties of rational and irrational
numbers.
Quantities

Reason quantitatively and use units to solve
problems.
Algebra
Seeing Structure in Expressions

Interpret the structure of expressions.

Write expressions in equivalent forms to
solve problems.
Arithmetic with Polynomials and Rational
Expressions

Perform arithmetic operations on
polynomials.
Creating Equations

Create equations that describe numbers or
relationships.
Reasoning with Equations and Inequalities

Understand solving equations as a process
of reasoning and explain the reasoning.

Solve equations and inequalities in one
variable.

Solve systems of equations.

Represent and solve equations and
inequalities graphically.
Functions
Interpreting Functions

Understand the concept of a function and
use function notation.

Interpret functions that arise in applications
in terms of the context.

Analyze functions using different
representations.
Building Functions

Build a function that models a relationship
between two quantities.

Build new functions from existing functions.
STANDARDS FOR
MATHEMATICAL PRACTICE
1. Make sense of problems and persevere
in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique
the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for an express regularity in
repeated reasoning.
Functions (cont’d.)
Linear, Quadratic, and Exponential Models

Construct and compare linear, quadratic,
and exponential models and solve problems.

Interpret expressions for functions in terms
of the situation they model.
Statistics and Probability
Interpreting Categorical and Quantitative
Data

Summarize, represent, and interpret data on
a single count or measurement variable.

Summarize, represent, and interpret data on
two categorical and quantitative variables.

Interpret linear models.
34
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Content Standards
Number and Quantity
The Real Number System
N-RN
Extend the properties of exponents to rational exponents.
1.
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we
define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
If
what is the value of x?
A) 4 [Took half of 8]
B) 8 [Lacks concept of fractional exponents]
C) 16 [Multiplied 8 and 2]
D) 64 [Correct]
2.
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Simplify
A)
[Exponential multiplication error - forgot to increase exponent of x]
B)
[Exponential multiplication error and arithmetic multiplication error]
C)
D)
[Exponential multiplication error - forgot to carry the negative sign]
[Correct]
Use properties of rational and irrational numbers.
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.
A rectangle has side lengths of 3 inches and
inches. Which statement must be true about the area
of the rectangle?
A) It is a rational number because the product of the side lengths is the rational number 15. [Selected a
false statement based on the improper application of the multiplication algorithm for rational and
irrational numbers, ignoring the radical sign in
]
B) It is an irrational number because the product of the side lengths is
[Correct]
C) It is a rational number because the product of
irrelevant information to justify a false statement]
and
an irrational number.
results in 5, a rational number. [Used
D) It is an irrational number because the product of the side lengths is
an irrational number.
[Used the incorrect application of the multiplication algorithm for rational and irrational numbers to
justify what otherwise would have been a true statement]
35
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Quantities
N-Q
Reason quantitatively and use units to solve problems.
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. 
Ms. Glick drew two line segments on the chalkboard. The first line segment was 168 cm long and the
other was 5 feet 2 inches long. If 1 inch = 2.54 cm, approximately how many inches longer was the first
line segment than the second?
A) 1 inch [Does not understand unit conversion]
B) 4 inches [Correct]
C) 8 inches [Does not understand unit conversion]
D) 11 inches [Does not understand unit conversion]
2.
Define appropriate quantities for the purpose of descriptive modeling. 
Natalie borrowed $1,800 from her mother to purchase a pre-owned car. She agrees to repay this amount
by paying her mother $45 per week. This situation can be modeled by the function
Which inequality represents the domain for this function?
A)
B)
C)
D)
3.
[Represents a symmetric x-axis]
[Represents a standard viewing window]
[Correct]
[Represents the 52 weeks in a year]
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 
Albert estimated that a stack of books weighed 16 kilos. The actual weight of the books was 20 kilos.
Which of the following is the relative error?
A) 0.20 [Correct]
B) 0.25 [
]
C) 0.80 [
]
D) 1.25 [
]

indicates Modeling standard.
36
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Quantities
N-Q
Reason quantitatively and use units to solve problems.
3.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities
MA.3.a. Describe the effects of approximate error in measurement and rounding on measurements and on
computed values from measurements. Identify significant figures in recorded measures and computed values
based on the context given and the precision of the tools used to measure
George recorded the amount of zinc per serving in some of his favorite fruits and vegetables in the table.
Zinc in Fruits and Vegetables
Food
Zinc per Serving
(milligrams)
Kiwi
0.3
Blackberries 0.4
Potatoes
0.45
Peas
1.9
If George eats one serving of each of the foods listed in this table, about how much zinc will George consume, rounded to the
appropriate number of significant digits?
A) 3.0 mg [ Rounds down ]
B) 3.1 mg [ Correct ]
C) 3.05 mg [ Incorrect number of significant digits ]
D) 3.050 mg [ Incorrect number of significant digits ]
37
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Algebra
Seeing Structure in Expressions
A-SSE
Interpret the structure of expressions. 2
1.
Interpret expressions that represent a quantity in terms of its context. 
a. Interpret parts of an expression, such as terms, factors, and coefficients.
What is the number of terms in the polynomial below?
A) 7 [Coefficient of 2nd term]
B) 4 [Exponent of 1st term]
C) 3 [Exponent of 2nd term]
D) 2 [Correct]
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example,
interpret P(1 + r)n as the product of P and a factor not depending on P.
A baker sells cookies for $1.50 each. If a minimum of two dozen cookies is ordered, the baker gives a 40%
discount for each cookie ordered after the minimum has been met. The cost of an order of cookies after
this discount is given by the expression below.
Which of the following parts of the expression represents the number of cookies to which the discount
will be applied?
A) 1.5c [ Chose the part of the expression that represents the total cost before the discount ]
B) c –24 [ Correct ]
C) 1.5c –0.4 [ Chose the part of the expression that combines unrelated values ]
D) 0.4(c –24) [ Chose the part of the expression that represents the amount of the discount ]
2.
Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus
recognizing it as a difference of squares that can be factored as
(x2 – y2)(x2 + y2).
Which expression is equivalent to
A)
[ Correct ]
B)
[ Does not understand equivalent expressions ]
C)
D)
2

[ Does not understand equivalent expressions ]
[ Does not understand equivalent expressions ]
Algebra I is limited to linear, quadratic, and exponential expressions.
indicates Modeling standard.
38
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Algebra
Seeing Structure in Expressions
A-SSE
Write expressions in equivalent forms to solve problems.
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.
Which of the following is equivalent to the equation below?
A)
[ Does not understand factoring quadratic polynomials ]
B)
[ Does not understand factoring quadratic polynomials ]
C)
[ Does not understand factoring quadratic polynomials ]
D)
[ Correct ]
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it
defines.
Which of the following is a true statement about the graph of the function
?
A) The graph has a maximum at
. [Confused maximum and minimum]
B) The graph has a minimum at
. [Correct]
C) The graph has a maximum at
confused maximum and minimum]
. [Did not multiply
by 4 before adding it to the other side and
D) The graph has a minimum at
. [Did not multiply
by 4 before adding it to the other side]
c.
Use the properties of exponents to transform expressions for exponential functions. For example, the
expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly
interest rate if the annual rate is 15%.
The expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
39
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Arithmetic with Polynomials and Rational Expressions
A-APR
Perform arithmetic operations on polynomials.
1.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 3
The expression
represents the height in feet of a rocket t seconds after it is
launched. The expression
represents the height in feet of a second rocket t
seconds after it is launched. Which expression is equivalent to the difference in the heights of
the two rockets in feet?
A)
B)
[
[Correct]
]
C)
[
D)
[
]
]
Creating Equations4
A-CED
Create equations that describe numbers or relationships.
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. 
2.
Mr. Hamilton, a sales clerk in a hardware store, earns a base salary of
$1,500 per month plus a commission of 8 percent on monthly sales over
$300. If Mr. Hamilton received $1,820 for the month of October, how
much were his monthly sales?
A) $2,275 [Used 1820 = 0.8x]
B) $3,620 [1500 + 300 + 1820]
C) $4,000 [Did not add in first $300]
Create
equations
in two or more variables to represent relationships between quantities; graph equations on
D) $4,300
[Correct]
coordinate axes with labels and scales. 
Which equation represents a line with a slope of 0 that passes
through the point
A)
[Would have an undefined slope]
B)
[Used the x-coordinate instead of the ycoordinate]
C)
[Would have an undefined slope]
D)
[Correct]
Creating Equations5
A-CED
3
For Algebra I, focus on adding and multiplying polynomial expressions, factoring or expanding polynomial
expressions to identify and collect like terms, applying the distributive property.
4
Create linear, quadratic, and exponential (with integer domain) equations in Algebra I.

indicates Modeling standard.
40
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Create equations that describe numbers or relationships.
3.
Represent constraints by equations or inequalities, 6 and by systems of equations and/or inequalities, and interpret
solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing
nutritional and cost constraints on combinations of different foods. 
The graph of a system of inequalities is shown. What are the constraints to the system?
A)
B)
C)
4.
[ Made sign mistake with the slope in the equation
[ Confused the equations
and
]
[ Correct ]
D)
[ Made sign mistake with the slope in the equation
equations
and
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For
example, rearrange Ohm’s law V = IR to highlight resistance R. 
A)
B)
. Which equation correctly describes the height, h?
[Divided by 2]
[Correct]
C)
[
D)
[
]
]
Reasoning with Equations and Inequalities
6
and confused the
]
The formula for the area of a trapezoid is
5
]
A-REI
Create linear, quadratic, and exponential (with integer domain) equations in Algebra I.
Equations and inequalities in this standard should be limited to linear.
41
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Understand solving equations as a process of reasoning and explain the reasoning.
1.
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous
step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify
a solution method.
An athletic booster club is ordering drinks and chips to sell at a football game. The club
treasurer uses the equation
to determine d, the number of cases of soft
drinks the club can order if $250.00 is spent on chips, the total cost (c) is known, and each
case of soft drinks costs $3.50. Which equation is equivalent to
A)
[Added 3.5s instead of subtracting 3.5s]
B)
[Subtracted 3.5 instead of 3.5s]
C)
[Added 250 instead of subtracting 250]
D)
[Correct]
Solve equations and inequalities in one variable.
3.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by
letters.
The suggested retail price per bottle of dish soap, y, is determined by the volume in liquid
ounces, x, as shown below.
If the suggested retail price of a bottle of dish soap is $4.08, what is the bottle’s volume in
ounces?
A) 8 [Did not distribute the 0.48 to –2 : y = 0.5x – 0.24x + 2]
B) 12 [Correct]
C) 23 [Did not distribute the –0.48 to –2 and solved y = 0.5x – 0.24x – 2 and rounded answer]
D) 30 [First divided 4.08 by 0.5 and dropped the resulting x on the right side, then incorrectly
distributed a positive 0.48 to the first term and a negative 0.48 to the second term and
simplified to 8.16 = 0.24x + 0.96]
MA.3.a. Solve linear equations and inequalities in one variable involving absolute value.
What are all the roots for the equation
A)
and
[Correct]
B)
and 6 [One correct root, one with wrong sign]
C)
and 12 [One correct root, one with wrong sign]
D) 6 and 12 [Wrong signs for both roots]
42
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Reasoning with Equations and Inequalities
A-REI
Solve equations and inequalities in one variable.
4.
Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form
(x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
What number should be added to both sides of the equation to complete the
square?
A) 5 [Halved the coefficient of x but did not square the result]
B) 25 [Correct]
C) 50 [Squared the coefficient of x before dividing by 2]
D) 100 [Did not halve the coefficient of x before squaring]
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the
quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the
quadratic formula gives complex solutions7 and write them as a ± bi for real numbers a and b.
What are the values of x in the equation
A)
[ Subtracted 6 ]
B)
[ Correct ]
C)
[ Added instead of subtracting 3 ]
D)
[ Added 6 ]
MA.4.c. Demonstrate an understanding of the equivalence of factoring, completing the square, or using the
quadratic formula to solve quadratic equations.
Solve the quadratic 𝑥 2 − 4𝑥 − 5 = 0 using all three methods. Make sure that all
answers are equivalent.
7
It is sufficient in Algebra I to recognize when roots are not real; writing complex roots is included in Algebra II.
43
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Reasoning with Equations and Inequalities
A-REI
Solve systems of equations.
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.
Solve the linear system 𝟐𝒙 + 𝒚 = 𝟕
SOLUTION: (3,1)
𝟓𝒙 + 𝟐𝒚 = 𝟏𝟕
𝟐𝒙 + 𝒚 = 𝟕
𝟐(𝟓𝒙 + 𝟐𝒚 = 𝟏𝟕) → 𝟏𝟎𝒙 + 𝟒𝒚 = 𝟑𝟒
Add 𝟐𝒙 + 𝒚 = 𝟕 and 𝟏𝟎𝒙 + 𝟒𝒚 = 𝟑𝟒 to get 𝟏𝟐𝒙 + 𝟓𝒚 = 𝟒𝟏. The new
system has the same solution as the original system.
6.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
𝟏𝟐𝒙 + 𝟓𝒚 = 𝟒𝟏
SOLUTION: (3,1)
Look at this system of equations.
𝟓𝒙 + 𝟐𝒚 = 𝟏𝟕
What is the value of b for the solution to this system of equations?
A) 3 [Opposite of b]
B) 2 [Opposite of the value of a]
C) – 2 [The value of a]
D) – 3 [Correct]
7.
Solve a simple system consisting of a linear equation and a quadratic8 equation in two variables algebraically and
graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
What are the solutions to the system of equations?
A)
and
B)
C)
D)
8
[ Correct ]
and
and
[ Selects points that lie on the graph of the first equation ]
[ Inputs
(simplifies first equation incorrectly and correctly for second equation) ]
[ Concludes that a parabola and a line cannot intersect ]
Algebra I does not include the study of conic equations; include quadratic equations typically included in Algebra I.
44
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Reasoning with Equations and Inequalities
A-REI
9
Represent and solve equations and inequalities graphically.
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).
The Point (2, −5) is on the graph of which equation?
A)
[Correct]
B)
[Adds 2 and
to get the
]
C)
[Subtracts 2 from 5 to get the 3]
D)
[Substitutes 2 for y and
for x, instead of vice versa]
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 equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the
functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 
The graphs of
and
are shown on the grid below.
What is the solution to
A)
[ Correct ]
B)
[ Does not understand how to solve inequalities with graphs given ]
C)
[ Does not understand how to solve inequalities with graphs given ]
D)
[ Does not understand how to solve inequalities with graphs given ]
9
In Algebra I, functions are limited to linear, absolute value, and exponential functions for this cluster.
45
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Reasoning with Equations and Inequalities
Represent and solve equations and inequalities
12.
A-REI
10
graphically.
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
the corresponding half-planes.
Graph the solution to the system of inequalities?
Functions
Interpreting Functions
F-IF
Understand the concept of a function and use function notation.
1.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each
element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then
f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
The following equation is used to calculate the profit (or loss), p, in dollars, when a
company sells x number of T-shirts.
What is the domain?
A) integers [Cannot include negative numbers]
B) whole numbers [Correct]
C) positive integers [Includes 0]
D) positive real numbers [Cannot include all rational numbers]
2.
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function
notation in terms of a context.
If
what is y when
A) 11 [Does not understand solving equations]
B) 7 [Does not understand solving equations]
C) 3 [Correct]
D) –1 [Does not understand solving equations]
10
In Algebra I, functions are limited to linear, absolute value, and exponential functions for this cluster.
46
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Interpreting Functions
F-IF
Understand the concept of a function and use function notation.
3.
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the
integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n  1) for
n ≥ 1.
The first two terms of the sequence below are each 1.
Each term after that is the sum of the previous two terms. What number belongs in the
box?
A) 7 [Does not understand the sequence]
B) 8 [Correct]
C) 9 [Does not understand the sequence]
D) 10 [Does not understand the sequence]
Interpret functions11 that arise in applications in terms of the context.
4.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key
features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and periodicity. 
The graphing calculator screen displays data on the outdoor temperature in degrees Fahrenheit over several
hours on a winter day. The horizontal axis represents time.
What does the graph indicate about the outdoor temperature over time?
A) It got warmer at a constant rate, and then colder at a decreasing rate. [ Takes the decrease in the function to
indicate a decreasing rate ]
B) It got warmer at a constant rate, and then colder at an increasing rate. [ Correct ]
C) It got warmer at an increasing rate, and then colder at a decreasing rate. [ Takes the decrease in the function
to indicate a decreasing rate, and the increase in the function to indicate an increasing rate ]
D) It got warmer at an increasing rate, and then colder at an increasing rate. [ Takes the increase in the function
to indicate an increasing rate ]
11

Limit to interpreting linear, quadratic, and exponential functions.
indicates Modeling standard.
47
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Interpreting Functions
Interpret functions
5.
12
F-IF
that arise in applications in terms of the context.
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For
example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then
the positive integers would be an appropriate domain for the function. 
What is the domain of
6.
?
A)
[Domain of
]
B)
[Correct]
C)
[Domain of
]
D)
[Domain of
]
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. 
The table and graph below show the average movie ticket prices in the United States over a 20-year period.
Based on this information, which value is closest to the average rate of change from 1990 to 2010?
A) $0.03 [ Calculated the rate of change from 1990 to 1995 ]
B) $0.18 [ Correct ]
C) $1.48 [ Subtracted the price values between 2005 and 2010 ]
D) $3.67 [ Subtracted the price values between 1990 and 2010 ]
12
Limit to interpreting linear, quadratic, and exponential functions.
48
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Interpreting Functions
Analyze functions
7.
13
F-IF
using different representations.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. 
a. Graph linear and quadratic functions and show intercepts, maxima, and minima. 
The graph of which quadratic function opens downward at vertex (2, 5)?
A)
[Chose an equation with a vertex at
B)
[Correct]
C)
[Chose an equation that opens upward]
D)
[Chose an equation with a vertex at
]
]
b. Graph square root, cube root,14 and piecewise-defined functions, including step functions and absolute value
functions. 
The graph of
is shown below.
What is the value of y when x = 0?
A)
[ Correct ]
B)
[ Incorrect solution ]
C)
[ Incorrect solution ]
D)
[ Incorrect solution ]
Interpreting Functions
Analyze functions
15
F-IF
using different representations.
13
In Algebra I, only linear, exponential, quadratic, absolute value, step, and piecewise functions are included in this
cluster.

indicates Modeling standard.
14
Graphing square root and cube root functions is included in Algebra II.
49
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
7.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases. 
e. Graph exponential and logarithmic16 functions, showing intercepts and end behavior, and trigonometric
functions, showing period, midline, and amplitude. 17 
Which function is represented by the following graph?
A)
[ Chose a linear function ]
B)
[ Correct ]
C)
[ Chose a quadratic function ]
D)
[ Chose a cubic function ]
Interpreting Functions
A)
[ Chose a linear function ]
18
Analyze functions
8.
F-IF
using different representations.
B) a function[defined
Correctby
] an expression in different but equivalent forms to reveal and explain different
Write
properties
of the[ function.
C)
Chose a quadratic function ]
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme
of thefunction
graph, and
D) values, and [symmetry
Chose a cubic
] interpret these in terms of a context.
A graph of a quadratic function has x-intercepts of
matches this graph?
and
Which quadratic function
A)
[Correct]
B)
[The student chose an equation with x-intercepts of (4, 0) and (–8, 0)]
C)
[The student chose an equation with x-intercepts of (4, 0) and (8, 0)]
D)
[The student chose an equation with x-intercepts of (–4, 0) and (–8, 0)]
15
In Algebra I, only linear, exponential, quadratic, absolute value, step, and piecewise functions are included in this
cluster.

indicates Modeling standard.
16
In Algebra I it is sufficient to graph exponential functions showing intercepts.
17
Showing end behavior of exponential functions and graphing logarithmic and trigonometric functions is not part of
Algebra I.
18
In Algebra I, only linear, exponential, quadratic, absolute value, step, and piecewise functions are included in this
cluster.
50
Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Interpreting Functions
Analyze functions
8.
19
F-IF
using different representations.
Write a function defined by an expression in different but equivalent forms to reveal and explain different
properties of the function.
b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify
percent rate of change in functions such as y = (1.02) t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and classify
them as representing exponential growth or decay.
The hydrogen ion concentration of an acid is given by the formula
where
p is the pH. If solution A has a pH of 4, and solution B has a pH of 2, what is the ratio
of the hydrogen ion concentrations of solution A to solution B?
A) 1:100 [ Correct ]
B) 1:2 [ Thinks ratio is equivalent to 4:2 and switches the numbers in the ratio
because of the negative on the exponent ]
C) 2:1 [ Thinks ratio is equivalent to 4:2 ]
D) 100:1 [ Does not take into account the negative sign in the exponent ]
MA.8.c. Translate among different representations of functions and relations: graphs, equations, point sets, and
tables.
Which point is on the line
A) (–3, 5)
19
B) (–2, 3)
C) (1, –6)
D) (2, –9)
In Algebra I, only linear, exponential, quadratic, absolute value, step, and piecewise functions are included in this
cluster.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Interpreting Functions
Analyze functions
9.
20
F-IF
using different representations.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic
expression for another, say which has the larger maximum.
Lines m, n, o, and p are graphed on the coordinate grid below. A function table for one of the lines,
represented by the equation
, is also provided.
Which line best represents the equation
A) m [ Correct ]
B) n [ Confused by y-intercept ]
C) o [ Confused by y-intercept and slope ]
D) p [ Used the negative slope ]
?
MA.10. Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial,
rational, logarithmic, exponential, or trigonometric.
Which scenario describes a pattern of exponential decay?
A) A backgammon competition has 10 players exiting after each round of games. [Confused a constant decay
with exponential decay]
B) A ping-pong club has had 10, 9, and 8 new members in three years, respectively. [Confused growth that
decreases at a constant rate with exponential decay]
C) A billiards organization lost 5%, 4%, and 3% of its members in three years, respectively. [Took decay at a
declining rate to be exponential decay]
D) An elimination chess tournament has half the number of players in each successive round. [Correct]
20
In Algebra I, only linear, exponential, quadratic, absolute value, step, and piecewise functions are included in this
cluster.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Building Functions21
F-BF
Build a function that models a relationship between two quantities.
1.
Write a function that describes a relationship between two quantities. 
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
A boat travels 8.6 miles per hour in still water. Let m represent the river current in miles per hour. If
the boat travels with the river current, which expression represents the number of hours the boat
takes to travel 79 miles?
A)
[ Correct ]
B)
[ Subtracts m instead of adding m ]
C)
[ Incorrect order of operations ]
D)
[ Combination of errors ]
b. Combine standard function types using arithmetic operations. For example, build a function that models the
temperature of a cooling body by adding a constant function to a decaying exponential, and relate these
functions to the model. 
If
and
what is the product of
A) –65 [Correct]
B) –13 [Did not substitute correctly]
C) –10 [Did not substitute correctly]
D) 8 [Added 13 and –5]
2.
Write arithmetic and geometric sequences both recursively and with an explicit formula, 22 use them to model
situations, and translate between the two forms. 
Which function produces the same sequence as
A)
where x is an integer and
[ Used g1 as slope ]
B)
as gn ]
where x is an integer and
[ Used g1 as slope and same y-intercept
C)
as y-intercept ]
where x is an integer and
[ Used y-intercept of gn as slope and g1
D)
where x is an integer and
[ Correct ]

indicates Modeling standard.
Functions are limited to linear, quadratic, and exponential in Algebra I.
22
In Algebra I, identify linear and exponential sequences that are defined recursively; continue the study of
sequences in Algebra II.
21
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Building Functions23
F-BF
Build new functions from existing functions.
3.
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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. Include recognizing even and odd functions from their graphs and
algebraic expressions for them.
If the graph below is translated 3 units up, which equation would the graph represent?
A)
B)
C)
D)
4.
[This is the equation of the original graph]
[This is the equation of the graph moved 2 units up]
[Correct]
[The slope has been changed on this equation]
Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for
the inverse. For example, f(x) =2x3 or f(x) = (x + 1)/(x  1) for x ≠ 1
What is the inverse,
A)
23
of the function
[Found the additive inverse]
B)
[Correct]
C)
[Added 8 instead of subtracting 8]
D)
[Swapped 5 and 8]
Functions are limited to linear, quadratic, and exponential in Algebra I.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Linear, Quadratic, and Exponential Models
F-LE
Construct and compare linear, quadratic, and exponential models and solve problems.
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. 
Values for the function
are shown in the table.
Which statement proves that
is an exponential function?
A) All of the values of
are odd numbers. [ All outputs are odd numbers ]
B) All of the values of
are multiples of 3. [ All outputs are multiples of 3 ]
C) The function
grows by equal factors over equal intervals. [ Correct ]
D) The function
differences ]
grows by equal differences over equal intervals. [ The x-values grow by equal
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 
Which of the following situations is not best modeled by a linear function?
A) The height of a ball as it is thrown up in the air and falls back to the ground, as a function of time.
[Correct]
B) The total distance run around a track as a function of the number of laps around the track. [Does not
recognize a linear relationship]
C) The distance traveled by a train moving at a constant speed, as a function of time. [Does not
recognize a linear relationship]
D) The price of a piece of fabric that varies directly with the length of the piece of fabric, as a function of
the length. [Does not recognize a linear relationship]
R
Recognize situations in which a quantity grows or decays by a constant rcent rate per unit interval relative to
a
A copy
machine depreciates at the rate of 15% each year. If the original cost of the copy machine was
n
o
$20,000,
what is the approximate value of the machine at the end of 3 years?
t
A) $14,450 [Calculated 20000 (1 – .15)²]
h
B)e$14,000 [Subtracted 15% of 20,000 twice]
C)r$12,283 [Correct]
D). $11,000 [Subtracted 15% of 20,000 three times]


indicates Modeling standard.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Linear, Quadratic, and Exponential Models
F-LE
Construct and compare linear, quadratic, and exponential models and solve problems.
2.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a
relationship, or two input-output pairs (include reading these from a table). 
Which function is represented by this graph?
3.
A)
[Used a constant of positive 1]
B)
[Correct]
C)
[Changed signs on the constant and used the reciprocal slope]
D)
[Used the reciprocal slope]
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly,
 indicates Modeling standard.
In the graph below, f(x) is a linear function, and g(x) is an exponential function.
Which statement best explains the behavior of the graphs of the functions as x increases?
A) g(x) eventually exceeds f(x) because the rate of change of f(x) increases as x increases, whereas the rate of change of g(x) is constant. [ The student
incorrectly reasoned that the rate of change of f(x) is increasing and the rate of change of g(x) is constant ]
B) g(x) eventually exceeds f(x) because the rate of change of g(x) increases as x increases, whereas the rate of change of f(x) is constant. [ Correct ]
C) f(x) eventually exceeds g(x) because the rate of change of g(x) decreases as x increases, whereas the rate of change of f(x) is constant. [ The student
did not recognize that g(x) will eventually exceed f(x) and that the rate of change of g(x) is increasing ]
D) f(x) eventually exceeds g(x) because the rate of change of f(x) decreases as x increases, whereas the rate of change of g(x) is constant. [ The student
did not recognize that g(x) will eventually exceed f(x) and that the rate of change of g(x) is increasing while the rate of change of f(x) is constant ]
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Linear, Quadratic, and Exponential Models
F-LE
Interpret expressions for functions in terms of the situation they model.
5.
Interpret the parameters in a linear or exponential24 function in terms of a context. 
The expression
can be used to determine the size of a population that grows over a period
of time. What does 500 represent in the expression?
A) the final size of the population [ Chose what the whole expression represents ]
B) the initial size of the population [ Correct ]
C) the amount of time necessary to double [ Chose what the variable represents ]
D) the rate at which the population is growing [ Chose what (2) represents ]
Statistics and Probability
Interpreting Categorical and Quantitative Data
S-ID
Summarize, represent, and interpret data on a single count or measurement variable.
1.
Represent data with plots on the real number line (dot plots, histograms, and box plots). 
The box-and-whisker plots below show the distribution of heights of plants (in centimeters) in the three
rows of a garden.
Which list shows the rows in order from least to greatest range of plant heights?
A) Row 3, Row 2, Row 1 [Compared medians or Q3s]
B) Row 2, Row 3, Row 1 [Correct]
C) Row 2, Row 1, Row 3 [Compared maximums]
D) Row 1, Row 2, Row 3 [Compared minimums]

24
indicates Modeling standard.
Limit exponential function to the form f(x) = bx + k.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Interpreting Categorical and Quantitative Data
S-ID
Summarize, represent, and interpret data on a single count or measurement variable.
2.
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile
range, standard deviation) of two or more different data sets. 
Which set of numbers has the mean with the greatest value?
A) I [Least sum]
B) II [Used absolute value]
C) III [Smallest sum of absolute values]
D) IV [Correct]
3.
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of
extreme data points (outliers). 
The following graphs show the test grades for four different algebra classes. Which class has the most symmetrical data?
A)
B)
[Does not understand symmetry]
C)
[Does not understand symmetry]
D)
[Does not understand symmetry]
[Correct]
indicates Modeling standard.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Statistics and Probability
Interpreting Categorical and Quantitative Data
S-ID
Summarize, represent, and interpret data on a single count or measurement variable.
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. 25
The selling prices of houses in a city during one year were normally distributed with
a mean of $259,000 and a standard deviation of $15,000. Which of the following is
closest to the percentage of these homes that had a selling price between $244,000
and $289,000?
A) 47.7% [Only added 34.1% and 13.6% (did not double 34.1%)]
B) 68.2% [Thought both prices were one standard deviation from the mean]
C) 81.8% [Correct ]
D) 95.4% [Thought both prices were two standard deviations from the mean]
Summarize, represent, and interpret data on two categorical and quantitative variables.26
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. 
Some of the students at a high school were surveyed to find out which location was preferred for a school dance. The results
of the survey are shown in the table below.
What percentage of the students surveyed were Grade 11 students who preferred the dance be held at a hotel ballroom?
A) 9% [Correct]
B) 18% [Used 36 out of the number who preferred the hotel ballroom]
C) 36% [Used 36 out of the number of 11th graders surveyed]
D) 75% [Added the total number of 11th graders surveyed to the total number who preferred the hotel ballroom (did not
subtract the overlap) and divided by 400]

indicates Modeling standard.
Introduce in Algebra I; expand in Algebra II.
26
Linear focus; discuss as a general principle in Algebra I.
25
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Statistics and Probability
Interpreting Categorical and Quantitative Data
S-ID
Summarize, represent, and interpret data on a single count or measurement variable.
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 culture of bacteria is being grown in a lab. The graph shows the number of bacteria measured at
certain intervals.
Which value is closest to the number of bacteria in the culture at 6.5 hours?
A) 78 [5.5 hours]
B) 95 [6 hours]
C) 115 [Correct]
D) 140 [7 hours]

indicates Modeling standard.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Statistics and Probability
Interpreting Categorical and Quantitative Data
S-ID
Summarize, represent, and interpret data on a single count or measurement variable.
6.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 
b. Informally assess the fit of a function by plotting and analyzing residuals. 
The height of a plant is measured each week after the first sprout shows above the soil. A botanist tries to predict
the height of the plant in the upcoming weeks using the observed data in the table below.
The two lines on the graph were drawn to fit a function to the data.
Based upon the residuals, which statement best describes the line that is a better fit for the given data?
A) Line a is a better fit for the given data since the sum of squares error is less for Line a than the sum of squares error
for Line b. [The sum of squares error for Line a is 65.5625, which is greater than that of Line b, which is 13.5625]
B) Line b is a better fit for the given data since the sum of squares error is less for Line b than the sum of squares error
for Line a. [Correct]
C) Line b is a better fit for the given data since the sum of squares error is greater for Line b than the sum of squares
error for Line a. [Mistook a greater sum of the squares error as more accurate; however, the sum of the squares error
for Line b is 13.5625, which is less than for Line a, which is 65.5625]
D) Line a is a better fit for the given data since the sum of squares error is greater for Line a than the sum of squares
error for Line b. [Mistook a greater sum of squares error as more accurate]
* indicates Modeling standard.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Statistics and Probability
Interpreting Categorical and Quantitative Data
S-ID
Summarize, represent, and interpret data on a single count or measurement variable.
6.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. 
c. Fit a linear function for a scatter plot that suggests a linear association. 
Which of the following equations best models the data in the scatterplot below?
A) y = x + 2 [ Wrong y-intercept ]
B) y = x – 2 [ Correct ]
C) y = –x + 2 [ Wrong slope and wrong y-intercept ]
D) y = –x – 2 [ Wrong slope ]
Interpret linear models.
7.
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 
A child attached a spool of string to a kite and started to fly the kite. The elapsed time in seconds and the length, in
feet, of the string between the spool and the kite is shown in the table below.
What information is provided by the slope of the linear equation that models this data?
A) The kite ends up 50 feet from the spool. [ The student confused slope and intercept ]
B) The kite starts out 50 feet from the spool. [ The student confused slope and intercept ]
C) The kite is being released at a rate of 5 feet per second. [ Correct ]
D) The kite is being reeled in at a rate of 5 feet per second. [ The student misinterpreted the positive nature of the slope ]

indicates Modeling standard.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14
MODEL TRADITIONAL PATHWAY: Model Algebra I
Statistics and Probability
Interpreting Categorical and Quantitative Data
S-ID
Interpret linear models.
8.
Compute (using technology) and interpret the correlation coefficient of a linear fit. 
A car dealer recorded the selling prices of his used cars in 2005. The table below shows the average
selling prices based on the age of the cars.
Prices of Used Cars
Age of Car Selling Price
(years) (in thousands)
1
$20
2
$18
3
$17
4
$15
5
$10
6
$7
Which best describes the correlation between the age of the car and the selling price of the car?
A) variable correlation [Does not see linear trend]
B) negative correlation [Correct]
C) no correlation [Does not see linear trend]
D) positive correlation [Interchanges positive and negative slope]
9.
Distinguish between correlation and causation. 
Which relationship is an example of causation?
A) Running longer increases the number of calories burned. [Correct]
B) The more education a person has, the higher their income. [Confused correlation and causation]
C) Students who watch a lot of television will have lower grades. [Confused correlation and causation]
D) College students with higher entrance exam scores also have higher grades. [Confused correlation
and causation]

indicates Modeling standard.
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Lynn Public Schools Algebra 1 Curriculum Map SY 13-14