New York State Testing Program
Next Generation Mathematics Test
Performance Level Descriptions
Algebra I
Spring 2023
Algebra I Performance Level Descriptions
Performance level descriptions (PLDs) help communicate to students, families, educators, and the public the specific
knowledge and skills expected of students when they demonstrate proficiency of a learning standard. The PLDs serve
several purposes in classroom instruction and assessment. They are the foundation of rich discussion around what
students need to do to perform at higher levels and to explain the progression of learning within a subject area. PLDs are
also crucial in explaining student performance on the NYS assessments since they make a connection between the scale
score, the performance level, and specific knowledge and skills typically demonstrated at that level.
Policy Definitions of Performance Levels
For each subject area, students perform along a continuum of the knowledge and skills necessary to meet the demands
of the Learning Standards for Mathematics. There are students who meet the expectations of the standards with
distinction, students who fully meet the expectations, students who minimally meet the expectations, students who
partially meet the expectations, and students who do not demonstrate sufficient knowledge or skills required for any
performance level. New York State assessments are designed to classify student performance into one of five levels
based on the knowledge and skills the student has demonstrated.
NYS Level 5
Students performing at this level meet with distinction grade-level expectations of learning standards.
NYS Level 4
Students performing at this level fully meet grade-level expectations of learning standards (likely prepared to succeed in
the next level of coursework).
NYS Level 3
Students performing at this level minimally meet grade-level expectations of learning standards (meet the content area
requirements for a Regents diploma but may need additional support to succeed in the next level of coursework).
NYS Level 2 (Safety Net)
Students performing at this level partially meet grade-level expectations of learning standards (sufficient for Local
Diploma purposes).
NYS Level 1
Students performing at this level demonstrate knowledge and skills below Level 2.
2
How were the PLDs developed?
Following best practice for the development of PLDs, the number of performance levels and their definitions were
specified prior to the articulation of the full descriptions. The New York State Education Department convened a group of
NYS mathematics educators to develop the initial draft PLDs for Algebra I. In developing PLDs, participants considered
policy definitions of the performance level and the knowledge and skill expectations for each grade level in the Learning
Standards. Once they established the appropriate knowledge and skills from a particular standard for NYS Level 4 (fully
meet), panelists worked together to parse the knowledge and skills across the other performance levels in such a way that
the progression of the knowledge and skills was clearly seen moving from Level 2 to Level 5. This process was repeated
for all of the standards within the course. The draft PLDs then went through additional rounds of review and edits from a
number of NYS-certified educators, content specialists, and assessment experts under NYSED supervision.
How can the PLDs be used by Educators and in Instruction?
The PLDs should be used as a guidance document to show the overall continuum of learning of the knowledge and skills
from the Learning Standards. NYSED encourages the use of the PLDs for a variety of purposes, including differentiating
instruction to maximize individual student outcomes, creating formative classroom assessments and rubrics to help
identify target performance levels for individual or groups of students, and tracking student growth along the proficiency
continuum as described by the PLDs. The knowledge and skills shown in the PLDs describe typical performance and
progression, however the order in which students will demonstrate the knowledge and skills within and between
performance levels may be staggered (i.e. a student who predominantly demonstrates Level 3 knowledge and skills may
simultaneously demonstrate certain knowledge and skills indicative of Level 4).
How are the PLDs used in Assessment?
PLDs are essential in setting performance standards (i.e., “cut scores”) for New York State assessments. Standard setting
panelists use PLDs to determine the expectations for students to demonstrate the knowledge and skills necessary to just
barely attain a Level 3, Level 4, or Level 5 on the assessment. These knowledge and skills drive discussions that influence
the panelists as they recommend the cut scores on the assessment. PLDs are also used in question development.
Question writers are assigned to write questions that draw on the specific knowledge and skills from a PLD. This ensures
that each test has questions that distinguish performance all along the continuum. Teachers can use the PLDs in the
same manner when developing both formative and summative classroom assessments. Tasks that require students to
demonstrate knowledge and skills from the PLDs can be tied back to the performance level with which the PLD is
associated, providing the teacher with feedback about the students’ progress as well as a wealth of other skills that the
student is likely able to demonstrate (or can aspire to in the case of the next-highest PLD).
Note: Certain level 5 PLD’s will be denoted with a star, indicating the knowledge and skills represented will not be
targeted by questions on the NYS Algebra I Regents Examination.
3
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Use Properties of
rational and
irrational
numbers.
N-RN.B
*Perform operations on
radicals that include
variables in the radicand.
1
Perform operations on
rational and irrational
numbers of unlike
radicals which require
more than one
simplification.
Rationalize numerical
denominators of
irrational fractions.
Perform operations on
rational and irrational
numbers including like and
unlike radicals which
require only one
simplification.
Perform operations on
radicals which do not
require simplification of
the radicand. (Addition
and subtraction may
include a variable in
front of the radical.)
Explain why sums or
products of given
numbers are rational or
irrational.
Categorize the sums or
products of rational
and/or irrational
numbers as rational or
irrational.
Identify rational and
irrational numbers.
Reason
quantitatively and
use units to solve
problems.
N-Q.A
Explain how altering the
units would affect the
degree of accuracy of the
solutions.
Convert units of measure
using multiple steps.
Choose and/or interpret
the appropriate unit and
scale in formulas, graphs,
and data displays.
Apply the given units of a
multi-step real world
problem to determine an
appropriate solution
pathway.
Identify the correct steps
necessary to convert units
of measure.
Determine an appropriate
unit of measure given a
real-world situation.
Convert accurately
between two units of
measure (does not
include rates).
Justify the accuracy of
Determine an
units and/or limitations on
appropriate level of
measurements used in
accuracy on
reporting quantities when
measurements in context
solving problems.
when reporting
quantities, (if units are
tenths and hundredths,
then the
appropriate level is
tenth).
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
4
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Interpret the
structure of
expressions.
A-SSE.A
Simplify expressions,
including combining like
terms, using the
distributive property or
other operations on
polynomials.
Arrange a polynomial
expression in standard
form.
Identify the terms of a
polynomial: coefficients,
degree, leading
coefficient, and constant
term.
Arrange a trinomial in
standard form.
Explain how an equivalent
but different form of an
expression reveals
different information
about the context it
models.
Interpret parts of an
expression in terms of
quantities they represent
within a context,
including cases that
involve rewriting the
expressions.
Write an appropriate
expression within the
context of a real-world
problem.
Translate a verbal
expression into a
mathematical
expression.
*Factor a polynomial
whose leading coefficient
is other than 1 (there is no
GCF).
1
Rewrite polynomials in
equivalent forms using a
combination of methods
to factor completely.
Determine equivalent
expressions by applying
factoring strategies that
include a GCF with a
variable, the difference of
perfect squares, or
trinomials in the form of
whose
leading coefficient is 1.
Identify and factor out a
numerical GCF.
Write expressions
in equivalent
forms to reveal
their
characteristics.
A-SSE.B
Explain how equivalent
but different forms of
exponential expressions,
(* including fractional
exponents
1
),
reveal different
characteristics about the
function they define.
Rewrite equivalent
monomial expressions
using more than one law
of exponents.
Rewrite expressions
using the laws of
exponents to create
equivalent polynomials.
Write equivalent
monomials or polynomials
that include coefficients
that are not equal to one
using one law of
exponents.
Write equivalent
monomials with
coefficients equal to one
using laws of exponents.
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
5
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Perform
Perform at least two
Perform at least two
Perform an operation
Perform an operation,
arithmetic
operations on polynomial
operations (addition,
(addition, subtraction, and
including addition or
operations on
expressions with
subtraction, and
multiplication) on
subtraction on
polynomials.
fractional coefficients.
multiplication) on
polynomial expressions
polynomial expressions
A-APR.A
polynomial expressions
which may include
multiplying a
trinomial by a binomial
or a trinomial by a
trinomial.
that may include a
fractional coefficient.
Perform multiplication on
two binomials.
with integral
coefficients.
Understand the
Create a possible
Determine the zeros of
Identify the zeros of
Identify the zeros of a
relationship
factorization of a
polynomial functions by
quadratic and cubic
quadratic function using
between zeros
polynomial function based
using different methods
functions when written in
a method other than
and factors of
upon known zeros.
of factorization.
factored form.
factorization
polynomials.
(graphically, use of a
A-APR.B
*Explain how the zero(s)
of a function relates to a
graph.
1
Explain the relationship
between a function and
its zeros.
table, or technology).
Create equations
that describe
numbers or
relationships
A-CED.A
Create a one variable
equation or inequality to
represent a real-world
context, which requires
more than two steps.
Create an exponential
function that describes a
relationship between
two quantities given a
real-world context.
Create equations and
inequalities in two
variables to represent a
real-world context.
Create a one variable
equation or inequality to
represent a real-world
context, which requires
one or two steps.
Create an equation or
inequality in one
variable given a verbal
description.
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
6
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Explain how the
solution(s) to equations
and inequalities represent
what is viable or not
viable within the modeling
context.
Create and solve a
multiple step equation or
inequality in one variable
to represent a real-world
context and/or interpret
the solutions.
Create and solve a
quadratic or exponential
equation in one variable
given the context of the
problem and/or interpret
the solutions.
Create and solve systems
of equations or
inequalities in two
variables to represent a
real-world context
and/or interpret the
solutions.
Create and solve a one or
two step equation or
inequality in one variable
to represent a real-world
context.
Identify a solution to the
context of a problem
using a method other
than algebraic.
Rewrite a formula or
identify an equivalent
expression that involves
taking the square root
and/or subscripts.
Rewrite a formula using
more than two steps to
solve for a given variable.
Rewrite formulas using
two steps to solve for a
given variable.
Understand
solving equations
as a process of
reasoning and
explain the
reasoning.
A-REI.A
Construct a viable
argument to justify a
quadratic solution
method.
State and/or explain
more than one step
when solving a linear or
quadratic equation.
State one property in the
algebraic solution of a
single variable equation
using precise
mathematical vocabulary.
Solve equations
and inequalities in
one variable.
A-REI.B
Solve literal equations
involving factoring.
Solve multi-step linear
equations and
inequalities in one
variable where the
coefficients and
constants are rational
numbers.
Solve literal equations.
Solve multi-step linear
equations and inequalities
in one variable where the
coefficients are rational
numbers, and the
constants are integers.
Solve two step
equations and
inequalities in one
variable where the
coefficients are rational
numbers, and the
constants are integers.
Graph the solution of an
inequality on a number
line.
7
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
*Rewrite a quadratic
equation into the form
by using the
method of completing the
square. The quadratic's
leading coefficient is other
than 1 and the coefficient
of the linear term may be
1
odd or even.
Rewrite the quadratic
equation in the form
into
the form
by using
the method of
completing the square.
The quadratic's leading
coefficient must be 1 and
the coefficient of the
linear term must be even
(after factoring out a
possible GCF).
Rewrite an equation in the
form
into the
form
by
completing the square,
where b is even.
Determine the value of c
given the trinomial
, where
and b is even, to
create a perfect square
trinomial.
*Solve a quadratic by
factoring whose leading
coefficient is other than 1
(there is no GCF).
1
Construct a viable
argument to justify the
advantage of using one
method over another.
Determine if a quadratic
equation has no real
solution using the
discriminant.
Predict, without solving,
when a quadratic
equation will have no real
solutions and explain
using algebraic or
graphical evidence.
Solve quadratic
equations by factoring or
graphing.
Solve quadratic
equations by completing
the square or the
quadratic formula. This
may include simplifying
radicals.
Determine the number of
the solutions to a
quadratic equation
algebraically.
Determine the solutions to
a quadratic equation that
is set equal to zero using
the difference of two
perfect squares.
Determine the solutions to
a quadratic equation that
is given in factored form
or in the form,
.
Determine the number of
solutions to a quadratic
equation from a given
graph.
Solve quadratic
equations by inspection
or by taking square
roots.
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
8
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Solve systems of
equations.
A-REI.C
Explain a method of
choice when solving
systems of linear
equations.
Determine approximate
solutions using
technology.
Solve systems of linear
equations in two
variables either
algebraically or
graphically. Equations
have rational coefficients
and/or constants.
Solve systems of linear
equations in two variables
either algebraically or
graphically. Equations
have integral coefficients
and constants.
Determine the number of
solutions for linear system
of equations. (One
solution, many solutions,
or no solution.)
Solve systems of linear
equations algebraically
(when one equation is
solved for a variable) or
graphically (when the
equations are solved for
y).
Identify a correct step in
the process of using
substitution to solve a
system of equations.
Determine the number
of solutions given the
graphs of a linear system
of equations. (One
solution, many
solutions, or no
solution.)
Solve a linear-quadratic
system of equations
graphically and
approximate the solutions
using technology.
Solve a linear-quadratic
system of equations in
two variables
algebraically.
Solve a linear-quadratic
system of equations in
two variables, with
integral solutions,
graphically.
Determine the number of
solutions of a linear-
quadratic system. (One
solution, two solutions, or
no solution.)
Justify that a given set of
coordinates is a solution
to a linear-quadratic
system of equations.
Represent and
solve equations
and inequalities
graphically.
A-REI.D
Determine if a point does
not fall on a line, given a
set of points when the
equation is not given.
Determine either the x or
y coordinate of a point
on the parabola when
given the equation of the
parabola.
Write the equation for a
line when given two
points on the line.
Determine if the graph of
an equation in two
variables is the set of all
solutions in the
coordinate plane where
the numbers are rational
values.
Determine either the x or
y coordinate of a point on
the line when given the
equation of the line.
Write the equation for a
line when given the slope
and a point on the line.
Write the equation of a
line when given its graph.
Determine if a point is
on a line or parabola
when given its equation.
Write the equation of a
line when given the
slope and y intercept.
Determine if the graph
of an equation in two
variables is the set of all
solutions in the
coordinate plane where
the numbers are integral
values.
9
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Explain why the solution
of two equations in two
variables occur at the
point of intersection of
their graphs.
Determine non-integral
solutions to
using
technology.
Interpret the meaning of
the intersection of the
graphs of y=f(x) and
y=g(x) in terms of a
context.
Graph f(x) and g(x) and
state all values of x for
which
This
may include quadratic,
absolute value,
exponential, and step
(piecewise) functions.
Graph the linear functions
f(x) and g(x) and state the
value of x for which
State all values of x for
which
when given the graphs
of f(x) and g(x).
Explain what a point in the
Write an inequality given
Justify that a point lies in
Justify that a point lies in
solution set means in the
its graph.
the solution set of a
the solution set of a
context of the problem.
system of inequalities.
given inequality.
Explain why there are
Graph the solution set to
Graph the solutions to one
Identify a point in the
multiple solutions to a
a system of linear
linear inequality in two
solution set given the
system of inequalities.
inequalities in two
variables as the
intersection of the
corresponding half-
planes.
variables as a half- plane.
graph of a system of
inequalities.
Understand the
concept of a
function and use
function notation.
F-IF.A
Explain 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.
State the domain and/or
range of a given function
using set builder
notation, interval notion,
inequalities, or a
verbal description.
Identify if a relation is a
function when given a
linear, exponential,
quadratic, or square root
equation.
Identify if a relation is a
function given a graph,
table, coordinates,
mapping, or a verbal
description.
Determine the input for a
Evaluate multiple
Evaluate a function when
Evaluate functions for
given output when the
functions for inputs in
given function notation,
inputs in their domains
equation is expressed in
their domains when
for inputs in its domain.
using a table or graph.
function notation.
given the equations in
function notation.
Interpret statements that
use function notation in
terms of a context.
Express inputs and
outputs using function
notation.
10
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
*Write a sequence in a
recursive form.
1
Write an explicit equation
in subscript notation given
two terms and the type of
sequence.
Determine a specific term
of a sequence given the
type of sequence and two
terms in the sequence
that includes variables.
Explain why sequences are
functions whose domain is
a subset of integers.
Explain if a function is
continuous or discrete in a
real-world context.
Identify the common
difference or ratio for
sequences that include
variables.
Write an explicit
equation in subscript
notation for a given
sequence.
Determine a specific
term of a sequence given
the type of sequence and
at least two terms in the
sequence.
Determine the nth term
for a given sequence
using the explicit
formula.
Identify the common
difference for an
arithmetic sequence.
Identify the common ratio
for a geometric sequence.
Determine a specific term
of a sequence given a
term in the sequence and
the common difference or
ratio.
Identify and continue
patterns of geometric
sequences.
Identify if a given
sequence is arithmetic,
geometric, or neither.
Interpret
functions that
arise in
applications in
terms of the
context.
F-IF.B
Determine non-integral
key features of a function
by using technology.
Interpret key features of
functions (including
absolute value, square
root, and piecewise),
from a verbal
description, equation, or
graph of the relationship.
Describe key features of
functions (including
absolute value, square
root, and piecewise.)
Describe an interval (set
of numbers) using set
builder notation, interval
notation, or inequalities.
Interpret key features of
functions (including linear,
quadratic, and
exponential), from an
equation, graph, or table
of values in the context of
the problem. The domain
of the exponent is limited
to positive integral values.
Describe the key features
of functions in the context
of the problem (including
linear, quadratic, and
exponential).
Describe the x and y
intercepts in the context
of the problem given its
graph.
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
11
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Determine the domain of
a function from its
equation.
Explain why a domain is
appropriate given the
real-world context.
Determine the
appropriate domain for a
function in context.
Determine the domain of
a function from its graph.
Determine the domain
of a function from its
table.
Calculate, interpret, and
compare the average rate
of change of two or more
functions over a specified
interval.
Calculate the average rate
of change over a specified
interval when the
equation is written in
function form.
Interpret the average
rate of change of a
function over a specified
interval in context, which
may include stating the
appropriate units.
Express the average rate
of change of a function
over a specified interval
using set builder
notation, interval
notation, or inequalities.
Calculate multiple average
rates of change of a
function over specified
intervals from a table or
graph.
Calculate the average
rate of change of a
function over a specified
interval from a table or
graph.
Analyze functions
using different
representations.
F-IF.C
*Graph exponential
equations, including the
asymptotes.
1
Identify key features of a
graph by hand or by using
technology where the
values are not integers.
Graph square root,
absolute value, and
piecewise functions by
hand or by using
technology where
appropriate.
Graph functions over a
given domain.
Graph quadratic and
exponential functions by
hand or by using
technology where
appropriate.
Identify key features of a
graph where the values
are integers.
Graph linear functions
by hand or by using
technology where
appropriate.
*Determine the vertex of
Write a quadratic
Write a linear function in
Write a linear function
a quadratic function by
function in different but
different but equivalent
in different but
using the process of
equivalent forms to
forms to reveal and/or
equivalent forms to
completing the square.
1
reveal and/or explain
different characteristics
of the function.
Algebraically determine
the vertex, maxima, or
minima of a quadratic
function.
Determine the zeros of a
quadratic function using
factorization.
Algebraically determine
the zeros of a quadratic
function using the
quadratic formula.
explain different
characteristics of the
function.
Determine the equation
for the axis of symmetry of
a quadratic function using
a formula.
Determine the zeros of a
function written in
factored form.
reveal different
characteristics of the
function.
State the equation for
the axis of symmetry of
a quadratic function
when given its graph.
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
12
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Compare key features of
more than two functions
represented in different
ways which must include a
verbal description.
Transform and/or graph
functions to justify an
interpretation of the key
features.
Compare key features of
more than two functions
represented in at least
three different ways.
Compare key features of
two or more functions
represented in at least
two different ways
(graphically, algebraically,
or numerically in tables).
Compare key features of
two functions each
represented graphically.
Build a function
that models a
relationship
between two
quantities.
F-BF.A
Write a quadratic function
that describes a
relationship between two
quantities given a real-
world context.
Write an explicit
geometric function when
given two non-
consecutive terms, neither
of which are the initial
term.
Write an explicit
geometric or arithmetic
function when the terms
include variables.
Generate the nth term of
a given sequence where n
is greater than 25.
Write an exponential
function that describes a
relationship between
two quantities given a
real-world context.
Write an explicit
geometric function using
subscript notation given
the initial term and a
common ratio or two
consecutive terms.
Write an explicit
arithmetic function when
given two non-
consecutive terms,
neither of which are the
initial term.
Write a linear function
that describes a
relationship between two
quantities given a real-
world context.
Write a linear function
that describes a
relationship between two
quantities given a table.
Write a geometric
sequence when given the
initial term and common
ratio or two consecutive
terms.
Write an explicit
arithmetic function using
subscript notation given
the initial term and a
common difference or two
consecutive terms.
Write a linear function
that describes a
relationship between
two quantities given a
graphical
representation.
Write an arithmetic
sequence when given
the initial term and
common difference or
two consecutive terms.
13
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Build new
functions from
existing functions.
F-BF.B
Explain the specific effect
on the graph when
replacing f(x) by
for values
of a, b, and c.
Generalize that the effect
of a constant, k, is the
same across different
function families.
Explain the specific effect
k has on the graph of f(x)
when replacing f(x) with
graphs of multiple
transformations.
Graph the image of f(x)
after multiple
transformations.
Write a new function
given a function f(x) and
a verbal description or
graph of multiple
transformations.
Explain the specific effect
k has on the graph of f(x)
given
,
or .
Determine the value of k
given the graphs f(x) and
the graph after one
transformation.
Graph a new function
given f(x) and a value of k
for one transformation.
Write a new function
given a function f(x) and a
verbal description or
graph of one
transformation.
Explore the general
effect (shift up, down,
right, left, wider, or
narrower) of k given the
graph of f(x) for
, , or
by using
technology.
Construct and
compare linear,
quadratic, and
exponential
models and solve
problems.
F-LE.A
Explain why situations can
be modeled either linearly
or exponentially as
depicted in real-world
situations.
Justify/explain why a
function is linear or
exponential.
Describe an exponential
pattern of change in a
real-world situation.
Describe the rate of
change depicted in a
real-world situation
where a quantity grows
or decays at a constant
percent rate per unit
interval.
Identify a situation as
linear or exponential given
equations, graphs, tables,
and/or verbal
descriptions.
Describe a linear pattern
of change in a real-world
situation.
Describe the rate of
change depicted in a real-
world situation where a
quantity grows or decays
at a constant rate per unit
interval.
Identify the type of
function given a
situation represented by
a graph, table, and/or
verbal description.
Write an exponential
function, f(x), given a
graph.
Write an exponential
function, f(x), given a
verbal description
(growth and decay) or
from a table of values.
Write a linear function,
f(x), given a verbal
description or from a table
of values.
Write a linear function,
f(x), given a graph.
14
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Explain, by using student
Justify that exponential
Justify that a quantity
State a value that will
generated graphs and
rates of growth
increasing exponentially
demonstrate when a
tables, that a quantity
eventually exceed the
eventually exceeds a
quantity increasing
increasing exponentially
rates of growth modeled
quantity increasing
exponentially will
eventually exceeds a
by linear and quadratic
linearly given equations,
exceed a quantity
quantity increasing
functions when given
graphs and/or tables.
increasing linearly given
linearly or quadratically or
graphs and/or tables of
a graph.
as a polynomial function.
multiple functions.
State the interval where
the linear function grows
faster than the
exponential function.
Interpret
expressions for
functions in terms
of the situation
they model.
F-LE.B
Interpret changes in
parameters based on the
comparison of multiple
functions in terms of a
real-world context.
Rewrite exponential
equations in different
forms in terms of a real-
world context.
Compare exponential
functions in a variety of
contexts.
Identify that exponential
relationships have a
percentage rate of
change in terms of a real-
world context.
Interpret the meanings
of the initial value, rate,
and/or exponent of an
exponential function in
terms of a real-world
context.
Interpret the meaning of
in a
variety of contexts.
Identify an appropriate
value of b to model
growth or decay.
Write exponential
functions that are
described by the
parameters in the
context of the problem.
Identify the slope and/or
y-intercept in a linear
function in terms of a real-
world context.
Interpret the meanings of
the initial value and/or
rate of a linear function in
terms of a real-world
context.
Interpret the meaning of
in a
variety of contexts.
Identify an appropriate
value for m to model
increase or decrease.
Write linear functions that
are described by the
parameters in the context
of the problem.
Identify that linear
relationships have a
constant rate of change.
Rewrite a linear
equation in
form to best describe
the parameters.
15
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Summarize,
represent, and
interpret data on
a single count or
measurement
variable.
S-ID.A
Choose, justify, and
represent the most
appropriate graphical
representation of a set of
data.
Represent data by
constructing a cumulative
frequency histogram using
correct labels and
intervals.
Represent data by
constructing a box plot
on a student generated
scaled number line.
Represent data by
constructing a histogram
using correct labels and
intervals.
Determine the five
number summary of a
data set. Construct a box
plot on a given scaled
number line.
Represent data by
constructing dot plots.
Interpret data given a
histogram, a dot plot,
and/or a box plot.
Identify whether a given
graph is a histogram, dot
plot, or box plot.
Interpret the sample
Calculate and/or
Calculate and/or compare
Calculate and/or
standard deviation to
compare the sample
quartile 1, quartile 3, and
compare the mean,
describe the variability of
standard deviation of
the interquartile range of
median and/or range of
a data set, or to compare
two or more different
data sets.
data sets.
two sets of data that are
data sets.
approximately symmetric.
Solve real-world problems
by interpreting graphical
representations or
statistical values drawn
from two or more
different data sets.
Decide when to include
the outliers as part of the
data set or to remove
them for purposes of
descriptive modeling.
Interpret the spread of
the data using range
(when the data is not
skewed),
inter-quartile range,
and/or sample standard
deviation.
Explain which is the most
appropriate measure of
center and spread to
describe a distribution
that is symmetric (mean)
or skewed(median).
Interpret differences in
shape, center and spread
in the context of the data
sets using either sample
standard deviation or
interquartile range (if
there are outliers).
Calculate the
inter-quartile range of a
set of data.
Determine if the data set
has an approximately
normal distribution or is
skewed (left or right).
Identify and interpret the
effect of outliers on the
mean and/or median on
data sets, and how it
affects the distribution of
the data (normal or
skewed).
Calculate the range of a
set of data.
Identify outliers of a
given data set.
16
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Summarize,
represent, and
interpret data on
two categorical
and quantitative
variables.
S-ID.B
Calculate and compare
two or more conditional
relative frequencies.
Complete a two-way
frequency table.
Interpret marginal, joint,
and conditional relative
frequencies of data
displayed in a two-way
table in terms of a
context of the data
and/or use them to
predict outcomes.
Calculate marginal, joint,
and conditional relative
frequencies (expressed as
probability and/or
percentages) of data
displayed in a two-way
table in terms of a context
of the data.
Describe the associations
and trends in the data
given a completed two-
way table.
Identify quantitative
differences of
categorical data given a
two-way frequency
table.
*Fit a non-linear function
to the data by using
technology.
1
Use the linear model to
extrapolate or interpolate
values.
Fit a linear function to
real world data.
Sketch the line of best fit
given the scatter plot and
use this line to predict
values.
Fit a linear function to the
data by using technology
and state the regression
equation for line of best
fit.
Create a scatter plot from
two quantitative variables.
Given only a scenario,
describe the relationship
between two variables.
Given a scenario and a
scatterplot, describe the
relationship between
two variables (positive,
negative or no
relationship).
*Explain, in context, the
meaning of the line of
best fit that models
quadratic and exponential
data.
1
Explain, in context, the
meaning of the line of
best fit that models
linear data.
Make a prediction given a
scatterplot.
Sketch the line of best fit
given the scatter plot.
1
Level 5 PLD’s denoted with a star, indicate the knowledge and skills represented will not be targeted by questions on
the NYS Algebra I Regents Examination.
17
Performance Level 5
Performance Level 4
Performance Level 3
Performance Level 2
Interpret linear
models.
S-ID.C
Compare the slope and y-
intercept of two linear
models in context.
Interpret the slope and
the y-intercept of a linear
model in the context of
the data.
Interpret the slope or y-
intercept of a linear model
in the context of the data.
State the slope and the
y-intercept of a linear
model.
Explain that the
correlation coefficient
describes a statistical
relationship and can be
used to judge the fit but
does not indicate a cause-
and-effect relationship.
Interpret the strength of
the correlation
coefficient for the line of
best fit in the context of
the problem.
Use technology to state
the regression equation
and/or the correlation
coefficient for the line of
best fit. Indicate if the
relationship is strong or
weak.
State if a relationship is
strong and
or weak
given a correlation
coefficient.
Generate and explain
examples of relationships
that are correlated and
causal or correlated but
not causal.
Distinguish between
correlation and causation
for multiple
relationships.
Explain the difference
between correlation and
causation for a given
example.
Distinguish between
correlation and causation
for two relationships.
Explain the difference
between correlation and
causation.
Explain why a given
relationship represents
correlation.
Indicate if a relationship
is a positive or negative
correlation.
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