NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Ratio and Proportional Reasoning
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Analyze proportional
relationships and use
them to solve real-world
and mathematical
problems.
7.RP.1 Compute unit rates associated with ratios of
fractions, including ratios of lengths, areas and other
quantities measured in like or different units. For
example, if a person walks ½ mile in each ¼ hour,
compute the unit rate as the complex fraction
miles
per hour, equivalently 2 miles per hour.
NY-7.RP.1 Compute unit rates associated with ratios of fractions.
e.g., If a person walks
mile in each
hour, compute the rate as the
complex fraction
miles per hour, equivalently 2 miles per hour with 2
being the unit rate.
Note: Problems may include ratios of lengths, areas, and other quantities measured in like
or different units, including across measurement systems.
7.RP.2 Recognize and represent proportional
relationships between quantities.
NY-7.RP.2 Recognize and represent proportional relationships
between quantities.
7.RP.2a Decide whether two quantities are in a
proportional relationship, e.g., by testing for equivalent
ratios in a table or graphing on a coordinate plane and
observing whether the graph is a straight line through the
origin.
NY-7.RP.2a Decide whether two quantities are in a proportional
relationship.
Note: Strategies include but are not limited to the following: testing for equivalent
ratios in a table and/or graphing on a coordinate plane and observing whether the graph is
a straight line through the origin.
7.RP.2b Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
NY-7.RP.2b Identify the constant of proportionality (unit rate) in
tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
7.RP.2c Represent proportional relationships by
equations. For example, if total cost t is proportional to
the number n of items purchased at a constant price p,
the relationship between the total cost and the number of
items can be expressed as t = pn.
NY-7.RP.2c Represent a proportional relationship using an equation.
e.g., If total cost t is proportional to the number n of items purchased at
a constant price p, the relationship between the total cost and the
number of items can be expressed as t = pn.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Ratio and Proportional Reasoning
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Analyze proportional
relationships and use
them to solve real-world
and mathematical
problems.
7.RP.2d Explain what a point (x, y) on the graph of a
proportional relationship means in terms of the situation,
with special attention to the points (0, 0) and (1, r) where
r is the unit rate.
NY-7.RP.2d Explain what a point (x, y) on the graph of a proportional
relationship means in terms of the situation, with special attention to
the points (0, 0) and (1, r) where r is the unit rate.
7.RP.3 Use proportional relationships to solve multistep
ratio and percent problems. Examples: simple interest,
tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease,
percent error.
NY-7.RP.3 Use proportional relationships to solve multistep ratio and
percent problems.
Note: Examples of percent problems include: simple interest, tax, markups and
markdowns, gratuities and commissions, fees, percent increase and decrease, and percent
error.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
The Number System
Cluster
NYS P-12 CCLS
Apply and extend
previous understandings
of operations with
fractions to add,
subtract, multiply and
divide rational numbers.
7.NS.1 Apply and extend previous understandings of
addition and subtraction to add and subtract rational
numbers; represent addition and subtraction on a
horizontal or vertical number line diagram.
subtraction to add and subtract rational numbers. Represent addition
and subtraction on a horizontal or vertical number line.
7.NS.1a Describe situations in which opposite quantities
combine to make 0. For example, a hydrogen atom has 0
charge because its two constituents are oppositely
charged.
to make 0.
7.NS.1b Understand p + q as the number located a
distance |q| from p, in the positive or negative direction
depending on whether q is positive or negative. Show
that a number and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational numbers by
describing real-world contexts.
number located a distance |q| from p, in the positive or negative
direction depending on whether q is positive or negative. Show that a
number and its opposite have a sum of 0 (are additive inverses).
Interpret sums of rational numbers by describing real-world contexts.
7.NS.1c Understand subtraction of rational numbers as
adding the additive inverse, p – q = p + (–q). Show that
the distance between two rational numbers on the
number line is the absolute value of their difference, and
apply this principle in real-world contexts.
additive inverse, p – q = p + (–q). Show that the distance between two
rational numbers on the number line is the absolute value of their
difference, and apply this principle in real-world contexts.
7.NS.1d Apply properties of operations as strategies to
add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of
multiplication and division and of fractions to multiply
and divide rational numbers.
multiplication and division and of fractions to multiply and divide
rational numbers.
7.NS.2a Understand that multiplication is extended from
fractions to rational numbers by requiring that operations
continue to satisfy the properties of operations,
particularly the distributive property, leading to products
such as (–1)(–1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers by
describing real-world contexts.
to rational numbers by requiring that operations continue to satisfy the
properties of operations, particularly the distributive property, leading
to products such as (–1)(–1) = 1 and the rules for multiplying signed
numbers. Interpret products of rational numbers by describing real-
world contexts.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
The Number System
Cluster
NYS P-12 CCLS
Apply and extend
previous understandings
of operations with
fractions to add,
subtract, multiply and
divide rational numbers.
7.NS.2b Understand that integers can be divided,
provided that the divisor is not zero, and every quotient
of integers (with non-zero divisor) is a rational number.
If p and q are integers, then –(p/q) = (–p)/q = p/(–q).
Interpret quotients of rational numbers by describing
real-world contexts.
divisor is not zero, and every quotient of integers (with non-zero
divisor) is a rational number. If p and q are integers, then -(
) =

=
. Interpret quotients of rational numbers by describing real-
7.NS.2c Apply properties of operations as strategies to
multiply and divide rational numbers.
7.NS.2d Convert a rational number to a decimal using
long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
that the decimal form of a rational number terminates in 0s or
7.NS.3 Solve real-world and mathematical problems
involving the four operations with rational numbers.
Note: Computations with rational numbers extend the rules for
manipulating fractions to complex fractions.
four operations with rational numbers.
Note: Computations with rational numbers extend the rules for manipulating fractions to
complex fractions limited to
where a, b, c, and d are integers and b, c, and d ≠ 0.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Expressions and Equations (Inequalities)
Cluster
NYS P-12 CCLS
Use properties of
operations to generate
equivalent expressions.
7.EE.1 Apply properties of operations as strategies to
add, subtract, factor, and expand linear expressions with
rational coefficients.
rational coefficients by applying the properties of operations.
7.EE.2 Understand that rewriting an expression in
different forms in a problem context can shed light on
the problem and how the quantities in it are related. For
example, a + 0.05a = 1.05a means that “increase by
5%” is the same as “multiply by 1.05.”
in real-world and mathematical problems can reveal and explain
how the quantities are related.
e.g., a + 0.05a and 1.05a are equivalent expressions meaning that
“increase by 5%” is the same as “multiply by 1.05.”
Solve real-life and
mathematical problems
using numerical and
algebraic expressions,
equations and
inequalities.
7.EE.3 Solve multi-step real-life and mathematical
problems posed with positive and negative rational
numbers in any form (whole numbers, fractions, and
decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form;
convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and
estimation strategies.
For example: If a woman making $25
an hour gets a 10% raise, she will make an additional 1/10 of
her salary an hour, or $2.50, for a new salary of $27.50. If you
want to place a towel bar 9 3/4 inches long in the center of a
door that is 27 1/2 inches wide, you will need to place the bar
about 9 inches from each edge; this estimate can be used as a
check on the exact computation.
posed with positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. Apply
properties of operations to calculate with numbers in any form; convert
between forms as appropriate. Assess the reasonableness of answers
using mental computation and estimation strategies.
e.g.,
• If a woman making $25 an hour gets a 10% raise, she will
make an additional

of her salary an hour, or $2.50, for a
new salary of $27.50.
• If you want to place a towel bar 9
inches long in the center
of a door that is 27
inches wide, you will need to place the
bar about 9 inches from each edge; this estimate can be used
as a check on the exact computation.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Expressions and Equations (Inequalities)
Cluster
NYS P-12 CCLS
Solve real-life and
mathematical problems
using numerical and
algebraic expressions,
equations and
inequalities.
7.EE.4 Use variables to represent quantities in a real-
world or mathematical problem, and construct simple
equations and inequalities to solve problems by
reasoning about the quantities.
mathematical problem, and construct simple equations and inequalities
to solve problems by reasoning about the quantities.
Note
7.EE.4a Solve word problems leading to equations of
the form px + q = r and p(x + q) = r, where p, q, and r are
specific rational numbers. Solve equations of these forms
fluently. Compare an algebraic solution to an arithmetic
solution, identifying the sequence of the operations used
in each approach. For example, the perimeter of a
rectangle is 54 cm. Its length is 6 cm. What is its width?
+ q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve
equations of these forms fluently. Compare an algebraic solution to an
arithmetic solution, identifying the sequence of the operations used in
each approach.
e.g., The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is
its width?
Notes: The words leading to in the standard may require students to simplify or
combine like terms on the same side of the equation before it is in the form stated in
the standard.
This standard is a fluency expectation for grade 7. For more guidance, see Fluency
in the Glossary of Verbs Associated with the New York State Next Generation
Mathematics Learning Standards.
7.EE.4b Solve word problems leading to inequalities of
the form px + q > r or px + q < r, where p, q, and r are
specific rational numbers. Graph the solution set of the
inequality and interpret it in the context of the problem.
For example: As a salesperson, you are paid $50 per
week plus $3 per sale. This week you want your pay to be
at least $100. Write an inequality for the number of sales
you need to make, and describe the solutions.
px + q > r, px + q ≥ r, px + q ≤ r, or px + q < r, where p, q, and r are
rational numbers. Graph the solution set of the inequality on the
number line and interpret it in the context of the problem.
e.g., As a salesperson, you are paid $50 per week plus $3 per sale. This
week you want your pay to be at least $100. Write an inequality for the
number of sales you need to make, and describe the solutions.
Note: The words leading to in the standard may require students to simplify or
combine like terms on the same side of the equation before it is in the form stated in
the standard.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Geometry
Cluster
NYS P-12 CCLS
Draw, construct and
describe geometrical
figures and describe the
relationships between
them.
7.G.1 Solve problems involving scale drawings of
geometric figures, including computing actual lengths
and areas from a scale drawing and reproducing a scale
drawing at a different scale.
figures, including computing actual lengths and areas from a scale
drawing and reproducing a scale drawing at a different scale.
7.G.2 Draw (freehand, with ruler and protractor, and
with technology) geometric shapes with given
conditions. Focus on constructing triangles from three
measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one
triangle, or no triangle.
sides, noticing when the conditions determine a unique triangle, more
than one triangle, or no triangle.
Note: Create triangles through the use of freehand drawings, materials (scaffolds
may include: pipe cleaners, Legos®, and toothpicks), rulers, protractors, and/or
7.G.3 Describe the two-dimensional figures that result
from slicing three-dimensional figures, as in plane
sections of right rectangular prisms and right rectangular
pyramids.
three-dimensional solids parallel or perpendicular to the base.
Note: Focus of standard is on plane sections resulting from the slicing of right
Solve real-life and
mathematical problems
involving angle measure,
area, surface area and
volume.
7.G.4 Know the formulas for the area and circumference
of a circle and use them to solve problems; give an
informal derivation of the relationship between the
circumference and area of a circle.
circle to solve problems.
Note: Students in grade 7 are not expected to calculate the radius of a circle given
7.G.5 Use facts about supplementary, complementary,
vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle
in a figure.
and adjacent angles in a multi-step problem to write and solve simple
equations for an unknown angle in a figure.
Note: Students in grade 7 are limited to solving equations that involve linear
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Expressions and Equations (Inequalities)
Cluster
NYS P-12 CCLS
Solve real-life and
mathematical problems
involving angle measure,
area, surface area and
volume.
7.G.6 Solve real-world and mathematical problems
involving area, volume and surface area of two- and
three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms.
area of two-dimensional objects composed of triangles and
trapezoids.
Solve surface area problems involving right prisms and right
pyramids composed of triangles and trapezoids.
Find the volume of right triangular prisms, and solve volume
problems involving three-dimensional objects composed of right
rectangular prisms.
Notes: The inclusive definition of a trapezoid will be utilized, which defines a
trapezoid as “A quadrilateral with at least one pair of parallel sides.” (This
definition includes parallelograms and rectangles.)
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Statistics and Probability
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Use random sampling to
draw inferences about a
population.
7.SP.1 Understand that statistics can be used to gain information
about a population by examining a sample of the population;
generalizations about a population from a sample are valid only if
the sample is representative of that population. Understand that
random sampling tends to produce representative samples and
support valid inferences.
STANDARD REMOVED.
7.SP.2 Use data from a random sample to draw inferences about a
population with an unknown characteristic of interest. Generate
multiple samples (or simulated samples) of the same size to gauge
the variation in estimates or predictions. For example, estimate the
mean word length in a book by randomly sampling words from the
book; predict the winner of a school election based on randomly
sampled survey data. Gauge how far off the estimate or prediction
might be.
STANDARD REMOVED
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Statistics and Probability
Cluster
NYS P-12 CCLS
Draw informal
comparative inferences
about two populations.
range, and determine if a data point is an outlier.
Note: Students in grade 7 are not expected to construct box-plots that include
outliers in the data, but students are expected to interpret box-plots that may
7.SP.3 Informally assess the degree of visual overlap of
two numerical data distributions with similar
variabilities, measuring the difference between the
centers by expressing it as a multiple of a measure of
variability. For example, the mean height of players on
the basketball team is 10 cm greater than the mean
height of players on the soccer team, about twice the
variability (mean absolute deviation) on either team; on
a dot plot, the separation between the two distributions
of heights is noticeable.
quantitative data distributions.
7.SP.4 Use measures of center and measures of
variability for numerical data from random samples to
draw informal comparative inferences about two
populations. For example, decide whether the words in a
chapter of a seventh-grade science book are generally
longer than the words in a chapter of a fourth-grade
science book.
quantitative data from random samples or populations to draw
informal comparative inferences about the populations.
Note: Measures of center are mean, median, and mode. The measures of variation
include range and the interquartile range.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Statistics and Probability
Cluster
NYS P-12 CCLS
Investigate chance
processes and develop,
use and evaluate
probability models.
7.SP.5 Understand that the probability of a chance event
is a number between 0 and 1 that expresses the
likelihood of the event occurring. Larger numbers
indicate greater likelihood. A probability near 0 indicates
an unlikely event, a probability around 1/2 indicates an
event that is neither unlikely nor likely, and a probability
near 1 indicates a likely event.
7.SP.6 Approximate the probability of a chance event by
collecting data on the chance process that produces it and
observing its long-run relative frequency, and predict the
approximate relative frequency given the probability.
For example, when rolling a number cube 600 times,
predict that a 3 or 6 would be rolled roughly 200 times,
but probably not exactly 200 times.
7.SP.7 Develop a probability model and use it to find
probabilities of events. Compare probabilities from a
model to observed frequencies; if the agreement is not
good, explain possible sources of the discrepancy.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Statistics and Probability
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Investigate chance
processes and develop,
use and evaluate
probability models.
7.SP.7a Develop a uniform probability model by assigning equal
probability to all outcomes, and use the model to determine
probabilities of events. For example, if a student is selected at
random from a class find the probability that Jane will be selected
and the probability that a girl will be selected.
STANDARD REMOVED
7.SP.7b Develop a probability model (which may not be uniform)
by observing frequencies in data generated from a chance process.
For example, fin the approximate probability that a spinning penny
will land heads up or that a tossed paper cup will land open-end
down. Do the outcomes for the spinning penny appear to be equally
likely based on the observed frequencies?
STANDARD REMOVED
7.SP.8 Find probabilities of compound events using organized lists,
tables, tree diagrams, and simulation.
NY-7.SP.8 Find probabilities of compound events using
organized list, sample space tables, tree diagrams, and
simulation.
7.SP.8a Understand that, just as with simple events, the probability
of a compound event is the fraction of outcomes in the sample space
for which the compound event occurs.
NY-7.SP.8a Understand that, just as with simple events, the
probability of a compound event is the fraction of outcomes
in the sample space for which the compound event occurs.
NYSED Grade 7 Draft
New York State Next Generation Mathematics Learning Standards
Grade 7 Crosswalk
Statistics and Probability
Cluster
Standard Code
NYS P-12 CCLS
NYS Next Generation Learning Standard
Investigate chance
processes and develop,
use and evaluate
probability models.
7.SP.8b
7.SP.8b Represent sample spaces for
compound events using methods such
as organized lists, tables and tree
diagrams. For an event described in
everyday language (e.g., “rolling
doubles sixes”), identify the outcomes
in the sample space which compose the
event.
NY-7.SP.8b Represent sample spaces for compound events
using methods such as organized lists, sample space tables,
and tree diagrams.
For an event described in everyday language, identify the
outcomes in the sample space which compose the event.
e.g., “rolling double sixes”
7.SP.8c
7.SP.8c Design and use a simulation to
generate frequencies for compound
events. For example, use random
digits as a simulation tool to
approximate the answer to the
question: If 40% of donors have type A
blood what is the probability that it will
take at least 4 donors to find one with
type A blood?
NY-7.SP.8c Design and use a simulation to generate
frequencies for compound events.
e.g., Use random digits as a simulation tool to approximate
the answer to the question: If 40% of donors have type A
blood, what is the probability that it will take at least 4
donors to find one with type A blood?