NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Operations and Algebraic Thinking
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Use the four
operations with whole
numbers to solve
problems.
4.OA.1 Interpret a multiplication equation as a comparison,
e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as
many as 7 and 7 times as many as 5. Represent verbal
statements of multiplicative comparisons as multiplication
equations.
NY-4.OA.1 Interpret a multiplication equation as a comparison.
Represent verbal statements of multiplicative comparisons as
multiplication equations.
e.g.,
• Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many
as 7 or 7 times as many as 5.
• Represent “Four times as many as eight is thirty-two” as an
equation, 4 x 8 = 32.
4.OA.2 Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and
equations with a symbol for the unknown number to
represent the problem, distinguishing multiplicative
comparison from additive comparison.
NY-4.OA.2 Multiply or divide to solve word problems involving
multiplicative comparison, distinguishing multiplicative comparison
from additive comparison. Use drawings and equations with a symbol
for the unknown number to represent the problem.
4.OA.3 Solve multistep word problems posed with whole
numbers and having whole-number answers using the four
operations, including problems in which remainders must be
interpreted. Represent these problems using equations with a
letter standing for the unknown quantity. Assess the
reasonableness of answers using mental computation and
estimation strategies including rounding.
NY-4.OA.3 Solve multistep word problems posed with whole numbers
and having whole-number answers using the four operations, including
problems in which remainders must be interpreted.
NY-4.OA.3a Represent these problems using equations or
expressions with a letter standing for the unknown quantity.
NY-4.OA.3b Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.
Note: Multistep problems need not be represented by a single
expression or equation.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Operations and Algebraic Thinking
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Gain familiarity with
factors and multiples.
4.OA.4 Find all factor pairs for a whole number in the range 1–100.
Recognize that a whole number is a multiple of each of its factors.
Determine whether a given whole number in the range 1–100 is a
multiple of a given one-digit number. Determine whether a given
whole number in the range 1–100 is prime or composite.
NY-4.OA.4 Find all factor pairs for a whole number in the
range 1-100. Recognize that a whole number is a multiple of
each of its factors. Determine whether a given whole number
in the range 1-100 is a multiple of a given one-digit number.
Determine whether a given whole number in the range 1-100
is prime or composite.
Generate and analyze
patterns.
4.OA.5 Generate a number or shape pattern that follows a given rule.
Identify apparent features of the pattern that were not explicit in the
rule itself. For example, given the rule “Add 3” and the starting
number 1, generate terms in the resulting sequence and observe that
the terms appear to alternate between odd and even numbers. Explain
informally why the numbers will continue to alternate in this way.
NY-4.OA.5 Generate a number or shape pattern that follows a
given rule. Identify and informally explain apparent
features of the pattern that were not explicit in the rule itself.
e.g., Given the rule “Add 3” and the starting number 1,
generate terms in the resulting sequence and observe that the
terms appear to alternate between odd and even numbers.
Explain informally why the numbers will continue to alternate
in this way.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Number and Operations in Base Ten
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Generalize place value
understanding for multi-
digit whole numbers.
4.NBT.1 Recognize that in a multi-digit whole number, a
digit in one place represents ten times what it represents
in the place to its right. For example, recognize that 700
÷ 70 = 10 by applying concepts of place value and
division.
Note: Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.
NY-4.NBT.1 Recognize that in a multi-digit whole number, a digit in
one place represents ten times what it represents in the place to its
right.
e.g., Recognize that 70 × 10 = 700 (and, therefore,
700 ÷ 10 = 70) by applying concepts of place value, multiplication,
and division.
Note: Grade 4 expectations are limited to whole numbers less than or
equal to 1,000,000.
4.NBT.2 Read and write multi-digit whole numbers
using base-ten numerals, number names, and expanded
form. Compare two multi-digit numbers based on
meanings of the digits in each place, using >, =, and <
symbols to record the results of comparisons.
Note: Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.
NY-4.NBT.2a. Read and write multi-digit whole numbers using base-
ten numerals, number names, and expanded form.
e.g., 50,327 = 50,000 + 300 + 20 + 7
NY-4.NBT.2b Compare two multi-digit numbers based on meanings
of the digits in each place, using >, =, and < symbols to record the
results of comparisons.
Note: Grade 4 expectations are limited to whole numbers less than or
equal to 1,000,000.
4.NBT.3 Use place value understanding to round multi-
digit whole numbers to any place.
Note: Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.
NY-4.NBT.3 Use place value understanding to round multi-digit whole
numbers to any place.
Note: Grade 4 expectations are limited to whole numbers less than or
equal to 1,000,000.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Number and Operations in Base Ten
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Use place value
understanding and
properties of operations
to perform multi-digit
arithmetic.
4.NBT.4 Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
Note: Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.
NY-4.NBT.4 Fluently add and subtract multi-digit whole numbers
using a standard algorithm.
Note: Grade 4 expectations are limited to whole numbers less than or equal to
1,000,000.
4.NBT.5 Multiply a whole number of up to four digits
by a one-digit whole number, and multiply two two-digit
numbers, using strategies based on place value and the
properties of operations. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or
area models.
Note: Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.
NY-4.NBT.5 Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using equations, rectangular
arrays, and/or area models.
Note on and/or: Students should be taught to use equations,
rectangular arrays, and area models; however, when illustrating
and explaining any calculation, students can choose any strategy.
Note: Grade 4 expectations are limited to whole numbers less than or equal to
1,000,000.
4.NBT.6 Find whole-number quotients and remainders
with up to four-digit dividends and one-digit divisors,
using strategies based on place value, the properties of
operations, and/or the relationship between
multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or
area models.
Note: Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.
NY-4.NBT.6 Find whole-number quotients and remainders with up to
four-digit dividends and one-digit divisors, using strategies based on
place value, the properties of operations, and/or the relationship
between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.
Notes on and/or: Students should be taught to use strategies based on
place value, the properties of operations, and the relationship between
multiplication and division; however, when solving any problem, students
can choose any strategy. Students should be taught to use equations,
rectangular arrays, and area models; however, when illustrating and
explaining any calculation, students can choose any strategy.
Note: Grade 4 expectations are limited to whole numbers less than or equal to
1,000,000.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Number and Operations - Fractions
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Extend understanding of
fraction equivalence and
ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a
fraction (n × a)/(n × b) by using visual fraction models,
with attention to how the number and size of the parts
differ even though the two fractions themselves are the
same size. Use this principle to recognize and generate
equivalent fractions.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.1 Explain why a fraction
is equivalent to a fraction
×
×
by
using visual fraction models, with attention to how the number and size
of the parts differ even though the two fractions themselves are the
same size. Use this principle to recognize and generate equivalent
fractions.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.2 Compare two fractions with different numerators
and different denominators, e.g., by creating common
denominators or numerators, or by comparing to a
benchmark fraction such as 1/2. Recognize that
comparisons are valid only when the two fractions refer
to the same whole. Record the results of comparisons
with symbols >, =, or <, and justify the conclusions,
e.g., by using a visual fraction model.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.2 Compare two fractions with different numerators and
different denominators.
Recognize that comparisons are valid only when the two fractions refer
to the same whole.
e.g., by creating common denominators or numerators, or by
comparing to a benchmark fraction such as
.
Record the results of comparisons with symbols >, =, or <, and justify
the conclusions.
e.g., using a visual fraction model.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Number and Operations - Fractions
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of
fractions 1/b.
a. Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the
same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions,
e.g., by using a visual fraction model. Examples: 3/8 =
1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8 ;
2
= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number
with an equivalent fraction, and/or by using properties of
operations and the relationship between addition and
subtraction.
d. Solve word problems involving addition and
subtraction of fractions referring to the same whole and
having like denominators, e.g., by using visual fraction
models and equations to represent the problem.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.3 Understand a fraction
with a > 1 as a sum of fractions
.
Note:
refers to the unit fraction for
.
NY-4.NF.3a Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
NY-4.NF.3b Decompose a fraction into a sum of fractions with the
same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions.
e.g., by using a visual fraction model such as, but not limited to:
•
=
+
+
•
=
+
• 2
= 1 + 1 +
=
+
+
NY-4.NF.3c Add and subtract mixed numbers with like denominators.
e.g., replacing each mixed number with an equivalent fraction, and/or
by using properties of operations and the relationship between addition
and subtraction.
NY-4.NF.3d Solve word problems involving addition and subtraction
of fractions referring to the same whole and having like denominators.
e.g., using visual fraction models and equations to represent the
problem.
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10,
12, and 100.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Number and Operations - Fractions
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
4.NF.4 Apply and extend previous understandings of
multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For
example, use a visual fraction model to represent 5/4 as
the product 5 × (1/4), recording the conclusion by the
equation 5/4 = 5 × (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and
use this understanding to multiply a fraction by a whole
number. For example, use a visual fraction model to
express 3 × (2/5) as 6 × (1/5), recognizing this product
as 6/5. (In general, n × (a/b) = (n × a)/b.)
c. Solve word problems involving multiplication of a
fraction by a whole number, e.g., by using visual fraction
models and equations to represent the problem.
For
example, if each person at a party will eat 3/8 of a pound of roast beef,
and there will be 5 people at the party, how many pounds of roast beef
will be needed? Between what two whole numbers does your answer
lie?
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.4 Apply and extend previous understandings of
multiplication to multiply a whole number by a fraction.
Note: This standard refers to n groups of a fraction (where n is a whole number),
e.g., 4 groups of
; which lends itself to being thought about as repeated addition. In
grade 5 (NY-5. NF.4) students will be multiplying a fraction by a whole number,
e.g.,
of 4.
NY-4.NF.4a Understand a fraction
as a multiple of
.
e.g., Use a visual fraction model to represent
as the product 5 ×
,
recording the conclusion with the equation
= 5 ×
.
NY-4.NF.4b Understand a multiple of
as a multiple of
, and use this
understanding to multiply a whole number by a fraction.
e.g., Use a visual fraction model to express 3 ×
as 6 ×
, recognizing
this product as
, in general,
n ×
=
( × )
.
NY-4.NF.4c Solve word problems involving multiplication of a
whole number by a fraction.
e.g., using visual fraction models and equations to represent the problem.
e.g., If each person at a party will eat
of a pound of roast beef, and there will
be 5 people at the party, how many pounds of roast beef will be needed?
Between what two whole numbers does your answer lie?
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10,
12, and 100.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Number and Operations - Fractions
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand decimal
notation for fractions,
and compare decimal
fractions.
4.NF.5 Express a fraction with denominator 10 as an
equivalent fraction with denominator 100, and use this
technique to add two fractions with respective
denominators 10 and 100. For example, express 3/10 as
30/100, and add 3/10 + 4/100 = 34/100.
Students who can generate equivalent fractions can develop strategies
for adding fractions with unlike denominators in general. But addition
and subtraction with unlike denominators in general is not a
requirement at this grade.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.5 Express a fraction with denominator 10 as an equivalent
fraction with denominator 100, and use this technique to add two
fractions with respective denominators 10 and 100.
e.g., express
as
, and add
+
=
.
Notes:
• Students who can generate equivalent fractions can develop
strategies for adding fractions with unlike denominators in
general. But addition and subtraction with unlike
denominators in general is not a requirement at this grade.
• Grade 4 expectations are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.6 Use decimal notation for fractions with
denominators 10 or 100. For example, rewrite 0.62 as
62/100; describe a length as 0.62 meters; locate 0.62 on
a number line diagram.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.6 Use decimal notation for fractions with denominators 10 or
100.
e.g.,
• Rewrite 0.62 as
or
as 0.62.
• Describe a length as 0.62 meters.
• Locate 0.62 on a number line.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.7 Compare two decimals to hundredths by
reasoning about their size. Recognize that comparisons
are valid only when the two decimals refer to the same
whole. Record the results of comparisons with the
symbols >, =, or <, and justify the conclusions, e.g., by
using a visual model.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NY-4.NF.7 Compare two decimals to hundredths by reasoning about
their size. Recognize that comparisons are valid only when two
decimals refer to the same whole. Record the results of comparisons
with the symbols >, =, or <, and justify the conclusions.
e.g., using a visual model.
Note: Grade 4 expectations are limited to fractions with denominators
2, 3, 4, 5, 6, 8, 10, 12, and 100.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Solve problems involving
measurement and
conversion of
measurements from a
larger unit to a smaller
unit.
4.MD.1 Know relative sizes of measurement units within
one system of units including km, m, cm; kg, g; lb, oz.; l,
ml; hr, min, sec. Within a single system of measurement,
express measurements in a larger unit in terms of a
smaller unit. Record measurement equivalents in a two-
column table. For example, know that 1 ft is 12 times as
long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing
the number pairs (1, 12), (2, 24), (3, 36), ...
NY-4.MD.1 Know relative sizes of measurement units: ft., in.; km,
m, cm
e.g.,
An inch is about the distance from the tip of your thumb to your
first knuckle.
A foot is the length of two-dollar bills.
A meter is about the height of a kitchen counter.
A kilometer is 2 ½ laps around most tracks.
Know the conversion factor and use it to convert measurements in a
larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min.,
sec.
e.g., Know that 1 ft. is 12 times as long as 1 in. and express the length
of a 4 ft. snake as 48 in.
Given the conversion factor, convert all other measurements
within a single system of measurement from a larger unit to a
smaller unit.
e.g., Given the conversion factors, convert kilograms to grams,
pounds to ounces, or liters to milliliters.
Record measurement equivalents in a two-column table.
e.g., Generate a conversion table for feet and inches.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Solve problems involving
measurement and
conversion of
measurements from a
larger unit to a smaller
unit.
4.MD.2 Use the four operations to solve word problems
involving distances, intervals of time, liquid volumes,
masses of objects, and money, including problems
involving simple fractions or decimals, and problems
that require expressing measurements given in a larger
unit in terms of a smaller unit. Represent measurement
quantities using diagrams such as number line diagrams
that feature a measurement scale.
NY-4.MD.2 Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects, and
money.
NY-4.MD.2a Solve problems involving fractions or decimals, and
problems that require expressing measurements given in a larger unit in
terms of a smaller unit.
NY-4.MD.2b Represent measurement quantities using diagrams that
feature a measurement scale, such as number lines.
Note: Grade 4 expectations are limited to fractions with
denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.MD.3 Apply the area and perimeter formulas for
rectangles in real world and mathematical problems. For
example, find the width of a rectangular room given the
area of the flooring and the length, by viewing the area
formula as a multiplication equation with an unknown
factor.
NY-4.MD.3 Apply the area and perimeter formulas for rectangles in
real world and mathematical problems.
e.g., Find the width of a rectangular room given the area of the flooring
and the length, by viewing the area formula as a multiplication
equation with an unknown factor.
Represent and interpret
data.
4.MD.4 Make a line plot to display a data set of
measurements in fractions of a unit (1/2, 1/4, 1/8). Solve
problems involving addition and subtraction of fractions
by using information presented in line plots. For
example, from a line plot find and interpret the
difference in length between the longest and shortest
specimens in an insect collection.
NY-4.MD.4 Make a line plot to display a data set of measurements in
fractions of a unit
,
,
. Solve problems involving addition and
subtraction of fractions by using information presented in line plots.
e.g., Given measurement data on a line plot, find and interpret the
difference in length between the longest and shortest specimens in
an insect collection.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Geometric measurement:
understand concepts of
angle and measure
angles.
4.MD.5 Recognize angles as geometric shapes that are
formed wherever two rays share a common endpoint,
and understand concepts of angle measurement:
a. An angle is measured with reference to a circle with
its center at the common endpoint of the rays, by
considering the fraction of the circular arc between the
points where the two rays intersect the circle. An angle
that turns through 1/360 of a circle is called a “one-
degree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is
said to have an angle measure of n degrees.
4.MD.5 Recognize angles as geometric shapes that are formed
wherever two rays share a common endpoint, and understand concepts
of angle measurement.
4.MD.5a. Recognize an angle is measured with reference to a circle
with its center at the common endpoint of the rays, by considering the
fraction of the circular arc between the points where the two rays
intersect the circle. An angle that turns through
of a circle is called
a “one-degree angle,” and can be used to measure angles.
4.MD.5b Recognize an angle that turns through n one-degree angles is
said to have an angle measure of n degrees.
4.MD.6 Measure angles in whole-number degrees using
a protractor. Sketch angles of specified measure.
NY-4.MD.6 Measure angles in whole-number degrees using a
protractor. Sketch angles of specified measure.
4.MD.7 Recognize angle measure as additive. When an
angle is decomposed into non-overlapping parts, the
angle measure of the whole is the sum of the angle
measures of the parts. Solve addition and subtraction
problems to find unknown angles on a diagram in real
world and mathematical problems, e.g., by using an
equation with a symbol for the unknown angle measure.
NY-4.MD.7 Recognize angle measure as additive. When an angle is
decomposed into non-overlapping parts, the angle measure of the
whole is the sum of the angle measures of the parts. Solve addition and
subtraction problems to find unknown angles on a diagram in real
world and mathematical problems.
e.g., using an equation with a symbol for the unknown angle measure.
NYSED Grade 4 Draft
New York State Next Generation Mathematics Learning Standards
Grade 4 Crosswalk
Geometry
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Draw and identify lines
and angles, and classify
shapes by properties of
their lines and angles.
4.G.1 Draw points, lines, line segments, rays, angles (right, acute,
obtuse), and perpendicular and parallel lines. Identify these in two-
dimensional figures.
NY-4.G.1 Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel lines.
Identify these in two-dimensional figures.
4.G.2 Classify two-dimensional figures based on the presence or
absence of parallel or perpendicular lines, or the presence or
absence of angles of a specified size. Recognize right triangles as a
category, and identify right triangles.
NY-4.G.2a. Identify and name triangles based on angle
size (right, obtuse, acute).
NY-4.G.2b Identify and name all quadrilaterals with 2
pairs of parallel sides as parallelograms.
NY-4.G.2c Identify and name all quadrilaterals with
four right angles as rectangles.
4.G.3 Recognize a line of symmetry for a two-dimensional figure as
a line across the figure such that the figure can be folded along the
line into matching parts. Identify line-symmetric figures and draw
lines of symmetry.
NY-4.G.3 Recognize a line of symmetry for a two-
dimensional figure as a line across the figure such that the
figure can be folded along the line into matching parts.
Identify line-symmetric figures and draw lines of symmetry.
