NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Operations and Algebraic Thinking
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Represent and solve
problems involving
multiplication and
division.
3.OA.1 Interpret products of whole numbers, e.g., interpret
5 × 7 as the total number of objects in 5 groups of 7 objects
each. For example, describe a context in which a total
number of objects can be expressed as 5 × 7.
NY-3.OA.1 Interpret products of whole numbers.
e.g., Interpret 5 × 7 as the total number of objects in 5 groups of 7
objects each. Describe a context in which a total number of objects can
be expressed as 5 × 7.
3.OA.2 Interpret whole-number quotients of whole numbers,
e.g., interpret 56 ÷ 8 as the number of objects in each share
when 56 objects are partitioned equally into 8 shares, or as a
number of shares when 56 objects are partitioned into equal
shares of 8 objects each. For example, describe a context in
which a number of shares or a number of groups can be
expressed as 56 ÷ 8.
NY-3.OA.2 Interpret whole-number quotients of whole numbers.
e.g., Interpret 56 ÷ 8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares
when 56 objects are partitioned into equal shares of 8 objects each.
Describe a context in which a number of shares or a number of groups
can be expressed as
56 ÷ 8.
3.OA.3 Use multiplication and division within 100 to solve
word problems in situations involving equal groups, arrays,
and measurement quantities, e.g., by using drawings and
equations with a symbol for the unknown number to
represent the problem.
NY-3.OA.3 Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and
measurement quantities.
e.g., using drawings and equations with a symbol for the unknown
number to represent the problem.
3.OA.4 Determine the unknown whole number in a
multiplication or division equation relating three whole
numbers. For example, determine the unknown number that
makes the equation true in each of the equations 8 × ? = 48,
5 = _ ÷ 3, 6 × 6 = ?
NY-3.OA.4 Determine the unknown whole number in a multiplication
or division equation relating three whole numbers.
e.g., Determine the unknown number that makes the equation true in
each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Operations and Algebraic Thinking
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand properties of
multiplication and the
relationship between
multiplication and
division.
3.OA.5 Apply properties of operations as strategies to
multiply and divide. Examples: If 6 × 4 = 24 is known,
then 4 × 6 = 24 is also known. (Commutative property of
multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15,
then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30.
(Associative property of multiplication.) Knowing that 8
× 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 +
2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property.)
Note: Students need not use formal terms for these properties.
NY-3.OA.5 Apply properties of operations as strategies to multiply
and divide.
e.g.,
• If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
(Commutative property of multiplication)
• 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5
× 2 = 10, then 3 × 10 = 30. (Associative property of
multiplication)
• Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as
8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property)
Note: Students need not use formal terms for these properties.
Note: A variety of representations can be used when applying the
properties of operations, which may or may not include
parentheses.
3.OA.6 Understand division as an unknown-factor
problem. For example, find 32 ÷ 8 by finding the number
that makes 32 when multiplied by 8.
NY-3.OA.6 Understand division as an unknown-factor problem.
e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied
by 8.
Multiply and divide
within 100.
3.OA.7 Fluently multiply and divide within 100, using
strategies such as the relationship between multiplication
and division (e.g., knowing that 8 × 5 = 40, one knows
40 ÷ 5 = 8) or properties of operations. By the end of
Grade 3, know from memory all products of two one-
digit numbers.
NY-3.OA.7a Fluently solve single-digit multiplication and related
divisions, using strategies such as the relationship between
multiplication and division or properties of operations.
e.g., Knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8.
NY-3.OA.7b Know from memory all products of two one-digit
numbers.
Note: Fluency involves a mixture of just knowing some answers,
knowing some answers from patterns, and knowing some answers
from the use of strategies.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Operations and Algebraic Thinking
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Solve problems involving
the four operations, and
identify and extend
patterns in arithmetic.
3.OA.8 Solve two-step word problems using the four
operations. 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.
Note: This standard is limited to problems posed with whole numbers
and having whole-number answers; students should know how to
perform operations in the conventional order when there are no
parentheses to specify a particular order.
NY-3.OA.8 Solve two-step word problems posed with whole
numbers and having whole-number answers using the four
operations.
NY-3.OA.8a Represent these problems using equations or
expressions with a letter standing for the unknown quantity.
NY-3.OA.8b Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.
Note: Two-step problems need not be represented by a single
expression or equation.
3.OA.9 Identify arithmetic patterns (including patterns in
the addition table or multiplication table), and explain
them using properties of operations. For example,
observe that 4 times a number is always even, and
explain why 4 times a number can be decomposed into
two equal addends.
NY-3.OA.9 Identify and extend arithmetic patterns (including
patterns in the addition table or multiplication table).
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 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.
3.NBT.1 Use place value understanding to round whole
numbers to the nearest 10 or 100.
NY-3.NBT.1 Use place value understanding to round whole numbers
to the nearest 10 or 100.
3.NBT.2 Fluently add and subtract within 1000 using
strategies and algorithms based on place value,
properties of operations, and/or the relationship between
addition and subtraction.
NY-3.NBT.2 Fluently add and subtract within 1,000 using strategies
and algorithms based on place value, properties of operations, and/or
the relationship between addition and subtraction.
Note: Students should be taught to use strategies and algorithms
based on place value, properties of operations, and the relationship
between addition and subtraction; however, when solving any
problem, students can choose any strategy.
Note: A range of algorithms may be used.
3.NBT.3 Multiply one-digit whole numbers by multiples
of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using
strategies based on place value and properties of
operations.
NY-3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in
the range 10-90 using strategies based on place value and properties of
operations.
e.g., 9 × 80, 5 × 60
NY-3.NBT.4a Understand that the digits of a four-digit number
represent amounts of thousands, hundreds, tens, and ones.
e.g., 3,245 equals 3 thousands, 2 hundreds, 4 tens, and 5 ones.
NY-3.NBT.4b Read and write four-digit numbers using base-ten
numerals, number names, and expanded form.
e.g., The number 3,245 in expanded form can be written as 3,245=
3,000 + 200 + 40 + 5.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Number and Operations - Fractions
Cluster
NYS Next Generation Learning Standard
Develop understanding of
fractions as numbers.
NY-3.NF.1 Understand a unit fraction,
1
𝑏
, is the quantity
formed by 1 part when a whole is partitioned into b equal
parts.
Understand a fraction
𝑎
𝑏
as the quantity formed by a parts of
size
1
𝑏
.
Note: Fractions are limited to those with denominators 2,
3, 4, 6, and 8.
NY-3.NF.2 Understand a fraction as a number on the number
line; represent fractions on a number line.
Note: Fractions are limited to those with denominators 2,
3, 4, 6, and 8.
NY-3.NF.2a Represent a fraction
1
𝑏
on a number line by
defining the interval from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each part has size
1
𝑏
and
that the endpoint of the part starting at 0 locates the number
1
𝑏
on the number line.
NY-3.NF.2b Represent a fraction
𝑎
𝑏
on a number line by
marking off a lengths
1
𝑏
from 0. Recognize that the resulting
interval has size
𝑎
𝑏
and that its endpoint locates the number
𝑎
𝑏
on the number line.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Number and Operations - Fractions
Cluster
NYS Next Generation Learning Standard
Develop understanding of
fractions as numbers.
NY-3.NF.3 Explain equivalence of fractions and compare
fractions by reasoning about their size.
Note: Fractions are limited to those with denominators 2,
3, 4, 6, and 8.
NY-3.NF.3a Understand two fractions as equivalent (equal) if
they are the same size, or the same point on a number line.
NY-3.NF.3b Recognize and generate equivalent fractions.
e.g.,
1
2
=
2
4
;
4
6
=
2
3
.
Explain why the fractions are equivalent.
e.g., using a visual fraction model.
NY-3.NF.3c Express whole numbers as fractions, and
recognize fractions that are equivalent to whole numbers.
e.g., Express 3 in the form 3 =
3
1
, recognize that
6
3
= 2, and
locate
4
4
and 1 at the same point on a number line.
NY-3.NF.3d. Compare two fractions with the same numerator
or the same denominator by reasoning about their size.
Recognize that comparisons rely on the two fractions referring
to the same whole. Record the results of comparisons with the
symbols >, =, or <, and justify the conclusions.
e.g., using a visual fraction model.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Solve problems involving
measurement and
estimation of intervals of
time, liquid volumes, and
masses of objects.
3.MD.1 Tell and write time to the nearest minute and
measure time intervals in minutes. Solve word problems
involving addition and subtraction of time intervals in
minutes, e.g., by representing the problem on a number
line diagram.
NY-3.MD.1 Tell and write time to the nearest minute and measure
time intervals in minutes. Solve one-step word problems involving
addition and subtraction of time intervals in minutes.
e.g., representing the problem on a number line or other visual model.
Note: This includes one-step problems that cross into a new hour.
3.MD.2 Measure and estimate liquid volumes and
masses of objects using standard units of grams (g),
kilograms (kg), and liters (l). Add, subtract, multiply, or
divide to solve one-step word problems involving
masses or volumes that are given in the same units, e.g.,
by using drawings (such as a beaker with a
measurement scale) to represent the problem.
Note: Excludes compound units such as cm
3
and finding the geometric
volume of a container.
Excludes multiplicative comparison problems.
NY-3.MD.2a Measure and estimate liquid volumes and masses of
objects using grams (g), kilograms (kg), and liters (l).
Note: Does not include compound units such as cm
3
and finding the
geometric volume of a container.
NY-3.MD.2b Add, subtract, multiply, or divide to solve one-step word
problems involving masses or liquid volumes that are given in the same
units.
e.g., using drawings (such as a beaker with a measurement scale) to
represent the problem.
Note: Does not include multiplicative comparison problems involving
notions of “times as much.”
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Represent and interpret data.
3.MD.3 Draw a scaled picture graph and a scaled bar graph to
represent a data set with several categories. Solve one- and
two-step “how many more” and “how many less” problems
using information presented in scaled bar graphs. For example,
draw a bar graph in which each square in the bar graph might
represent 5 pets.
NY-3.MD.3 Draw a scaled picture graph and a scaled
bar graph to represent a data set with several
categories. Solve one- and two-step “how many
more” and “how many less” problems using
information presented in a scaled picture graph or a
scaled bar graph.
e.g., Draw a bar graph in which each square in the bar
graph might represent 5 pets.
3.MD.4 Generate measurement data by measuring lengths
using rulers marked with halves and fourths of an inch. Show
the data by making a line plot, where the horizontal scale is
marked off in appropriate units— whole numbers, halves, or
quarters.
NY-3.MD.4 Generate measurement data by
measuring lengths using rulers marked with halves
and fourths of an inch. Show the data by making a
line plot where the horizontal scale is marked off in
appropriate units—whole numbers, halves, or
quarters.
Geometric measurement:
understand concepts of area and
relate area to multiplication and
addition.
3.MD.5 Recognize area as an attribute of plane figures and
understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit
square,” is said to have “one square unit” of area, and
can be used to measure area.
b. A plane figure which can be covered without gaps or
overlaps by n unit squares is said to have an area of n
square units.
NY-3.MD.5 Recognize area as an attribute of plane
figures and understand concepts of area measurement.
NY-3.MD.5a Recognize a square with side length 1
unit, called “a unit square,” is said to have “one
square unit” of area, and can be used to measure area.
NY-3.MD.5b Recognize a plane figure which can be
covered without gaps or overlaps by n unit squares is
said to have an area of n square units.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Geometric measurement:
understand concepts of area
and relate area to
multiplication and to addition.
3.MD.6 Measure areas by counting unit squares
(square cm, square m, square in, square ft., and
improvised units).
NY-3.MD.6 Measure areas by counting unit squares.
Note: Unit squares include square cm, square m, square in., square ft.,
and improvised units.
3.MD.7 Relate area to the operations of
multiplication and addition.
a. a. Find the area of a rectangle with whole-number
side lengths by tiling it, and show that the area is
the same as would be found by multiplying the side
lengths.
b. b. Multiply side lengths to find areas of rectangles
with whole-number side lengths in the context of
solving real world and mathematical problems, and
represent whole-number products as rectangular
areas in mathematical reasoning.
c.
d.
e. c. Use tiling to show in a concrete case that the
area of a rectangle with whole-number side lengths
a and b + c is the sum of a × b and a × c. Use area
models to represent the distributive property in
mathematical reasoning.
f.
g.
h. d. Recognize area as additive. Find areas of
rectilinear figures by decomposing them into non-
overlapping rectangles and adding the areas of the
non-overlapping parts, applying this technique to
solve real world problems.
NY-3.MD.7 Relate area to the operations of multiplication and
addition.
NY-3.MD.7a Find the area of a rectangle with whole-number side
lengths by tiling it, and show that the area is the same as would be
found by multiplying the side lengths.
NY-3.MD.7b Multiply side lengths to find areas of rectangles with
whole-number side lengths in the context of solving real world and
mathematical problems, and represent whole-number products as
rectangular areas in mathematical reasoning.
NY-3.MD.7c Use tiling to show in a concrete case that the area of a
rectangle with whole-number side length a and side length b + c is the
sum of a × b and a × c. Use area models to represent the distributive
property in mathematical reasoning.
NY-3.MD.7d Recognize area as additive. Find areas of figures
composed of non-overlapping rectangles, and apply this technique to
solve real world problems.
Note: Problems include no more than one unknown side length.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Measurement and Data
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Geometric measurement:
recognize perimeter as an
attribute of plane figures and
distinguish between linear and
area measures.
3.MD.8 Solve real world and mathematical
problems involving perimeters of polygons,
including finding the perimeter given the side
lengths, finding an unknown side length, and
exhibiting rectangles with the same perimeter and
different areas or with the same area and different
perimeters.
NY-3.MD.8a Solve real world and mathematical problems involving
perimeters of polygons, including finding the perimeter given the side
lengths or finding one unknown side length given the perimeter and
other side lengths.
NY-3.MD.8b Identify rectangles with the same perimeter and
different areas or with the same area and different perimeters.
NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Grade 3 Crosswalk
Geometry
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Reason with shapes and
their attributes.
3.G.1 Understand that shapes in different categories (e.g.,
rhombuses, rectangles, and others) may share attributes (e.g.,
having four sides), and that the shared attributes can define a larger
category (e.g., quadrilaterals). Recognize rhombuses, rectangles,
and squares as examples of quadrilaterals, and draw examples of
quadrilaterals that do not belong to any of these subcategories.
NY-3.G.1 Recognize and classify polygons based on the
number of sides and vertices (triangles, quadrilaterals,
pentagons, and hexagons). Identify shapes that do not
belong to one of the given subcategories.
Note: Include both regular and irregular polygons,
however, students need not use formal terms “regular”
and “irregular,” e.g., students should be able to classify
an irregular pentagon as “a pentagon,” but do not need
to classify it as an “irregular pentagon.”
3.G.2 Partition shapes into parts with equal areas. Express the area
of each part as a unit fraction of the whole. For example, partition a
shape into 4 parts with equal area, and describe the area of each
part as 1/4 of the area of the shape.
NY-3.G.2 Partition shapes into parts with equal areas.
Express the area of each part as a unit fraction of the whole.
e.g., Partition a shape into 4 parts with equal area, and
describe the area of each part as
1
4
of the area of the shape.