Major Cluster
Standards

Represent
and solve problems involving multiplication and division.

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.

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.

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 = ?.

Understand properties of
multiplication and the relationship between multiplication and division.

3.OA.5

Apply
properties of operations as strategies to multiply and divide. (Students
need not use formal terms for these properties.) 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.)

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.

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 onedigit numbers.

Solve problems involving the four operations, and identify and
explain patterns in arithmetic.

3.OA.8

Solve twostep 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.

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.

Use place value understanding
and properties of operations to perform multidigit arithmetic. A range of
algorithms may be used.

3.NBT.3

Multiply
onedigit 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.

Foundational
Standards

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.

3.OA.2

Interpret wholenumber 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.

3.OA.6

Understand division as an
unknownfactor problem. For example, find 32 ÷ 8 by finding the number that
makes 32 when multiplied by 8.

Mathematical
Practices

MP.1

Make sense of problems and
persevere in solving them.
Students engage in exploratory lessons to discover and interpret patterns,
and apply their observations to solving multistep word problems involving
all four operations.

MP.3

Construct viable arguments and
critique the reasoning of others.
As students
compare solution strategies, they construct arguments and critique the
reasoning of their peers. This practice is particularly exemplified in
daily Application Problems and problemsolving specific lessons in which
students share and explain their work with one another.

MP.4

Model with mathematics. Students use arrays, tape
diagrams, and equations to represent word problem situations.

MP.5

Use appropriate tools
strategically.
Students analyze problems and select the appropriate tools and pathways to
solutions. This is particularly evident as students select problemsolving
strategies, and use arithmetic properties as simplifying strategies when
appropriate.

MP.7

Look for and make use of
structure. In
this module, patterns emerge as tools for problem solving. Students make
use of structure as they utilize the distributive property to establish the
9 = 10 – 1 pattern, for example, or when they check the solution to a fact
using units of 9 by making sure the sum of the digits in the product adds
up to 9. They make use of the relationship between multiplication and
division as they determine unknown factors and interpret the meanings
thereof.

Instructional
Outcomes
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.
 I
can find the quotient of whole numbers using equal groups.
 I
can tell what the numbers in a division problem mean.
 I
can explain what division means.
 I
can show division as equal sharing.
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.
 I
can multiply to solve word problems.
 I
can divide to solve word problems.
 I
can decide when to multiply or divide to solve word problems.
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 = ?.
 I
can find the missing number in a multiplication problem.
 I
can find the missing number in a division problem.
3.OA.5: Apply properties of
operations as strategies to multiply and divide. (Students need not use
formal terms for these properties.) 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.)
 I
can use the properties of multiplication and division to solve
problems.
 I
can explain the commutative property of multiplication.
 I
can explain the associative property of multiplication.
 I
can explain the distributive property of multiplication.
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.
 I
can identify the multiplication problem related to the division
problem.
 I
can use multiplication to solve division problems.
 I
can recognize and explain the relationship between multiplication and
division.
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 onedigit numbers.
 I
can memorize all products within 100.
 I
can use strategies to solve a multiplication problem.
 I
can use strategies to solve a division problem.
3.OA.8: Solve twostep 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.
 I
can identify the order of operations of a problem.
 I
can identify different strategies for estimating.
 I
can construct and equation with a letter standing for the unknown
quantity.
 I
can solve twostep word problems using the four operations.
 I
can justify my answer using estimation strategies and mental
computation.
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.
 I
can identify patterns.
 I
can explain rules for a pattern using properties of operations.
 I
can explain relationships between the numbers in a pattern.
3.NBT.3: Multiply onedigit 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.
·
I
can define “round or rounding” in relation to place value.
·
I
can identify strategies to multiply onedigit numbers by multiples of 10.
·
I
can round a whole number to the nearest 10.
·
I
can round a whole number to the nearest 100.




