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CCSS
Operations and Algebraic Thinking
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(OA)
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Unpacking the Standards
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Grade 3
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Standard: 3.OA.1 Cluster (m)
Related CA Standard
Math Practices: 1, 4, 7
NS2.4
______________________________________________________________________________________
Interpret products of whole numbers, e.g., interpret 5x7 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_______________
5x7.__________________________________________________________________________________
______________________________________________________________________________________
Essential Skills/Concepts
Teaching Notes/Strategies
the meaning of multiplication
Use equal groups of objects, arrays,
and square tiles to represent a
multiplication story or situation.
Understand that the symbol x means
“groups of.” 5 x 7 is 5 groups/rows
of 7.
Recognize multiplication as finding
the total number of objects in a
certain number of equal sized
groups.
Interpret a multiplication problem
situation using pictures, objects,
words, numbers, and equations.
Academic Vocabulary:
array
columns
factor
rows
multiplication
multiply
product
times
Resources
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
(array picture cards)
Describe in words.
Express as an equation.
Grid Paper
Use pictures and models.
Square Tiles
Say what they see.
Ask: What is going on when you
multiply? You work with equal groups.
Say: Multiplication is a way to find
how many in all.
Number Talks
Standard: 3.OA.2 Cluster (m)
Math Practices:
1, 4, 7
Related CA Standard
NS2.5
______________________________________________________________________________________
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.___________________________________________________________
______________________________________________________________________________________
Essential Skills/Concepts
the meaning of multiplication
Understand division as sharing
–knowing the number of equal shares
–finding the number in each share or
group
Partition models provide students
with a total number and the number
of groups.
Teaching Notes/Strategies
Partition models Question: How many http://www.kobjects are in each group so that the 5mathteachingresources.com/3rdgroups are equal?
grade-number-activities.html
(sharing of groups activity)
Repeated subtraction model
question: How many equal groups can The Door Bell Range by Pat Hutchins
The Door Bell Range on You Tube
you make?
Describe in words.
Counters
Express as an equation.
Index Cards for groups
Repeated subtraction models provide
students with a total number and the Use pictures and models.
number of objects in each
group.
Say what they see.
Academic Vocabulary:
division
Factor
divisor
dividend
number of shares
number of groups
Resources
Ask: What is going on when you
divide numbers? We take a total and
break it up into groups.
Say: You can use division to find the
number in each group.
Goldfish
Standard: 3.OA.3 Cluster (m)
Math Practices:
1, 4, 7
Related CA Standard
NS2.8
______________________________________________________________________________________
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.1
Essential Skills/Concepts
Word Problems
Use problem solving strategies to
solve word problems involving
multiplication and division.
Teaching Notes/Strategies
Picture it / Draw it out
Act it out with manipulatives
Draw a table to solve
Solve multiplication and division word Linking cubes, tiles
problems involving equal groups.
Solve multiplication and division word
problems involving arrays.
Solve multiplication and division word
problems involving area models.
Understand what is being asked
Academic Vocabulary:
Equal groups
Arrays
Resources
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
(activities: building arrays, number
story arrays, multiplication word
problems, equal rows in a marching
band, sharing marbles equally)
(math read aloud task cards: 100
Hungry Ants, Six Dinner Sid,
Amanda Bean’s Amazing Dream, Each
Had 8 Slices, The Doorbell Rang)
Multiplication and division word
problems see table on page 9 in
Frame work
PUSD Problem Solving Strategy
Poster
Standard: 3.OA.4 Cluster (m)
Math Practices:
1, 2, 6, 7
Related CA Standard
NS2.3
______________________________________________________________________________________
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 = ?________________________________________________________________
______________________________________________________________________________________
Essential Skills/Concepts
To solve determine the unknown
whole number in a multiplication or
division equation relating three
whole numbers.
Teaching Notes/Strategies
Use numbers, words, pictures,
http://www.kphysical objects, equations to explain 5mathteachingresources.com/3rdtheir thinking.
grade-number-activities.html
(activities: missing numbers
Find missing quotient with an array
multiplication, what is the missing
number division)
Number Talks
Counters
Fact Families
Build Arrays (make a model)
Academic Vocabulary:
Resources
Math Practices:
Standard: 3.OA.5 Cluster (m)
Related CA Standard
1, 4, 7, 8
AF1.5
______________________________________________________________________________________
Apply properties of operations as strategies to multiply and divide.2 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.)_______________________
______________________________________________________________________________________
Essential Skills/Concepts
Commutative Property of
Multiplication
Associative property of
Multiplication
Distributive Property
Teaching Notes/Strategies
Distributive Property: breaking an array apart
By creating an array, I want to find how many
total stars there are in 7 columns of 8 stars.
*******
*******
*******
*******
*******
*******
*******
*******
I see that I can arrange the 7 columns into a
group of 5 rows and a group of 2 columns.
Academic Vocabulary:
Properties
Commutative
Associative
distributive
*****
*****
*****
*****
*****
*****
*****
*****
**
**
**
**
**
**
**
**
I know that the 5 × 8 array gives me 40 and the
2 × 8 array gives me 16. So altogether I have
5x8+2x8=40+16=56 stars.
Resources
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
(activities: split a factor, decompose
a factor)
Board Math
Standard: 3.OA.6 Cluster (m)
Math Practices:
1, 7
Related CA Standard
NS2.3
______________________________________________________________________________________
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32
when multiplied by 8.______________________________________________________________________
______________________________________________________________________________________
Essential Skills/Concepts
Teaching Notes/Strategies
Understand the relationship between How are multiplication and division
multiplication and division
related to each other?
Multiplication joins equal groups to
Demonstrate that fact families
find the total. Division starts with
produce related multiplication and
the total and breaks it up into equal
division number sentences
groups.
Find the unknown number in a whole
number multiplication or division
problem.
Academic Vocabulary:
Divide
Factor
Product
Use same array to solve
multiplication and division problems.
Fact Families
Resources
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
(activities: division as unknown
factor problems,
multiplication/division number
stories)
Standard: 3.OA.7 Cluster (m)
Math Practices:
Related CA Standard
2, 7, 8
NS2.2, NS2.4, NS2.5
______________________________________________________________________________________
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.___________________________________________________
______________________________________________________________________________________
Essential Skills/Concepts
Through ample experiences working
with manipulatives, pictures, arrays,
word problems, and numbers
internalize the basic facts.
Fluency: The word “fluent” is used in the
standards to mean “reasonably fast and
accurate” and the ability to use certain facts and
procedures with enough facility that using them
does not slow down or derail the problem solver
as he or she works on more complex problems.
Academic Vocabulary:
Teaching Notes/Strategies
•Multiplication by zeros and ones
• Doubles (2s facts), Doubling twice
(4s), Doubling three times (8s)
• Tens facts (relating to place value,
5 x 10 is 5 tens or 50)
• Five facts (half of tens)
• Skip counting (counting groups of
__ and knowing how many groups
have been counted)
• Square numbers (ex: 3 x 3)
• Nines (10 groups less one group,
e.g., 9 x 3 is 10 groups of 3 minus one
group of 3)
• Decomposing into known facts (6 x
7 is 6 x 6 plus one more group of 6)
• Turn-around facts (Commutative
Property)
• Fact families (Ex: 6 x 4 = 24; 24 ÷
6 = 4; 24 ÷ 4 = 6; 4 x 6 = 24)
• Missing factors
Resources
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
activities:
Multiples Look/Say/Cover/Write/Check
x2-x5 Arrays
Cuisenaire Multiplication
Cuisenaire Rectangles
Multiples (2,5,10)
Multiples Game (3,4,6,7,8,9,11,100)
Multiplication Four in a Row (1,2,5,10)
Multiplication Four in a Row (3,4,5,6)
Multiplication Wheel
Multiplication Bump (x2 - x10)
Multiplication Challenge
Division Bump
Division Race
Division Riddles
Division Squares
Division Spin
The Product is ...
The Answer is ...
Multiply It!
Six Sticks
Multiplication Grid (blank)
I Have ... Who Has?
Standard: 3.OA.8 Cluster (m)
Math Practices:
1, 2, 4, 5
Related CA Standard
NS2.8, AF1.2
______________________________________________________________________________________
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.3
_____________________________________________________________________________________
Essential Skills/Concepts
Teaching Notes/Strategies
Use a letter for the unknown
Picture representations using a tapequantity in an expression or equation. like diagram.
2
2
2
2
2
m
Estimate during problem solving and
then revisit their estimate to check
25
for reasonableness.
Rounding - Estimation
Academic Vocabulary:
Estimate
Round(ing)
Pair / Group Work
Manipulatives
Error Analysis
-find the error
Group Presentations
Collaborative Conversations
4 Corners Activities
Draw Pictures to Solve
Resources
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
(activity: two-step word problems)
PUSD Problem Solving Strategy
Poster
Standard: 3.OA.9 Cluster (m)
Math Practices:
1, 2, 3, 6, 7
Related CA Standard
______________________________________________________________________________________
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.______________________________________________
_____________________________________________________________________________________
Essential Skills/Concepts
Investigate addition and
multiplication tables in search of
patterns.
Explain & discuss why these patterns
make sense mathematically.
Explain how they are related to
properties of operats.
Academic Vocabulary:
Pattern
Rule
Teaching Notes/Strategies
Resources
Use hundreds charts, addition
tables, and multiplication tables to
model addition or multiplication
patterns and explain why patterns
make sense. (color code)
http://www.k5mathteachingresources.com/3rdgrade-number-activities.html
Activities:
Use (informally) number properties
to find and explain patterns.
Roll a Rule
Odd and Even Sums
Odd and Even Products
Roll a Rule (2 Step)
Using Number Patterns to Describe Multiples
Increasing and Decreasing Number Patterns
Use knowledge of even and odd
numbers to find and explain
patterns.
What pattern do you notice in this
addition table?
What pattern do you notice when 2,
4, 6, 8, 10 are multiplied by any
number?
Two Step Number Patterns
Patterns in the Addition Table
Patterns in the Multiplication Table
Drawing Multiplication Patterns