MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
Unit Description
Unit 4
Operations and Algebraic Operations
Suggested Length: 9 – 10 weeks
Big Idea(s)
What enduring
understandings are essential
for application to new
situations within or beyond
this content?
Enduring Understandings
Develop an understanding of multiplication and division.
Essential Question(s)
What questions will provoke
and sustain student
engagement while focusing
learning?
Curriculum and Instruction
Enduring Skills Rubric measures competency of the following skills:
 Solves for products within 100 using equal sized groups, arrays,
and/or area models.

Solves for quotients within 100 using unknown number of
groups and/or unknown number of group size. Student is able
to explain thinking.

Solve multiplication problems correctly choosing and using
one of the properties of operation or a combination of
properties to solve a multiplication problem correctly.

Solve two-step problems using the four operations when there
is an unknown quantity. Can assess reasonableness of answers
using various strategies.
Choose the essential question(s) that best fits the needs of your
student(s).
 Can the same area measurement produce different size
rectangles? (Ex. 24 sq. units can produce a rectangle that is a
3 X 8, 4 X 6, 1 X24, 2 X 12)
 Do different factors with the same area cover the same
amount of space? (Ex. Is a 3 X8 the same area as a 1 X 24?)
 How are patterns related to multiplication?
 How can area be determined without counting each square?
 How can multiple math operations be used to solve real world
problems?
 How can multiplication and addition be used to determine a
rectangle’s area?
 How can multiplication be used when reading a pictograph?
How could it be used when creating a bar graph?
 How can the knowledge of area be used to solve real world
problems?
 How do estimation, multiplication, and division help us solve
problems in everyday life?
 How do rectangle dimensions impact the area of the
rectangle?
 How do two-step word problems differ from one-step word
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
problems?
How does understanding the distributive property help us
multiply large numbers?
 How is the commutative property of multiplication evident in
an area model?
 How is the decomposition of a factor in an equation related to
the distributive property of multiplication?
 What does it mean to decompose a number?
 What is a pattern?
 What is area?
 What is the connection between area models and skip
counting?
 What strategies can be used to solve word problems?
 Why are square units commonly associated with finding area?
 Why is an area model a representation for multiplication?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students
make sense of problems involving multiplication and division.

Standards
2. Reason abstractly and quantitatively. Students demonstrate
abstract reasoning by connecting arrays with multiplication problems.
3. Construct viable arguments and critique the reasoning of others.
Students construct and critique arguments regarding area by
creating or drawing arrays or area models to prove answers.
4. Model with mathematics. Students are asked to use tiles to model
various understandings of multiplication by creating arrays or groups.
They record their thinking using words, pictures, and numbers to
further explain their reasoning.
5. Use appropriate tools strategically. Students use graph paper to
find all the possible rectangles for a given product. Students use tiles
and drawings to solve multiplication problems.
6. Attend to precision. Students will learn to use terms such as multiply,
divide, factor, and product with increasing precision.
7. Look for and make use of structure. Students use the distributive
property of multiplication as a strategy to multiply.
8. Look for and express regularity in repeated reasoning. Students use
the distributive property of multiplication to solve for products they do
not know.
Curriculum and Instruction
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
Standards for Mathematical Content
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 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. (See
Glossary)
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 = ?.
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.
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
3.OA.8 Solve two-step word problems using the four operations.
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
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.
(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 (Order of Operations).)
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
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
Supporting Standard(s)
Which related standards will
be incorporated to support
and enhance the enduring
standards?
3.NBT.1
Instructional Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
I am learning to….
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.
3.OA.1
 Find the product of multiple groups of objects.
3.OA.2
 Explain what the numbers in a division problem mean.
 Explain how division relates to multiplication and equal shares.
 Identify quotients as the number of objects in each share or
the number of equal shares.
3.OA.3/3.OA.4
 Multiply and divide within 100.
 Solve word problems in situations involving equal groups,
arrays, and measurement quantities.
 Represent a word problem using a picture, an equation with a
symbol for the unknown number, or in other ways.
3.OA.5
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3


Split a number apart into smaller chucks to make it easier to
multiply. (Distributive Property)
Rearrange the order of numbers I am multiplying to make it
easier to mentally.
3.OA.6
 Identify the multiplication problem related to the division
problem.
 Identify the unknown factor in the related multiplication
problem.
 Use multiplication to solve division problems.
 Recognize multiplication and division as related operations
and explain how they are related.
3.OA.7
 Know from memory all products of two one-digit numbers. (K)
 Analyze a multiplication or division problem in order to choose
an appropriate strategy to fluently multiply or divide within 100.
(R)
3.OA.8
 Know the order of operations (without parentheses).
 Know strategies for estimating.
 Construct an equation with a letter standing for the unknown
quantity.
 Solve two-step word problems using the four operations.
 Justify your answer using various estimation strategies.
 I can read a problem critically, visualize the situation, and solve
for the answer.
3.OA.9
 Identify arithmetic patterns (such as even and odd numbers,
patterns in an addition table, patterns in a multiplication table,
patterns regarding multiples and sums) (K)
 Explain rules for a pattern using properties of operations.
(Properties of operations, glossary page 90 Common Core
State Standards) (R)
 Explain relationships between the numbers in a pattern. (R)
3.NBT.3
 Multiply one-digit whole numbers by multiples of 10 using
strategies based on place value and properties of operations.
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Essential Vocabulary (Assessed)
Associative Property of Multiplication, Commutative Property of
Multiplication, Distributive Property, divide, factor, multiple, multiply
Supporting Vocabulary
Arithmetic patterns, array, associative property of Multiplication,
Commutative Property of Multiplication, decompose, Distributive
Property, divide, dividend, divisor, equal, equal groups, equation,
expression, fact family, factor, inverse operations, multiple,
Multiplicative Identity Property of 1, multiply, number line, odd
number, order of operations, pattern, product, quotient,
reasonableness, related facts, repeated addition, repeated
subtraction, skip count, tiling, unit square, variable, Zero Property of
Multiplication
Resources/Activities
What resources could we
use to best teach this unit?
Resources/Activities
Making Math Magic Resources:
http://www.makingmathmagic.net/kcm.html
Computation with Meaning: Multiplication and Division PowerPoint
Stepping Stones www.origoeducation.com
Games are under the Fundamentals Channel located on top left of
the screen.
3.OA.1
o Module 1: Lessons 5
o Module 9: Lesson5
o Multiplication Mania Game
3.OA.2
o Module 3: Lesson 2
o Module 5: Lesson 1, 2
o Module 7: Lesson 6
o Module 9: Lesson 8
o Seeing Double Game
3.OA.3
o Module 1: Lesson 6
o Module 5: Lesson 6, 8
o Module 8: Lesson 9
3.AO.4
o Module 3: Lesson 2, 5
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
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Module 5: Lesson 3, 4, 5, 7
Module 6: Lesson, 1, 4,5,6
Module 7: Lesson 3, 7, 8, 9
Module 8: Lesson 8
Module 9: Lesson 1, 6, 9
Double, Double Game
Do the D’s game
Do the D’s Again (multiplying by 4 and 8) game
For Division game
Missing Divisors game
Quick Quotients game
3.OA.5
o Module 3: Lesson 1, 4
o Module 5: Lesson 3
o Module 8: Lesson 7
o Module 9: Lesson 1, 2
o Double, Double game
3.OA.6
o Module 5: Lesson 4
o Module 8: Lesson 7
3.OA.7
o Module 3: Lesson 3
o Seeing Double
3.OA.8
o Module 3:
o Module 6:
o Module 7:
o Module 9:
Lesson 6
Lesson 7
Lesson 5
Lesson 7, 10, 11, 12
3.OA.9
o Module 1: Lesson 8, 9
o Module 6: Lesson 2
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
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Module 7: Lesson 2, 4
Module 9: Lesson 4,
Times Tussle game
Times This (Multiplication by 9 and 10) game
It’s a Fact game
3.NBT.3
o Module 1: Lesson 7
o Module 7: Lesson 1
o Times That (multiplying by 5 and 10) game
o It’s a Fact game
K-5 Math Teaching Resources www.k-5mathteachingresources.com
Games are easy to find. Go the website listed above and click on 3rd
grade.
3.OA.1
 Array Picture Cards
3.OA.2
 Sharing or Grouping?
3.OA.3
 Building Arrays
 Number Story Arrays (Set 1)
 Number Story Arrays (Set 2
 Multiplication Word Problems
 Equal Rows in a Marching Band
 Sharing Marbles
3.OA.4
 Missing Numbers: Multiplication
 Missing Numbers: Division: 3.OA.5
 Turn Your Array
 Decompose a Factor (version 1)
 Decompose a Factor (version 2)
3.OA.6
 Division as Unknown Factor Problems
 Multiplication/Division Number Stories
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 3
3.OA.7
 Multiplication Bump (x2 – x10)
 Multiplication Four in a Row
 Multiples Game
 Multiples Look, Say, Cover, Write, Check
 Multiply It!
 Domino Multiplication
 Who Has? (Multiple versions)
3.OA.8
 Two-Step Word Problems Set 1
 Two-Step Word Problems Set 2
3.OA.9
 Odd and Even Sums
 Odd and Even Products
 Roll a Rule
 Roll a Rule (2 step)
 Creating and Representing Patterns
 Number Patterns
 Two Step Number Patterns
 Patterns in the Addition Table
 Patterns in the Multiplication Table
 Drawing Multiplication Patterns
3.NBT.3
 Multiples of Ten Multiply
 Multiply by Multiples of 10 Problems
Remember there are other sources in your school that may not be
listed on this common resources list due to variation in each individual
school. Examples of other great resources your school may have
access to include: Everyday Math Games, Investigations, Everyday
Partner Games, AVMR file folders, Ongoing Assessment Project, etc.
The Kentucky Numeracy Project is also a great resource that can be
searched by AVMR strand, CCSS, and grade level. Find this resource
at http://knp.kentuckymathematics.org/#!/page_knphome.
Kentucky teachers can use it for free. Just put in your school email
address and the username “mathfun”, and password is “859”.
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