Unit #: 3
Subject: Math
Grade: 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Lindsey Wensil. Lori Westerholt
PREAMBLE
In this unit, students will demonstrate understanding of multiplication and division by solving two-step word problems, fluently multiplying and dividing
within 100, and applying the associative, commutative and distributive properties. Students with a deep understanding are able use strategies such as area
models, arrays, and visual representations. When using the addition and multiplication table to help students discover arithmetic patterns, it is important
for students to use the following language: doubling twice, doubling three times, skip counting, groups of, square numbers and fact families.
Representations required to support the work of operations and algebraic thinking across grade levels involve model drawings, numeric expressions,
arrays, tables, letter notation, order pairs, concrete materials and manipulatives. The four areas across grade levels that support development of these
representations are:
 Properties and Structures: properties, including but not limited to, part whole relationships
 Interpreting Reasonableness: using mental computations and estimations to promote reflection
 Generating and Analyzing Patterns: using input-output relations or number sequence using rules
 Syntax of Expressions: involving boxes or placeholders, parentheses, brackets, and braces in expressions
STAGE 1 – DESIRED RESULTS
Unit Title: Properties of Multiplication & Division
Transfer Goal: Students will be able to independently use their learning to apply properties of operations as strategies to multiply and divide.
Enduring Understandings:
Essential Questions:
Students will understand that…
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In what ways can we use properties to more efficiently and effectively
solve multiplication and division problems?
Patterns are evident when multiplying or dividing a number.
Different multiplication properties and strategies can be used to solve
problems.
Related operations are used to solve for an unknown.
Students will know:
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That you can solve a division equation by finding the unknown
factor.
When to use multiplication properties to solve multiplication and
division problems.
Strategies to multiply one-digit numbers by multiples of 10.
Strategies for solving product unknown, group size unknown, and
number of groups unknown
Key Vocabulary: associative property, commutative property,
distributive property, unknown, multiple, factor, product,
divisor, dividend, quotient
Students will be able to:
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Fluently multiply and divide numbers within 100.
Multiply one-digit whole numbers by multiples of 10.
Determine if and when a property is beneficial in solving mathematic
situations.
Solve for product unknown, group size unknown, and number of groups
unknown in multiplication and division problems within 100.
Describe the relationship between multiplication and division.
Write an equation to represent a multiplication or division word problem.
Use key vocabulary in mathematical discussions.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last Revision 9/12/16
1
Unit #: 3
Subject: Math
Grade: 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Lindsey Wensil. Lori Westerholt
STAGE 1– STANDARDS
Cluster
3.OA
3.OA
3.OA
3.OA
3.NBT
3.MD
Standards
Represent and solve problems involving multiplication and
division.
Determine the unknown whole number in a multiplication or
division equation relating three whole numbers.
Apply properties of operations as strategies to multiply and divide.
3.OA.5
(Commutative, Associative, Distributive)
Understand properties of multiplication and the relationship
Understand division as an unknown-factor problem. For example,
between multiplication and division.
3.OA.6
find 32 ÷ 8 by finding the number that makes 32 when multiplied by
8.
Fluently multiply and divide within 100, using strategies such as the
Multiply and divide within 100.
3.OA.7
relationship between multiplication and division or properties of
operations.
3.OA.8
Solve 2 step word problems using the four operations.
Solve problems involving the four operations, and identify
Identify arithmetic patterns and explain them using properties of
and explain patterns in arithmetic.
3.OA.9
operations.
Multiply one-digit whole numbers by multiples of 10 in the range
Use place value understanding and properties of operations
3.NBT.3 10-90 using strategies based on place value and properties of
to perform multi-digit arithmetic.
operations.
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
Represent and interpret data.
3.MD.3
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.
8 Mathematical Practices
3.OA.4
MP.1
Make sense of problems and persevere in solving them.
MP.2
Reason abstractly and quantitatively.
MP.3
Construct viable arguments and critique the reasoning of others.
MP.4
Model with mathematics.
MP.5
Use appropriate tools strategically.
MP.6
Attend to precision.
MP.7
Look for and make use of structure
MP.8
Look for and express regularity in repeated reasoning.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last Revision 9/12/16
2
Unit #: 3
Subject: Math
Grade: 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Lindsey Wensil. Lori Westerholt
Performance Tasks:
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3rd Grade Unit Performance Task
NYC Performance Task – Isabella’s Garden
STAGE 2 – ASSESSMENT EVIDENCE
Other Evidence:
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Click to access the resources listed above.
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Howard County Instructional Tasks
o 3.OA.7 Assessment Task 18
o 3.OA.7 Assessment Task 19
o 3.OA.7 Assessment Task 20
o 3.OA.8 Adapted Task 1
o 3.OA.8 Adapted Task 2
o 3.OA.8 Assessment Task 10
o 3.OA.8 Assessment Task 11
o 3.OA.8 Assessment Task 12
o 3.OA.8 Performance Task 1
o 3.OA.9 Assessment Task 1
o 3.OA.9 Assessment Task 2
o 3.OA.9 Assessment Task 3
o 3.OA.9 Assessment Task 7
o 3.OA.9 Assessment Task 8
o 3.OA.9 Performance Task 1
o 3.OA.9 Performance Task 2
o Howard County Rubric Unit 3
Unit 3 Summative Assessment
DPI Assessment Tasks
o 3.NBT.3 - Task 1 – What’s the Best Deal?
o 3.OA.4 – Task 2 – Glue for the Tables
o 3.OA.5 – Task 2 – Prove It!
o 3.OA.7 – Task 2 –Planting Tomatoes
o 3.OA.8 - Task 1 – Earning Money
o 3.OA.9 – Task 1- Patterns in a Table
Click to access the resources listed above.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last Revision 9/12/16
3
Unit #: 3
Subject: Math
Grade: 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Lindsey Wensil. Lori Westerholt
STAGE 3 – RESOURCES FOR LEARNING PLAN
District Resources: When designing the learning plan, these resources
Supplemental Resources: These are considered additional resources that are
are intended to be a primary resource used by all teachers.
recommended by the Curriculum Writing Teams. Those resources with an
asterisk* may be purchased by each individual school.
 Unpacking Document Unit 3
 Find the Missing Numbers
 NCDPI Lessons for Learning
o Counting Around the Class
 Georgia Unit 2:
o Seeing Arrays as Equal Groups
o Arrays on the Farm
o Array-nging Fact Families
 NCDPI Conceptual Fluency Games
o Finding Factors
o Money Wheel
o Making the Hard Facts Easy
o Race to 300
o Making up Multiplication
o Division Duel
o Multiplication Chart Mastery
o Double Up
o My Special Day
o Multiple Madness I and II
o Use What You Know
o No Leftovers Wanted
o Raging Rectangles
 K-5 Math Teaching Resources: 3.OA
o Snakes Alive, Go for Fives
 Number Talks: Doubles/Near Doubles
o Whose Winning Products?
 Skip Counting
Click here to access the resources listed above.
Click here to access the resources above.
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Thinking Blocks Game: Multiplication and Division
Greg Tang Math Books
o Math for all Seasons
o Grapes of Math
o Math Potatoes
Greg Tang Math Games
o Kakooma (M & D)
o Break Apart (M & D)
o Expresso (M & D)
o Missing
Brain Pop Videos
o Associative Property
o Distributive Property
o Commutative Property
o Equations with Variables
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last Revision 9/12/16
4
Unit #: 3
Subject: Math
Grade: 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Lindsey Wensil. Lori Westerholt
Considerations for Differentiating Instruction (AIG, EL, EC, etc.):
These resources are intended to be used when differentiating instruction to meet the varied needs of students in your classroom.
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Learnzillion: Operations and Algebraic Thinking
Achieve the Core: Coherence Map shows progression of skills and can be used for EC and AIG.
Study Jams
o Distributive Property
o Multiplication and Division Equations
o Determine the Missing Operation in an Equation
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NC AIG Field Trip Exploration
Click here to access the resource listed above.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last Revision 9/12/16
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