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SCUSD Curriculum Map-Last Updated 12/02/14
Curriculum
Map
DRAFT Last Updated December 18, 2014
Grade 3 Mathematics
Mathematics
Grade 3
Sacramento City Unified School District
1
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
Table of Contents
Third Grade Year-at-a-Glance .................................................................................................................................................................................................................................................................................................3
Unit #1: Represent and Understand Multiplication and Division ...........................................................................................................................................................................................................................................4
Unit #2: Place Value and Problem with Units of Measure................................................................................................................................................................................................................................................... 12
Unit #3: Problem Solving Using Multiplication and Division ............................................................................................................................................................................................................................................... 20
Unit #4: Multiplication and Area.......................................................................................................................................................................................................................................................................................... 29
Unit #5: Developing Understanding of Fractions ................................................................................................................................................................................................................................................................. 36
Unit #6: Representing and Interpreting Data ...................................................................................................................................................................................................................................................................... 49
Unit #7: Geometric Figures and Problem Solving Involving Perimeters and Areas ............................................................................................................................................................................................................. 55
Bar modeling in enVision = tape diagrams in CCSS-M
2
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Year-at-a-Glance
Month
District Benchmark 1
Unit
September
Unit #1
Represent and Understand Multiplication and Division
October
Unit #2
Place Value and Problem Solving with Units of Measure
November/
December
Unit #3
Problem Solving Using Multiplication and Division
January/February
Unit #4
Exploring Multiplication with Area
March/April
Unit #5
Developing Understanding of Fractions
*Alignment TBD
District Benchmark 2
*Alignment TBD
District Benchmark 3
*Alignment TBD
CAASPP
(Smarter Balanced Summative Test)
May
May/June
Unit #6
Representing and Interpreting Data
Unit #7
Geometric Figures and Problem Solving Involving Perimeter and Area
Content Standards
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.NBT.1
3.NBT.2
3.MD.1
3.MD.2
3.OA.8
3.OA.5
3.OA.6
3.OA.7
3.OA.8
3.OA.9
3.NBT.3
3.MD.5
3.MD.6
3.MD.7
3.NF.1
3.NF.2
3.NF.3
3.G.2
3.MD.4
3.MD.3
3.MD.4
3.G.1
3.MD.8
3
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
(Approx. # Days- )
Content Standards: 3.OA.1-4
In this unit, students will develop understanding of, interpreting, representing, and solving problems involving multiplication and division.
Common Core State Standards-Mathematics:
Operations and Algebraic Thinking
3.OA
Represent and solve problems involving multiplication and division
1. Interpret products of whole numbers, e.g., interpret 5 x 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 x 7.
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. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawing and equations with a symbol for the
unknown number to represent the problem.
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 x ? = 48, 5 = □ ÷ 3, 6 x 6 = ?.
Standards for Mathematical Practice:
SMP. 1 Make sense of problems and persevere in solving them
SMP. 2 Reason abstractly and quantitatively
SMP. 3 Construct viable argument and critique the reasoning of others
SMP. 6 Attend to precision
SMP. 7 Look for and make use of structure
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
4
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways
A. Collaborative
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area
8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience,
topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
5
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
Essential
Questions
Assessments
for Learning
Essential Questions are
thought- provoking,
open-ended questions
to be used within daily
lessons that and are
therefore connected to
the Sequence of
Learning Outcomes.
Assessments for
Learning address
Diagnostic,
Formative, and
Summative
assessments used
throughout the unit
to inform instruction
connected to the
Sequence of Learning
Outcomes.
Note: These
assessments are
suggested, not
required.
Unit 1 Post
Assessment modified
from GA DOE
“Ice Cream Scoops,”
PartII “Multiplication
and Division” only,
pp. 156-162
Sequence of Learning
Outcomes (3.OA.1-4)
Strategies
for Teaching and Learning
Differentiation
e.g. EL, SpEd, GATE
Resources
Sequence of Learning Outcomes General Strategy Support for Unit:
Differentiation
From the CA Mathematics Framework
Support for Unit:
is intentionally organized for
Use of math journals

“Instructional
Strategies”
chapter
student success. Each outcome
for differentiation
provides research-based strategies for
is not necessarily intended to be
and formative
teaching math, K-12
taught within one class session.
assessment (use link
 “Supporting High Quality Common
below)
Core Instruction” chapter addresses
Each Outcome begins with
https://www.teachin
the development, implementation,
Students will be able to…
gchannel.org/videos/
and maintenance of high-quality,
math-journals
standards-based mathematics
instructional programs
Flexible grouping:
 Content
“Universal Design for Learning” from
CAST, the Center for Applied Special
 Interest
Technology
 Project/product
 Level
(Heterogeneous/
Homogeneous)
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1-5 “What students Learn in Grade Three”
 p. 6-15 Operations and Algebraic Thinking Domain
 p. 34-37 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional strategies,
additional resources/tools and misconceptions by
standard.
 p. 1-11 Operations and Algebraic Thinking domain
NC Unpacking Documents
 Provide illustrated examples, instructional strategies,
additional resources/tools and misconceptions by
standard.
 p. 4-7 Operations and Algebraic Thinking domain
Progressions for CCSS-M
 Narrative documents describing the progression of a
topic across a number of grade levels, informed both
by research on children's cognitive development and
Tiered:
by the logical structure of mathematics.
 Independent
 p. 2-3, and 22-28 Operations and Algebraic Thinking
Management Plan
domain
(Must Do/May Do) Videos from The Teaching Channel
 Grouping
 Think Time and Collaborative Learning
o Content
 Third Grade Math: A Complete Lesson
o Rigor w/in the  Catch and Release: Encourage Independence
concept
 Adjusting Lessons: Have a Plan B
o Project-based
6
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
Essential
Questions
Assessments
for Learning
How can I relate what I NC Wikispace, 3rd
know about skip
Grade Tasks
counting to multiply?
Sequence of Learning
Outcomes (3.OA.1-4)
Strategies
for Teaching and Learning
1. Recognize multiplication as The standard defines multiplication of
finding the total number of
whole numbers a x b as finding the total
objects in a certain number
number of objects in a groups of b
of equal-sized groups.
objects.
What patterns can be
Provide students context
Use the terms “number of objects in each
used to find certain
(story problems) as they
group”(3 x __ = 18 and 18 ÷ 3 = __) or
multiplication facts?
learn equal groupings.
“number of groups” (__ x 6 = 18 and 18
3.OA.1 ÷ 6 = __) with students.
How are addition and
Number bond can be used as a visual
multiplication related?
representation of this skip counting
strategy.
What is the
Draw pictures to represent equal groups
May use a variety of models (tile squares,
relationship between
counters, linking cubes, beans, etc.) for
factors and product?
students to manipulate equal groups
rd
NC Wikispace, 3
2. Interpret factors as the size Use context to help students determine
Grade Tasks
of the group or the number
the factors.
of groups. Show with
Use number lines to show equal groups
From Illustrative
models “a number of groups
Mathematics:
of a certain number of
object (or size)” when the
 “Fish Tanks”
language of “groups of” is
 “Markers in Boxes”
presented with various
terms (for example, “piles
of,” “stacks of,” “rows of,”
“cups of,” “teams of,” etc.).
3.OA.1
How can multiplication NC Wikispace, 3rd
3. Represent multiplication
Build rectangular arrays using “rows of.”
be represented?
Grade Tasks
with the array to show the Describe arrays in terms of equal groups
relationship among all the
(by rows or by columns). For example, 4
What is the
numbers involved (factor x
x 5: “There are 4 rows of 5 chairs.” which
Differentiation
e.g. EL, SpEd, GATE
o
o
o
learning
Homework
Grouping
Formative
Assessment
Anchor Activities:
 Content-related
 Tasks for early
finishers
o Game
o Investigation
o Partner Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
o Complexity
From GA DOE,
Differentiation via
Math Centers (Tubs)
Resources
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Tchr of Mathematics, pg. 4-5
NC Unpacking, pg. 4
Video from engageny Number bond
From engageny Downloadable Resources PDF, Module 1,
Topic A “Mulitplcation and the Meaning of the
Factors”, pg. 1.A.1-1.A.40
enVision, Topic 4:
 Math Background, pp. 95A-95B
 Interactive Learning, pp. 96-97
 Lesson 4-1 “Multiplication as Repeated Addition”
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Teacher of Mathematics, pg.
4-5
NC Unpacking, pg. 4
From engageny Downloadable Resources PDF, Module 1,
Topic A “Mulitplcation and the Meaning of the Factors”,
pg. 1.A.1-1.A.40
enVision, Topic 4:
 Lesson 4-1 “Multiplication as Repeated Addition”
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Teacher of Mathematics, pg.
4-5
NC Unpacking, pg. 4
7
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
Essential
Questions
Assessments
for Learning
relarionship beween
factors and product?
How can division be
represented?
NC Wikispace, 3rd
Grade Tasks
How can I use what I
know about
subtraction, equal
sharing, and forming
equal groups to solve
division problems?
From Illustrative
Mathematics:
 “Two
Interpretations of
Division”
 “Gifts from
Grandma”
Variation1
 “Finding the
unknown in a
division equation”
How can the same
array model represent
multiplication and
division?
How can I use the array
model to explain
Strategies
for Teaching and Learning
factor = product). Use
is different from 5 rows of 4 chairs
context so students will be
where the meaning and representation
able to visualize
are different. The product is the same.
“rows/columns of” a
Partition arrays into smaller arrays
particular group.
(concept of decomposition)
3.OA.1 Use tape diagrams
What strategies can be
used to find the factors
or prodcuts?
How are subtraction
and division related?
Sequence of Learning
Outcomes (3.OA.1-4)
NC Wikispace, 3rd
Grade Tasks
4. Recognize division in two
Use the terms “number of objects in a
different situations – equal
group”(3 x __ = 18 and 18 ÷ 3 = __) or
sharing (e.g., how many are
“number of groups” (__ x 6 = 18 and 18
in each group?), and
÷ 6 = __) with students rather than
determining how many
“partitive division” or “quotitive
groups (e.g., how many
division.”
groups can you make?)
Use the array model to determine the
3.OA.2 unknown in division.
5. Model the relationship
Model division as the unknown factor in
between multiplication and
multiplication in multiple ways (for
division by using a variety of
example, bar modeling, number line,
methods, such as bar
arrays, etc.).
modeling, number line,
arrays, etc.
3.OA.3
Differentiation
e.g. EL, SpEd, GATE
Resources
From engageny Downloadable Resources PDF, Module 1,
 Topic A “Mulitplcation and the Meaning of the
Factors”, pg. 1.A.1-1.A.40
 Video on Word Problems with tape Diagrams
enVision, Topic 4:
 Math Background, pp. 95A-95B
 Interactive Learning, pp. 96-97
 Lesson 4-2 “Arrays and Multiplication”
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Teacher of Mathematics, pg. 6
NC Unpacking, pg. 4
From engageny Downloadable Resources PDF, Module 1,
Topic B “Division as an Unknown Factor Problem”, pg.
1.B.1-1.B.35
enVision, Topic 7:
 Math Background, pp. 167A-167B
 Interactive Learning, pp. 168-169
 Lesson 7-1 “Division as Sharing”
 Lesson 7-2 “Division as Repeated Subtraction”
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Teacher of Mathematics, pg.
7-9
NC Unpacking, pg. 5-6
From engageny Downloadable Resources PDF, Module 1,
 Topic A “Mulitplcation and the Meaning of the
Factors”, pg. 1.A.1-1.A.40
8
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
Essential
Questions
Assessments
for Learning
Sequence of Learning
Outcomes (3.OA.1-4)
Strategies
for Teaching and Learning
multiplication and
division?
How can I model
division?
How are multiplication
and division alike and
different?
How can I use the array NC Wikispace, 3rd
6. Use multiplication and
Model problems using pictural
model to explain
Grade Tasks
division within 100 to solve
representations and manipulatives.
multiplication and
word problems in situations
division?
From Illustrative
involving equal groups,
Mathematics:
arrays, and measurement
How can I use known
quantities.
 “Analyzing Word
facts to find unknown
3.OA.3
Problems Involving
facts?
Multiplication”
Differentiation
e.g. EL, SpEd, GATE
Resources

Topic B “Division as an Unknown Factor Problem”, pg.
1.B.1-1.B.35
Lesson from LearnZillion: “Solve Multiplication and
Division Problems: Using a Diagram”
enVision, Topic 4:
 Math Background, pp. 95A-95B
 Interactive Learning, pp. 96-97
 Lesson 4-4 “Writing Multiplication Stories”
enVision, Topic 7:
 Math Background, pp. 167A-167B
 Interactive Learning, pp. 168-169
 Lesson 7-5 “Writing Division Stories”
enVision, Topic 8:
 Math Background, pp. 187A-187B
 Interactive Learning, pp. 188-189
 Lesson 8-6 “Making Sense of Multiplication and
Division Equations”
 Lesson 8-9 “Problem Solving: Draw a Picture and Write
a Number Sentence”
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Teacher of Mathematics, pg.
7-9
NC Unpacking, pg. 5-6
From engageny Downloadable Resources PDF, Module 1,
 Topic A “Mulitplcation and the Meaning of the
Factors”, pg. 1.A.1-1.A.40
 Topic B “Division as an Unknown Factor Problem”, pg.
1.B.1-1.B.35
9
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
Essential
Questions
Assessments
for Learning
Sequence of Learning
Outcomes (3.OA.1-4)
Strategies
for Teaching and Learning
Differentiation
e.g. EL, SpEd, GATE
Resources
enVision, Topic 4:
 Math Background, pp. 95A-95B
 Interactive Learning, pp. 96-97
 Lesson 4-5 “Problem Solving”
enVision, Topic 5:
 Math Background, pp. 113A-113B
 Interactive Learning, pp. 114-115
enVision, Topic 5:
 Lesson 5-1 “2 and 5 as Factors”
enVision, Topic 6:
 Math Background, pp. 137A-137B
 Interactive Learning, pp. 138-139
 Lesson 6-2 “3 as a Factor”
 Lesson 6-3 “4 as a Factor”
 Lesson 6-4 “6 and 7 as Factors”
 Lesson 6-5 “8 as a Factor”
 Lesson 6-7 “Multiplication Facts”
 Lesson 6-8 “Multiplying to Find Combinations”
enVision, Topic 7:
 Math Background, pp. 167A-167B
 Interactive Learning, pp. 168-169
 Lesson 7-6 “Problem Solving:Use Objects and Draw a
Picture”
How are multiplication NC Wikispace, 3rd
and division related?
Grade Tasks
How can different
strategies be helpful
when solving
7. Determine the unknown
Use manipulatives, pictures, words,
whole number in a
and/or equations to represent the
multiplication or division
problem and explain thinking process.
equation relating three
whole numbers to make the
equation true.
CA Mathematics Framework “3rd Grade” pg. 9 chart
Flipbook from KS Assoc. of Teacher of Mathematics, pg.
10-11, and 24
NC Unpacking, pg. 7
engageny Downloadable Resources PDF, Module 1, Topic
10
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #1: Represent and Understand Multiplication and Division
Essential
Questions
problems?
Assessments
for Learning
Sequence of Learning
Outcomes (3.OA.1-4)
3.OA.4
Strategies
for Teaching and Learning
Differentiation
e.g. EL, SpEd, GATE
Resources
B “Division as an Unknown Factor Problem”, pg.
1.B.1-1.B.35
enVision, Topic 7:
 Math Background, pp. 167A-167B
 Interactive Learning, pp. 168-169
 Lesson 7-4 “Problem Solving: Choose an Appropriate
Equation”
11
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
(Approx. # Days- )
Content Standards: 3.NBT.1, 3.NBT.2, 3.MD.1, 3.MD.2, 3.OA.8
In this unit, students will use place value understanding, properties of addition and subtraction, and estimation strategies to solve problems involving measurement.
Common Core State Standards-Mathematics:
Number and Operations in Base Ten
3.NBT
Use place value understanding and properties of operations to perform multi-digit arithmetic.
1. Use place value understanding to round whole numbers to the nearest 10 or 100.
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.
Operations and Algebraic Thinking
3.OA
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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.
Measurement and Data 3.MD
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
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.
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 problems involving masses
or volumes that are given in the same units, e.g., by using drawings (such as beaker with a measurement scale) to represent the problem.
Standards for Mathematical Practice:
SMP. 1 Make sense of problems and persevere in solving them
SMP. 2 Reason abstractly and quantitatively
SMP. 3 Construct viable argument and critique the reasoning of others
SMP. 4 Model with mathematics
SMP. 6 Attend to precision
SMP. 7 Look for and make use of structure
SMP. 8 Look for and express regularity in repeated reasoning
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills,
Responsible decision making
12
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways
A. Collaborative
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area
8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience,
topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
2. Understanding cohesion
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
13
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.NBT.1-2,
3.MD.1-2, 3.OA.8
Essential Questions are
thought- provoking,
open-ended questions
to be used within daily
lessons that and are
therefore connected to
the Sequence of
Learning Outcomes.
Assessments for
Learning address
Diagnostic,
Formative, and
Summative
assessments used
throughout the unit
to inform instruction
connected to the
Sequence of
Learning Outcomes.
Sequence of Learning Outcomes is
intentionally organized for student
success. Each outcome is not
necessarily intended to be taught
within one class session.
Note: These
assessments are
suggested, not
required.
Mid-point Check
and Post
Assessments –
from engageNY,
Module 2 Tasks
1-5
Gr 3_Unit
2_Mid-Post
Assessments.pdf
Each Outcome begins with
Students will be able to…
Strategies
for Teaching and Learning
General Strategy Support for Unit:
From the CA Mathematics Framework
 “Instructional Strategies” chapter
provides research-based strategies
for teaching math, K-12
 “Supporting High Quality Common
Core Instruction” chapter addresses
the development, implementation,
and maintenance of high-quality,
standards-based mathematics
instructional programs
“Universal Design for Learning” from
CAST, the Center for Applied Special
Technology
Differentiation e.g.
EL,SpEd, GATE
Resources
Differentiation
Support for Unit:
Use of math journals
for differentiation
and formative
assessment (use link
below)
https://www.teachin
gchannel.org/videos/
math-journals
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1-5 “What students Learn in Grade Three”
 p. 15-16 Number and Operations in Base Ten domain
 p. 24-25 Measurement and Data domain
 p. 10-14 Operations and Algebraic Thinking
 p. 34-37 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional strategies,
additional resources/tools and misconceptions by
standard.
Flexible grouping:
 p. 13-14 Operations and Algebraic domain
 Content
 p. 15-16 Number and Operations in Base Ten domain
 Interest
 p. 24 Measurement and Data domain
 Project/product
 NC Unpacking Documents
 Level
 Provide illustrated examples, instructional strategies,
(Heterogeneous/
additional resources/tools and misconceptions by
Homogeneous)
standard.
 p. 13-14 Operations and Algebraic Thinking domain
Tiered:
 p. 18-19 Number and Operations in Base Ten domain
 Independent
 p. 26-28 Measurement and Data domain
Management Plan Progressions for CCSS-M
(Must Do/May Do)
 Narrative documents describing the progression of a
 Grouping
topic across a number of grade levels, informed both
o Content
by research on children's cognitive development and
o Rigor w/in the
by the logical structure of mathematics.
concept
 p. 2-4, 11 Number and Operations in Base Ten
o Project-based
domain
learning
 p. 2-4, 15-19 Measurement and Data domain
14
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.NBT.1-2,
3.MD.1-2, 3.OA.8
Strategies
for Teaching and Learning
Differentiation e.g.
EL,SpEd, GATE
o
o
o
What does “base ten”
mean?
From NC Wikispace: 1. Use place value to round
Describe the distance of the two decade
numbers
to
the
nearest
10
on
a
numbers (see KATM, p. 26-27).
 “Cafeteria Lunch
number line.
Using a number line, plot decade
Orders” 3.NBT.1
What does “rounding”
3.NBT.1
numbers to identify the halfway point
Task 1
mean?
between two possible answers on a
 “Comparing
number line
Heights” 3.NBT.1
When might you round
Use a number line or a hundreds chart as
Task 2
to the nearest 10?
tools to support students’
When might you round From Illustrative
understanding of place value
to the nearest 100?
Mathematics:
 “Rounding to 50
What is an interval?
or 500”
 “Rounding to the
How do you select an
Nearest Ten and
appropriate interval for
Hundreds”
a number line?
How can a number line From Illustrative
2. Use place value to round
Students can use a number line or a
help me round?
Mathematics:
numbers to the nearest 100 on
hundreds chart as tools to support
“Rounding to the
a number line.
their 245 work with rounding.
How do you select an
Nearest Ten and
3.NBT. 1
appropriate interval for Hundreds”
a number line?
From NC Wikispace:
“All About
Rounding”
Homework
Grouping
Formative
Assessment
Anchor Activities:
 Content-related
 Tasks for early
finishers
o Game
o Investigation
o Partner Activity
o Stations
Resources
 p. 2-3, 27-28 Counting and Cardinality and
Operations and Algebraic Thinking domains
CA Framework p. 15
Flipbook p.26-27
NC Unpacking, p. 19
enVision, Topic 1:
 Math Background, pp. 2G-2H
 Interactive Learning, pp. 4-5
 Lesson 1-1 “Representing Numbers”
 Lesson 1-2 “Understanding Number Lines”
 Lesson 1-3 “Counting on the Number Line”
 Lesson 1-4 “Finding the Halfway Number”
Depth and Complexity  Lesson 1-5 “Rounding”
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
CA Framework p. 15
o Unanswered
Flipbook p.26-27
Questions
NC Unpacking, p. 19
o Rules
o Trends
enVision, Topic 1:
o Big Ideas
o Complexity
 Math Background, pp. 2G-2H
 Interactive Learning, pp. 4-5
http://scusd-math.wiki  Lesson 1-5 “Rounding”
spaces.com/home
 Lesson 1-6 “More Rounding”
15
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.NBT.1-2,
3.MD.1-2, 3.OA.8
Strategies
for Teaching and Learning
Differentiation e.g.
EL,SpEd, GATE
Resources
3.NBT.1 Task 3
In what kinds of
situations is it
appropriate to
estimate? Why?
In what kinds of
situations is it
appropriate to
estimate? Why?
From NC Wikispace: 3. Estimate to solve one-step
Prior to implementing rules for rounding
“Toys for Us, Task
addition and subtraction
students need to have opportunities to
#2” 3.NBT.2 Task 2
problems using rounding
investigate place value. A strong
strategies.
understanding of place value is
3.NBT. 1 essential for the developed number
sense and the subsequent work that
involves rounding numbers.
Building on previous understandings of
the place value of digits in multi-digit
numbers, place value is used to round
whole numbers. Dependence on
learning rules can be eliminated with
strategies such as the use of a number
line to determine which multiple of 10
or of100, a number is nearest (5 or
more rounds up, less than 5 rounds
down). As students’ understanding of
place value increases, the strategies for
rounding are valuable for estimating,
justifying and predicting the
reasonableness of solutions in
problem-solving.
From Illustrative
4. Solve word problems involving Have students make estimations before
Mathematics:
three digit numbers using
solving the word problems. After
“Classroom
estimation to check for
students have solved the problems with
Supplies”
reasonableness in the solution.
the exact answer, have students
CA Framework p. 15
Flipbook p.26-27
NC Unpacking, p. 19
enVision, Topic 1:
 Math Background, pp. 2G-2H
 Interactive Learning, pp. 4-5
 Lesson 1-7 “Ordering Numbers”
 Lesson 1-8 “Problem Solving: Make an Organized
List” (Missing in printed materials?)
CA Framework p.13-15
Flipbook p. 19-21, 26-29
NC Unpacking, p. 14-15, 19-20
16
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
Essential
Questions
Why does place value
play a significant role
when using the
properties of
operations to solve
problems?
Assessments
for Learning
From NC Wikispace:
 “From 100 to 0”
3.NBT.2 Task 3
 “Mrs. Snyder’s
Game Board”
3.NBT.2 Task 1
Sequence of Learning Outcomes
3.NBT.1-2,
3.MD.1-2, 3.OA.8
Strategies
for Teaching and Learning
Use strategies and algorithms
explain how close their estimation was
based on place value,
to the actual solution.
properties of operations,
Have students solve problems with the
and/or the relationship
unknown in all positions.
between addition and
subtraction.
3.NBT.2
3.OA.8
Students need the opportunity
to practice adding and
subtracting within 1,000
throughout the school year.
Differentiation e.g.
EL,SpEd, GATE
Resources
enVision, Topic 2:
 Math Background, pp. 27A-27B
 Interactive Learning, pp. 28-29
 Lesson 2-1 “Addition Meaning and Properties”
 Lesson 2-2 “Subtration Meanings”
 Lesson 2-3 “Using Mental Math to Add”
 Lesson 2-4 “Using Mental Math to Subtract”
 Lesson 2-5 “Estimating Sums”
 Lesson 2-6 “Estimating Differences”
 Lesson 2-7 “Problem Solving: Reasonableness”
enVision, Topic 3:
 Math Background, pp. 55A-55B
 Interactive Learning, pp. 56-57
 Lesson 3-1 “Adding with an Expanded Algorithm”
 Lesson 3-2 “Model for Adding 3-Digit Numbers”
 Lesson 3-3 “Adding 3-Digit Numbers”
 Lesson 3-4 “Adding 3 or More Numbers”
 Lesson 3-5 “Problem Solving: Draw a Picture”
 Lesson 3-6 “Subtracting with an Expanded Algorithm”
 Lesson 3-7 “Models for Subtracting 3-Digit Numbers”
 Lesson 3-8 “Subtracting 3-Digit Numbers”
 Lesson 3-9 “Subtracting Across Zero”
 Lesson 3-10 “Making Sense of Addition Equations”
 Lesson 3-11 “Making Sense of Subtraction Equations”
 Lesson 3-12 “Adding and Subtracting”
 Lesson 3-13 “problem Solving: Draw a Picture and
Write a Number Sentence”
17
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
Essential
Questions
Why is it useful to tell
and write time to the
nearest minute?
What is an interval?
When might you
measure and estimate
masses of objects in
your everyday life?
What is an interval in
this situation?
When might you
measure and estimate
liquid volumes in your
everyday life?
What is an interval in
this situation?
Assessments
for Learning
Sequence of Learning Outcomes
3.NBT.1-2,
3.MD.1-2, 3.OA.8
Strategies
for Teaching and Learning
From NC Wikispace: 5. Tell, write, and measure
Relate clock to a number line when
 “Morning
lengths of time using analog
solving for elapsed time.
Schedule” 3.MD.1
and digital clocks. Solve real
Make a schedule (for example, 15
Task 1
world problems involving
minutes for breakfast, 10 minutes in
 “Edna’s Busy
elapsed time by representing
the bathroom, 5 minutes to get
Day,” 3.MD.1 Task
the problems on a number line
dressed, etc.) to determine time
2
diagram.
elapsed by using a number line, clock,
3.MD.1 or numbers.
 “Norman’s
Number Line”
3.MD.1 Task 3
From NC Wikispace: 6. Estimate, then measure weight Connect the metric system to the
“Weighing Fruits”
in metric units (grams and
base-ten place value system
3.MD.2 Task 1
kilograms).
Give students opportunity to weigh
3.MD.2 objects.
Students need opportunities to estimate
before measuring (see KATM, p.40).
Be aware of this misconception: students
often determine mass based on the size
of the object.
From NC Wikispace: 7. Estimate, then measure liquid Give students opportunity to fill
“Measuring Water”
volume in metric units (liters).
containers.
3.MD.2 Task 2
3.MD.2 Students need opportunities to estimate
before measuring (see KATM, p.40).
Differentiation e.g.
EL,SpEd, GATE
Resources
CA Framework p. 24
Flipbook p. 39-40
NC Unpacking, p. 27
enVision, Topic 12:
 Math Background, pp. 289A-289B
 Interactive Learning, pp. 290-291
 Lesson 12-1 “Time to the Half Hour and Quarter Hour”
 Lesson 12-2 “Time to the Minute”
 Lesson 12-3 “Elapsed Time”
 Lesson 12-4 “Problem Solving: Work Backward”
CA Framework p. 24
Flipbook p. 41
NC Unpacking, p. 28-29
enVision, Topic 15:
 Math Background, pp. 361A-361B
 Interactive Learning, pp. 362-363
 Lesson 15-3 “Units of Mass”
 Lesson 15-4 “Measuring Mass”
CA Framework p. 24
Flipbook p. 41
NC Unpacking, p. 28-29
enVision, Topic 15:
 Math Background, pp. 361A-361B
 Interactive Learning, pp. 362-363
 Lesson 15-1 “Metric Units of Capacity”
18
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #2: Place Value and Problems with Units of Measure
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.NBT.1-2,
3.MD.1-2, 3.OA.8
Strategies
for Teaching and Learning
Differentiation e.g.
EL,SpEd, GATE
Resources
 Lesson 15-2 “Measuring Capacity”
How do you select an
From NC Wikispace: 8. Add and subtract to solve
Students should solve measurement
appropriate interval for
3.MD
one-step word problems
problems with the unknown in all
a number line?
involving masses that are given
positions, while conserving units.
in the same units by using
drawings to represent the
problem.
3.MD.2
CA Framework p. 24
Flipbook p. 41
NC Unpacking, p. 28-29
How do you select an
From NC Wikispace: 9. Add and subtract to solve
Students should solve measurement
appropriate interval for
3.MD
one-step word problems
problems with the unknown in all
a number line?
involving volumes that are
positions, while conserving units.
given in the same units by using
drawings to represent the
problem.
3.MD.2
CA Framework p. 24
Flipbook p. 41
NC Unpacking, p. 28-29
enVision, Topic 15:
 Math Background, pp. 361A-361B
 Interactive Learning, pp. 362-363
 Lesson 15-5 “problem Solving: Draw a Picture”
enVision, Topic 15:
 Math Background, pp. 361A-361B
 Interactive Learning, pp. 362-363
 Lesson 15-5 “problem Solving: Draw a Picture”
19
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
(Approx. # Days- )
Content Standards: 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8, 3.OA.9, 3.NBT.3
In this unit, students will use place value understanding, properties of operations, and relationship between multiplication and division to solve word problems within 100.
Common Core State Standards-Mathematics:
Operations and Algebraic Thinking 3.OA
Understand properties of multiplication and the relationship between multiplication and division.
5. Apply properties of operations as strategies to multiply and divide (students need not use formal terms for these properties). Examples: If 6 x 4 is known, then 4 x 6 = 24 is also known (Commutative
property of multiplication.). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30 (Associative property of multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can
find 8 x 7 as 8 x (5 + 2) = (8 x 2) = 40 + 16 = 56 (Distributive property).
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.
7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 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.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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 (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}).
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.
Number and Operations in Base Ten 3.NBT
Use place value understanding and properties of operations to perform multi-digit arithmetic (a range of algorithms may be used).
3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
Standards for Mathematical Practice:
SMP. 1 Make sense of problems and persevere in solving them
SMP. 2 Reason abstractly and quantitatively
SMP. 3 Construct viable argument and critique the reasoning of others
SMP. 4 Model with mathematics
SMP. 5 Use appropriate tools strategically
SMP. 6 Attend to precision
SMP. 7 Look for and make use of structure
SMP. 8 Look for and express regularity in repeated reasoning
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
20
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways
A. Collaborative
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
2. Understanding cohesion
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
21
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning
Essential Questions
are thoughtprovoking,
open-ended
questions to be used
within daily lessons
that and are
therefore connected
to the Sequence of
Learning Outcomes.
Assessments for
Learning address
Diagnostic,
Formative, and
Summative
assessments used
throughout the unit
to inform instruction
connected to the
Sequence of Learning
Outcomes.
Note: These
assessments are
suggested, not
required.
Mid-point Check and
Post Assessmentsfrom engageNY,
Module 3, All Tasks
Gr 3_Unit 3_Mid &
Post
Assessments.pdf
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Sequence of Learning Outcomes is
intentionally organized for student
success. Each outcome is not
necessarily intended to be taught
within one class session.
Each Outcome begins with
Students will be able to…
Strategies for Teaching and
Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
General Strategy Support for Unit:
From the CA Mathematics
Framework
 “Instructional Strategies”
chapter provides research-based
strategies for teaching math,
K-12
 “Supporting High Quality
Common Core Instruction”
chapter addresses the
development, implementation,
and maintenance of
high-quality, standards-based
mathematics instructional
programs
Differentiation Support
for Unit:
Use of math journals for
differentiation and
formative assessment
(use link below)
https://www.teaching
channel.org/videos/m
ath-journals
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1 “What students Learn in Grade Three”
 p. 10-16 Operations and Algebraic Thinking and Number
and Operations in Base Ten domains
 p. 34-37 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional strategies,
additional resources/tools and misconceptions by
standard.
 p. 10-15, 24-25 Operations and Algebraic Thinking domain
 p. 26-31 Number and Operations in Base Ten domain
NC Unpacking Documents
 Provide illustrated examples, instructional strategies,
additional resources/tools and misconceptions by
standard.
 p. 7-17 Operations and Algebraic Thinking domain
 p. 18-20 Number and Operations in Base Ten domain
Progressions for CCSS-M
 Narrative documents describing the progression of a topic
across a number of grade levels, informed both by
research on children's cognitive development and by the
logical structure of mathematics.
 p. 2-3, 22-31 Operations and Algebraic Thinking domain
 p. 11 Number and Operations in Base Ten domain
Flexible grouping:
 Content
 Interest
 Project/product
 Level
(Heterogeneous/
Homogeneous)
“Universal Design for Learning” from
CAST, the Center for Applied
Tiered:
Special Technology
 Independent
Management Plan
(Must Do/May Do)
 Grouping
o Content
o Rigor w/in the
concept
o Project-based
learning
22
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
From NC Wikispace: 1. Understand and apply the
Why does the
3.OA.3 Task 3:
commutative
commutative property of
Raking Leaves
property applies to
multiplication as a strategy to
some operations, but
multiply when solving word
not to others?
problems. Students use the
array, drawings, manipulatives,
How can I model
etc. to justify why the
multiplication?
commutative property only
applies to addition and
When can you use
multiplication, but not to
multiplication and
subtraction or division.
division in real life?
3.OA.5
Strategies for Teaching and
Learning
Students are learning and
o Homework
understanding the concept of
o Grouping
commutative property; they do
o Formative
not need to use the formal terms.
Assessment
Use the array model to represent
the commutative property of
Anchor Activities:
multiplication.
 Content-related
Skip counting on the array model
 Tasks for early
can be used to practice
finishers
multiplication facts.
o Game
Spend time interpreting rows and
o Investigation
columns by rotating array by 90˚.
o Partner Activity
o Stations
How is the
commutative
proprety of
multiplication
evident in an array
model?
What is an
associative property
in multiplication?
From NC Wikispace:
 3.OA.5 Task 1:
Patterns on the
Multiplication
Chart
How is the
associative property
of multiplication used 
in solving a problem?
3.OA.5 Task 2:
Prove It!
2. Understand and apply the
associative property of
multiplication as a strategy to
multiply when solving word
problems. Students use
drawings, arrays, etc. to justify
why multiplying “three or more
whole numbers without using
any parentheses will yield the
same result regardless of how
we group the factors.” (NCTM,
Multiplication and Division,
Differentiation e.g.
EL, SpEd, GATE
Students are learning and
understanding the concept of
associative property; they do not
need to use the formal terms
(refer to North Carolina’s Unpack
Content, p. 9-10.
Have students draw or create
rectangular prisms with 3
different side lengths and
compute or reason “the number
of cubic units is the same no
matter how we compute the
Depth and Complexity
Prompts/Icons:
 Depth
o Language of the
Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
o Complexity
http://scusd-math.wikis
paces.com/home
Resources
CA Framework p. 10-11
Flipbook p. 12-15
NC Unpacking, p. 9-10
Mathematics International, Unit1 “Multiplication”
 Section 1, “Properties of Mutliplication”
o Lesson 1, p.A5-7
Teaching Student-Centered Mathematics: Grades 3-5
 “The Order Property in Multiplication,” p.66
engageNY, Module 3 “Multiplication and Division with Units
of 0, 1, 6-9, and 10”
 Topic 1, Lesson 1
enVision, Topic 4:
 Math Background, pp. 95A-95B
 Interactive Learning, pp. 96-97
 Lesson 4-3 “The Commutative property”
CA Framework p. 10-11
Flipbook p. 12-15
NC Unpacking, p. 9-10
enVision, Topic 6:
 Math Background, pp. 137A-137B
 Interactive Learning, pp. 138-139
 Lesson 6-6 “Multipying with 3 Factors”
23
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Grade 3-5, p.30).
3.OA.5
How does
decomposing
numbers help you
solve multiplication
problems?
From Illustrative
Mathematics:
Valid Equalities?
(Part 2)
How are
multiplication and
division related?
From NC Dept. of
Public Instruction
"Prove it!"
Strategies for Teaching and
Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
volume.” (NCTM Multiplication
and Division, Grades 3-5, p.31)
3. Decompose and re-compose
Students use other methods (area
numbers to apply the
model, partial products,
associative property to solve
calculator, etc.) to justify their
multiplication word problems.
reasoning from applying
Students solve 7 × 6 by
decomposition and the
decomposing the 6 as two 3s (2
associative property.
× 3) to get
7 × 2 × 3. They apply the
associative property to solve (7
× 2) and then × 3  (7 × 2) × 3
(refer to the Progression
Document K, Counting and
Cardinality, K-5, Operations and
Algebraic Thinking, p.26).
3.OA.5
4. Use an area model to
Students need opportunities to
understand and apply the
continue to decompose numbers
distributive property of
in order to apply the distributive
multiplication(as a strategy) to
property {for example, 32 x 7 =
multiply and divide. Students
(30 + 2) x 7 = (30 x 7) + (2 x 7)}
begin using the conventional
(refer to North Carolina’s Unpack
order of operations
Content, p. 9-10).
(multiplication and division are Students are learning and
done before addition and
understanding the concept of
subtraction).
distributive property; they do not
3.OA.5
need to use the formal terms.
Use the area model to guide
students to understand the
CA Framework p. 10-11
Flipbook p. 12-15
NC Unpacking, p. 9-10
Mathematics International, Unit 1 “Multiplication”
 Section 1, “Properties of Multiplication”
o Lesson 2, p.A8
CA Framework p. 10-11
Flipbook p. 12-15
NC Unpacking, p. 9-10
Mathematics International, Unit 2 “Multiplication”
 Section 1 “Properties of Multiplication”
o Lesson 5, p.A11-13
enVision, Topic 6:
 Math Background, pp. 137A-137B
 Interactive Learning, pp. 138-139
 Lesson 6-1 “The Distributive Property”
24
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning
How does
From NC Dept. of
understanding the
Public Instruction:
"Sharing Pencils"
distributive property
help us multiply large
numbers?
How does drawing an
array help us think
about the different
ways to decompose a
number (factors or
product)?
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and
Learning
relationship between the
distributive property and
decomposition of numbers.
5. Use an area model to apply the Students may decompose other
distributive property of
factor pairs and use the area
multiplication over addition as a
model/diagram to support their
strategy to solve products they
reasoning. Ask students if they see
do not know (for example, 3 × 5
a pattern (refer to the Progression
is 15, so 3 × 6 is 15 + 3 more is
document K-5, Operations and
18) to solve word problems.
Algebraic Thinking p.26).
3.OA.5
Differentiation e.g.
EL, SpEd, GATE
Resources
CA Framework p. 10-11
Flipbook p. 12-15
NC Unpacking, p. 9-10
Teaching Student-Centered Mathematics: Grades 3-5
 “The Distributive Property,” p.66
o “Slice It Up” activity 2.27
 “Strategies for Multiplication Facts”
o “If You Didn’t Know” activity 3.9, p.92 & 98-99
How does
decomposing
numbers help you
solve multiplication
and division
problems?
What strategies can
be used to solve
multiplication
problems?
What strategies can
be used to solve
From Illustrative
Mathematics:
“Two
Interpretations of
Division”
6. Use the relationship between
Interpret the unknown in division
multiplication and division to
using the array model.
solve division word problems as Students solve word problems that
an unknown factor problem (48
involve unknown product, group
÷ 8 = ?  8 × ? = 48).
size unknown, and number of
3.OA.6 groups unknown.
CA Framework p. 10-12
Flipbook p. 16
NC Unpacking, p. 11
Mathematics International, Unit 3 “Division”
 Section 1 “Calculations for Finding How Many for 1
Person”
25
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and
Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
real-world dividion
problems?

o Lesson 1, p.A25-27
o Lesson 2, p.A28
Section 2, “Calculations for fidning the Number of
People We Can Divide Something Into”
o Lesson 1, p.A29=31
o Lesson 2, p.A31-32
o Lesson 3, p.A33
enVision, Topic 7:
 Math Background, pp. 167A-167B
 Interactive Learning, pp. 168-169
 Lesson7-3 “Find Missing Numbers in a Multiplication
Table”
enVision, Topic 8:
 Math Background, pp. 187A-187B
 Interactive Learning, pp. 188-189
 Lesson 8-1 “Relating Multiplication and Division”
 Intervention/“Teamwork” Center Activity
 Lesson 8-8 “Multiplication and Division Facts”
What patterns canbe From Illustrative
used to find certain
Mathematics
multiplication facts?
“Finding the
Unknown in a
Why is the
Division Equation”
multiplication table
symmetric about its
diagonal?
What strategies can
be used to learn
7. Develop multiplication and
Strategies for learning multiplication
division facts by studying
facts include:
patterns and relationships in
 Patterns
multiplication facts and relating
 General strategies
multiplication and division.
 Other strategies
Students record the patterns
Strategies for learning division facts
after using arrays, drawings,
include:
hundreds chart, manipulatives,
 Unknown factors
etc. and justify their reasoning.
 Related facts
3.OA.7 (For further details, refer to CA
Mathematics Framework, p.12)
CA Framework p. 13
Flipbook p. 17-18
NC Unpacking, p. 12-13
Mathematics International, Unit 3 “Division”
 “Power Builder,” p.A36
 “Mastery Problems, p.A37
enVision, Topic 8:
 Math Background, pp. 187A-187B
 Interactive Learning, pp. 188-189
26
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning
multiplication facts?
How do the
properties of
operations enable
you to solve
problems?
From Illustrative
Mathematics
 “The Stamp
Collection”
 “The Class Trip”
What strategies can
be used to solve
multiplication
problems?
From NC Dept. of
Public Instruction
"Mario's Designs"
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and
Learning
Students need the opportunity
to practice multiplying and
dividing within 100 and know
all products of 2 one-digit
numbers from memory
throughout the school year.
8. Solve two-step word problems Students should have opportunities
using the four operations.
to assess the reasonableness of
Represent these problems using
their answers using mental
equations with a letter standing
computation and estimation
for the unknown quantity by
strategies including rounding.
using tape diagrams.
Students should have opportunities
3.OA.8 to use visual representations, such
as, part-part-whole, bar models,
tape diagrams to solve problems
(refer to CA Mathematics
Framework, p.14)
Why does place value From Illustrative
9. Identify arithmetic patterns and For example, that 4 times a number
play a significant role
Mathematics:
explain the patterns using
is always even, and explain why 4
when using the
properties of operations.
times a number can be
 Addition Patterns
properties of
3.OA.9 decomposed into two equal
 Patterns in a
operations to solve
addends (4 x 7 can be thought of
Mulitiplication
problems?
as double 2 x 7).
Table
 Symmetry of the
Addition Table
Differentiation e.g.
EL, SpEd, GATE
Resources




Lesson 8-2 “Fact Families with 2, 3, 4, and 5”
Lesson 8-3 “Fact Families with 6 and 7”
Lesson 8-4 “Fact Families with 8 and 9”
Lesson 8-7 “Dividing with 0 and 1”
CA Framework p. 13-14
Flipbook p. 19-21
NC Unpacking, p. 14-15
enVision, Topic 5:
 Math Background, pp. 113A-113B
 Interactive Learning, pp. 114-115
 Lesson 5-7 “Problem Solving: Two-Question Problems”
enVision, Topic 6:
 Math Background, pp. 137A-137B
 Interactive Learning, pp. 138-139
 Lesson 6-9 “Problem Solving: Multiple-Step Problems”
enVision, Topic 8:
 Math Background, pp. 187A-187B
 Interactive Learning, pp. 188-189
 Lesson 8-5 “Problem Solving: Multiple-Step Problems”
CA Framework p. 14-15
Flipbook p. 22-23
NC Unpacking, p. 16-18
“Discover Number Patterns with Skip Counting” Video from
the Teaching Channel
Mathematics International, Unit 3 “Division”
 Section 3 “Calculations for Finding Times as Much”
27
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #3: Problem Solving Using Multiplication and Division
Essential
Questions
Assessments
for Learning

How is place value
related to multiples
of ten?
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and
Learning
Making a Ten
From Illustrative
10. Use decomposition of factors of Give students the opportunity to
Mathematics:
ten and properties of operations develop the conceptual
How Many Colored
to multiply one-digit whole
understanding before teaching the
Pencils?
numbers by multiples of ten (10
standard algorithm. This skill will
How is multiplying by
– 90). Recognize and explain
support students’ later learning of
ten related to palce
patterns when multiplying by
standard algorithm for
value?
multiples of ten.
multiplication of multi-digit
3.NBT.3 numbers.
What happens to a
For example, 40 × 3 can be
number when it is
interpreted as 3 groups of 4 tens
multiplied by ten?
or 12 tens. Twelve tens equals 120
(refer to Mathematics Framework,
p.16).
Differentiation e.g.
EL, SpEd, GATE
Resources
o
Lesson 1, p.A35-36
enVision, Topic 5:
 Math Background, pp. 113A-113B
 Interactive Learning, pp. 114-115
 Lesson 5-2 “9 as a Factor”
 Lesson 5-3 “Multiplying with 0 and 1”
 Lesson 5-4 “Patterns for Facts”
 Lesson 5-5 “10 as a Factor”
CA Framework p. 15-16
Flipbook p. 30
NC Unpacking, p. 21
Mathematics International, Unit 9 “Multiplication
Algorithm,” Part 1
 Section 1 “Multiplication by 10 and 100”
o Lesson 1, p.A91-92
o Lesson 2, p.A92
 Section 2, “Mulitplication of 2-Digit by 1-Digit Numbers”
o Lesson 1, p.A93-95
o Lesson 2, p.A96
o Lesson 3, p.A97
o Lesson 4, p.A98
enVision, Topic 5:
 Math Background, pp. 113A-113B
 Interactive Learning, pp. 114-115
 Lesson 5-6 “Multipying by Multiples of 10”
28
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #4: Multiplication and Area
(Approx. # Days- )
Content Standards: 3.MD.5, 3.MD.6, 3.MD.7
In this unit students will develop understanding of concepts of area and its relationship to multiplication and addition.
Common Core State Standards-Mathematics:
Measurement and Data 3.MD
Geometric measurement: understand concepts of area and relate area to multiplication and to addition
5. Recognize area as an attribute of plane figures and understand concepts of area and 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.
6. Measure areas by counting unit squares (square cm, square m, square n, square ft, and improvised units).
7. Relate area to the operations of multiplication and addition.
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. 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. 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 x b and a x c. Use area models to represent the distributive property in
mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of non-overlapping parts, applying this technique to solve
real world problems.
Standards for Mathematical Practice:
SMP. 1 Make sense of problems and persevere in solving them
SMP. 2 Reason abstractly and quantitatively
SMP. 3 Construct viable argument and critique the reasoning of others
SMP. 4 Model with mathematics
SMP. 5 Use appropriate tools strategically
SMP. 6 Attend to precision
SMP. 7 Look for and make use of structure
SMP. 8 Look for and express regularity in repeated reasoning
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
29
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
ELD Standards to Support Unit:
Part I: interacting in Meaningful Ways
A. Collaborative
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose,
audience, topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
2. Understanding cohesion
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
30
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #4: Multiplication and Area
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.MD.5, 3.MD.6, 3.MD.7
Essential Questions
are thoughtprovoking,
open-ended
questions to be
used within daily
lessons that and are
therefore
connected to the
Sequence of
Learning Outcomes.
Assessments for Learning
address Diagnostic,
Formative, and Summative
assessments used
throughout the unit to
inform instruction
connected to the Sequence
of Learning Outcomes.
Sequence of Learning Outcomes is
intentionally organized for student
success. Each outcome is not
necessarily intended to be taught
within one class session.
Each Outcome begins with
Students will be able to…
Note: These assessments
are suggested, not
required.
Mid-point Check and Post
Assessments- from
engageNY, Module 3, All
Tasks
Gr 3_Unit 3_Mid & Post
Assessments.pdf


What is an area?
How does
knowing the
area of a square
or rectangle
relate to
knowing
1. Describe an area as the amount
of surface space.
3.MD.5
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
General Strategy Support for Unit:
Differentiation
From the CA Mathematics Framework
Support for Unit:
Use of math journals
 “Instructional Strategies” chapter
for differentiation
provides research-based strategies for
and formative
teaching math, K-12
 “Supporting High Quality Common Core assessment (use
link below)
Instruction” chapter addresses the
https://www.teachi
development, implementation, and
ngchannel.org/vide
maintenance of high-quality,
os/math-journals
standards-based mathematics
instructional programs
Flexible grouping:
 Content
“Universal Design for Learning” from CAST,  Interest
the Center for Applied Special Technology  Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management
Plan (Must
Do/May Do)
 Grouping
o Content
o Rigor w/in
the concept
o Project-base
d learning
o Homework
Resources
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1 “What students Learn in Grade Three”
 p. 26-30 Measurement and Data domain
 p. 32-34 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 45-49 Measurement and Data domain
NC Unpacking Documents
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 34-39 Measurement and Data domain
Progressions for CCSS-M
 Narrative documents describing the progression
of a topic across a number of grade levels,
informed both by research on children's cognitive
development and by the logical structure of
mathematics.
 p. 2-5, 16-19 K-5, Geometric Measurement
domain
CA Framework p. 26-27
Flipbook p. 45-46
NC Unpacking, p. 34-35
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
engageNY Module 4 Overview
 Topic A: “Foundation for Understanding Area”
31
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #4: Multiplication and Area
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.MD.5, 3.MD.6, 3.MD.7
Strategies for Teaching and Learning
o
o
multiplication
facts?



2. Color in a square from a grid
Continue to have students color in squares
(for example, centimeter grid)
and explain the number of colored
and reason about the side
squares is that number “square unit.”
lengths as “a unit” and the
space colored is “one square
unit.”
3.MD.5a
Why are square
units commonly
associated with
finding area?
From NC Dept. of Public
Why is it
important to not Instruction:
"Maggie’s Jelewry Box"
have gaps or
overlaps when
determining the
area ofa figure?
What symbols
can be used to
represent an
Differentiation e.g.
EL, SpEd, GATE
From NC Dept. of Public
Instruction:
"Playgrounds"
Grouping
Formative
Assessment
Anchor Activities:
 Content-related
 Tasks for early
finishers
o Game
o Investigation
o Partner
Activity
o Stations
Depth and
Complexity
Prompts/Icons:
 Depth
o Language of
3. Describe and reason that an
Continue to give students an opportunity to
the Discipline
“area” or space to be colored
shade in/color grids and explain the
o
Patterns
or covered does not overlap or
number of squares shaded in is n unit
o
Unanswered
have no gaps is n unit squares.
squares.
Questions
3.MD.5b
o Rules
o Trends
o Big Ideas
o Complexity
4. Measure areas from grids by
counting (or adding) the unit
squares and describe that
SCUSD Wikispace
o
Resources
Teaching Student-Centered Mathematics, Grades
3-5, Ch. 9 “Developing Measurement Concepts”
 “Measuring Length,” p.257-265
enVision, Topic 14:
 Math Background, pp. 289A-289B
 Interactive Learning, pp. 290-291
CA Framework p. 26-27
Flipbook p. 45-46
NC Unpacking, p. 34-35
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic A: “Foundation for Understanding Area”
enVision, Topic 14:
 Lesson 14-1 “Covering Regions”
CA Framework p. 26-27
Flipbook p. 45-46
NC Unpacking, p. 34-35
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic A: “Foundation for Understanding Area”
enVision, Topic 14:
 Lesson 14-2 “Area and Units”
CA Framework p. 26-27
Flipbook p. 47
NC Unpacking, p. 35
32
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #4: Multiplication and Area
Essential
Questions
Assessments
for Learning
unknown
amount?
Sequence of Learning Outcomes
3.MD.5, 3.MD.6, 3.MD.7
Strategies for Teaching and Learning
space as n unit squares.
3.MD.6
Differentiation e.g.
EL, SpEd, GATE
Resources
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic A: “Foundation for Understanding Area”
enVision, Topic 14:
 Lesson 14-3 “Standard Units”
 Lesson 14-6 “Solve a Simpler Problem”
5. Describe and reason “unit”
squares can be labeled
centimeters squared, meters
squared, etc.
3.MD.6
CA Framework p. 26-27
Flipbook p. 47
NC Unpacking, p. 35
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic A: “Foundation for Understanding Area”
enVision, Topic 14:
 Lesson 14-11 “Selecting Appropriate
Measurement Units and Tools”

What is tiling?

How does
knowing the
dimensions for a
rectangle relate
to area?
From Illustrative
Mathematics:
"The Square Counting
Shortcut"
6. Find the area of any rectangles This an opportunity to remind students to
when given side lengths (cm,
connect back to Unit 1 and 3 when they
m, in, ft, etc.) by tiling it and
created arrays to represent equal groups
counting all the tiles.
of rows and columns. However, the new
3.MD.7a learning is using units of measurement
and understand the relationship among
those different units.
CA Framework p. 27-30
Flipbook p. 48-49
NC Unpacking, p. 35-39
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic B: “Concepts of Area Measurement”
enVision, Topic 14:
 Lesson 14-4 “Area of Squares and Rectangles”
33
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #4: Multiplication and Area
Essential
Questions




Assessments
for Learning
Why is an area From NC Dept. of Public
Instruction:
model a
"Gino’s New Room"
representation
for
multiplication?
What is the
relationship
between
dimensions and
factors?
How can area be
determined
without
counting each
square?
What strategies From NC Dept. of Public
Instruction:
can be used to
"All Areas"
solve word
problems?
Sequence of Learning Outcomes
3.MD.5, 3.MD.6, 3.MD.7
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
7. Find the area of any rectangle Students should see the progression from
with given side lengths by
tiling and counting, to adding an equal
adding every row or column, or
number in every row or column (additive
by multiplying the side lengths.
thinking), to multiplying equal groups
Reason that the total number
(multiplicative thinking).
of tiles stays the same (yields
the same measurement area)
whether counting all, adding
every row or column, or
multiplying the side lengths.
3.MD.7a
CA Framework p. 27-30
Flipbook p. 48-49
NC Unpacking, p. 35-39
8. Solve problems to find the
areas of rectangles with
different dimensions as they
design a room or a playground.
3.MD.7b
CA Framework p. 27-30
Flipbook p. 48-49
NC Unpacking, p. 35-39
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic B: “Concepts of Area Measurement”
enVision, Topic 14:
 Lesson 14-4 “Area of Squares and rectangles”
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”
 Topic C: “Arithmetic Properties Using Area
Models”
enVision, Topic 14:
 Lesson 14-8 “Different Area, Same Perimeter”
 Lesson 14-9 “Same Area, Different Perimeter”

From NC Dept. of Public
Why is it
Instruction:
important to
"Antonio's Garden"
understand that
more than one
9. Solve problems to find the
Students decompose the “L-shaped” rooms
areas of complex figures
to apply the distributive property to solve
(figures that an be decomposed these problems (for example, 13 cm by 5
into smaller rectangles, such as
cm can be solved by finding 13 × 5 or
CA Framework p. 27-30
Flipbook p. 48-49
NC Unpacking, p. 35-39
34
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #4: Multiplication and Area
Essential
Questions


Assessments
for Learning
math operation
may be needed From Illustrative
to solve a
Mathematics:
problem?
"Three Hidden
Rectangles"
How can
knowledge of
area be used to
solve real-world
problems?
From NC Dept. of Public
How is the
Instruction:
decomposition
"Micah & Nina
of a factor in an
Rectangle"
equation related
to the
From Illustrative
distributive
Mathematics:
property of
"Finding
th Area of
multiplication?
Polygon"
Sequence of Learning Outcomes
3.MD.5, 3.MD.6, 3.MD.7
Strategies for Teaching and Learning
an “L-shaped” room). Students
practice rotating the shapes
and reason that the area is
conserved.
3.MD.7d
decomposing 13 to get (6 + 7) × 5 = 6 × 5
+ 7 × 5.
10. Use area models to represent
the distributive property.
3.MD.7c
Differentiation e.g.
EL, SpEd, GATE
Resources
enVision, Topic 14:
 Lesson 14-7 “Area of Irregular Shapes”
CA Framework p. 27-30
Flipbook p. 48-49
NC Unpacking, p. 35-39
enVision, Topic 14:
 Lesson 14-5 “Area and the Distributive Property”
Mid-Point Check and Post
Assessments-engageNY,
Module 4, All Tasks
Gr 3_Unit 4_Mid & Post
Assessments.pdf
35
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
(Approx. # Days- )
Content Standards: 3.G.2, 3.NF.1, 3.NF.2, 3.NF.3, 3.MD.4
In this unit students will develop understanding of fractions as numbers and apply those concepts to partition shapes and lengths.
Common Core State Standards-Mathematics:
Number and Operations -- Fractions 3.NF
Develop understanding of fractions as numbers
1. Understand a fraction 1/b as 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.
2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram 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 based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram 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.
3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same endpoint on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/2; recognize that 6/1 = 6; locate 4/4 and 1 at the same point
on a number line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a fraction model.
Geometry 3.G
Reason with shapes and their attributes
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 aprt as
1/4 of the area of the shape.
Measurement and Data 3.MD
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
4. Generate measurement data by measruring lengths using rulers marked with halves and fourths of an inch. Show the data by marking a line plot, where the horizontal scale is marked off in appropriate
units—whole numbers, halves, or quarters.
36
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Standards for Mathematical Practice:
SMP. 1 Make sense of problems and persevere in solving them
SMP. 2 Reason abstractly and quantitatively
SMP. 3 Construct viable argument and critique the reasoning of others
SMP. 4 Model with mathematics
SMP. 5 Use appropriate tools strategically
SMP. 6 Attend to precision
SMP. 7 Look for and make use of structure
SMP. 8 Look for and express regularity in repeated reasoning
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
ELD Standards to Support Unit:
Part I: interacting in Meaningful Ways
A. Collaborative
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area
8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience,
topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
2. Understanding cohesion
37
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
38
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions
Essential
Questions are
thoughtprovoking,
open-ended
questions to be
used within
daily lessons
that and are
therefore
connected to
the Sequence of
Learning
Outcomes.
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Assessments for Learning
address Diagnostic,
Formative, and Summative
assessments used
throughout the unit to
inform instruction
connected to the Sequence
of Learning Outcomes.
Sequence of Learning Outcomes is
intentionally organized for student
success. Each outcome is not
necessarily intended to be taught
within one class session.
Note: These assessments
are suggested, not
required.
Mid-point Check and Post
Assessments- from
engageNY, Module 3, All
Tasks
Gr 3_Unit 3_Mid & Post
Assessments.pdf
Each Outcome begins with
Students will be able to…
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
General Strategy Support for Unit:
Differentiation
From the CA Mathematics Framework
Support for Unit:
Use of math journals
 “Instructional Strategies” chapter
for differentiation
provides research-based strategies for
and formative
teaching math, K-12
 “Supporting High Quality Common Core assessment (use
link below)
Instruction” chapter addresses the
https://www.teachi
development, implementation, and
ngchannel.org/vide
maintenance of high-quality,
os/math-journals
standards-based mathematics
instructional programs
Flexible grouping:
 Content
“Universal Design for Learning” from CAST,  Interest
the Center for Applied Special Technology  Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management
Plan (Must
Do/May Do)
 Grouping
o Content
o Rigor w/in
the concept
o Project-base
d learning
o Homework
Resources
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1 “What students Learn in Grade Three”
 p. 10-16 Operations and Algebraic Thinking and
Number and Operations in Base Ten domains
 p. 34-37 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 10-15, 24-25 Operations and Algebraic Thinking
domain
 p. 26-31 Number and Operations in Base Ten
domain
NC Unpacking Documents
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 7-17 Operations and Algebraic Thinking domain
 p. 18-20 Number and Operations in Base Ten
domain
Progressions for CCSS-M
 Narrative documents describing the progression
of a topic across a number of grade levels,
informed both by research on children's cognitive
development and by the logical structure of
mathematics.
 p. 2-3, 22-31 Operations and Algebraic Thinking
domain
 p. 11 Number and Operations in Base Ten domain
39
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
o
o






1. Partition, or divide, a whole
Students should continue to build upon
“Naming the Whole for a
(line segments, rectangles,
their 1st & 2nd grade prior knowledge
Fraction”
circles, etc.) into equal-sized
/experience related to partitioning circles
parts.
Orally
describe
each
part
and rectangles into two, three, or four
What does
"Selling
Bubble
Gum"
as “halves, thirds, fourths,
equal shares and use the words: halves,
“equal parts”
sixths, or eighths” (depending
half of, thirds, a third of, fourth, fourth of,
mean?
"Rudy's
Rectangle"
on
the
number
of
partitions.
quarter of. They can further explore
What is a
Count the number of
concepts of fractions using other
fraction?
"Geometric Pictures of One
equal-sized parts that make up
concrete models such as pattern blocks.
Half"
the
whole
(“1
third,
2
thirds,
3
Have
students practice counting with
How can I
thirds and 3 thirds make a
fractions just as they counted with whole
represent
"Representing Half of a
whole”
–
repeat
with
other
numbers.
fractions of
Circle"
fractional parts).
Counting equalized parts will help them
different sizes?
3.NF.1 determine the number of parts it takes to
make a whole and recognize fractions
How are sixths
Note: (Understanding that a
that are equivalent to whole numbers.
related to the
fraction
is
a
quantity
formed
by
“Example
of Instruction”: 3.NF.1 & 3.G.2
whole?
part of a whole is essential to
number sense with fractions. Common Misconception:
How can I use
Fractional parts are the
Students may think that all shapes can
fractions to
building
blocks
for
all
fraction
be divided the same way. Studets may
name parts of a
concepts, in the same sense
not understand that when partitioning
whole?
that the number 1 is the basic
a whole shape, number line, or a set
building
block
of
the
whole
into unit fractions, the interval must be
What is a
numbers.)
equal.
real-life example
of using
fractions?
What is a
whole?
Resources
Grouping
Formative
Assessment
Anchor Activities:
Possible Resources:
 Content-related
𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 3 “Addition and Subtraction of
 Tasks for early
Fractions”
finishers

Topic B: “Making Like Units Pictorially”
o Game
o Lesson 3: “Add fractions with unlike units
o Investigation
using the strategy of creating equivalent
o Partner
fractions.
Activity
o Lesson 4: “Add fractions with sums between
o Stations
1 and 2”
o
Lesson 5: “Subtract fractions with unlike
Depth and
units using the strategy of creating
Complexity
equivalent fractions”
Prompts/Icons:
o Lesson 6: “Subtract fractions from numbers
 Depth
between 1 and 2”
o Language of
Mathematics International, Unit 10: “Addition and
the Discipline
Subtraction of Fractions
o Patterns

Section 2: “Addition and Subtraction of
o Unanswered
Fractions”
Questions
o Lesson 5, p.B24
o Rules
o Lesson 6, p.B24
o Trends
Teaching
Student-Centered Mathematics, Grades
o Big Ideas
3-5, Ch. 6 “Fraction Computation”
o Complexity
 “Addition and Subtraction,” p.162-167
http://scusd-math.wi
kispaces.com/home
40
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions
Assessments
for Learning

How can I use
pattern blocks
to name
fractions?

How can I use
pattern blocks
to represent
fractions?

"Equal Shares"
What are the
important
"Making a Scarf"
features of a
unit of fraction?

Why is the
denominator
important to the
unit fractions?
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
2. Use fraction bars and
geometric shapes to partition
the whole into 1 where b
Students will need many opportunites to
analyze and discuss fractional parts using
concrete models to develop familiarity
b
and understanding of fractions.
represents the number of
Students need to recognize and represent
equal-sized parts. Understand
that the numerator is the top number
and describe each fractional
(term) of a fraction and that it represents
part of a whole is called a unit
the number of equal-sized parts of a
fraction. Read, count, and label
whole.
unit fractions using words and Students can reason about fractional parts
using decomposition strategy and/or
numbers 1 .
b
number bond representation (e.g., 4 is
3.NF.1
6
the same as 1 and 3 , 2 and 2 , or
6
6
6
6
3 and 1 ).
6
6
Students need to recognize and represent
that the denominator is the bottom
number (term) of a fraction and that it
represents the total number of
41
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions


Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
3. Understand that the size of a
fractional part is relative to the
size of a whole.
Why is the size
of the whole
important?
3.NF.1
How can I
compare
fractions?

How can I
compare
fractions when
they have the
same
numerators?

How can I
compare
fractions when
"Sharing Pie"
Differentiation e.g.
EL, SpEd, GATE
Resources
equal-sized parts.
Common Misconception:
Students see the numbers in fractions as
two unrelated whole numbers separated
by a line.
Students need to recognize that 1 of the
2
liquid in a small bottle could be less liquid
than 1 of the liquid in a larger bottle, but
3
1 of a ribbon is longer than 1
8
3
What is the
relationship
between a unit
fraction and a
unit of 1?

Strategies for Teaching and Learning
of the
same ribbon because when the ribbon is
divided into 3 equal parts, the parts are
longer than when the ribbon is divided
into 8 equal parts.
4. Represent and compare
Students can use fraction bars that show
common fractions with like
the same sized whole as models to
numerators or denominators
compare fractions.
and tell why one fraction is
They can also use Venn diagrams to
greater than, less than, or
organize and compare fractions to
equal to the other by using
determine the relative size of the
concrete and pictorial models.
fractions, such as more than 1 , exactly
2
3.NF.3d
1 or less than 1 .
2
2
Encourage students to write the results of
the comparisons with the symbols >, =, or
<, and justify the conclusions with a
model.
Common Misconception:
42
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
they have the
same
denominators?
When we
compare two
fractions, how
do we know
which has the
greater value?

When we
compare two
fractions, how
do we know
which has the
greater value?

Why is the
denominator
important to the
unit fractions?
6. Use number lines to
How are tenths “Locating Fractions Less
than
One
on
the
Number
understand that the whole is
related to the
Line”
the unit interval, measured by
whole?
length from one number to
“Locating
Fractions
Greater
another number. Using the
How can I
than One on the Number
understanding of consecutive
represent
Line”
whole numbers, create unit
fractions of
fractions on number lines,
different
“Find 1”
focusing on halves, thirds,
lengths?

Differentiation e.g.
EL, SpEd, GATE
Resources
Students may not understand fractions
can be greater than 1.


Strategies for Teaching and Learning
"Comparing Fractions"
5. Understand and explain the
Students should understand that
concept that the larger the
decomposing into more equal shares
denominator, the smaller the
equals smaller shares, and that equal
size of the piece.
shares of identical wholes need not have
3.NF.1 the same shape.
Students need to relate dividing a shape
into equal parts and representing this
relationship on a number line, where
the equal parts are between two whole
numbers, starting with partitioning equal
lengths between 0 and 1. They then work
with number lines that have endpoints
other than o and 1, or that include
multiple whole number intervals.
43
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
fourths, sixths, and eighths.

How is the odd
and even
pattern with
unit of fractions
on a number
line similar to
units of 1 on a
number line?
Whole numbers on a number
line:
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
Students need to know how to plot
fractions on a number line, by using the
meaning of the fraction (e.g., to plot 4
6
on a number line, there are 6 equal parts
with 4 copies of one of the 6 equal parts).
Common Misconception:
Students do not count correctly on the
number line. For example, students may
Unit fractions on a number line: count the hash mark at zero as the first
unit fraction.
3.NF.2
"Placing Fractions on a
Number Line"
7. Understand and show that two Having students count equalized parts
fractions as equivalent (equal)
will help them determine the number of
if they are the same size,
parts it takes to make a whole and
(though not necessarily the
recognize fractions that are equivalent to
same shape) or the same point
whole numbers.
on a number line.
44
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions


Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
3.NF.3a
"Halves,
Thirds,
and
Sixths"
8.
Create
simple
equivalent
Stduents need to understand that two
What equivalent
equivalent fractions are two ways of
groups of
fractions, (e.g., 1 = 2 , 4 =
2
4 6
describing the same amount by using
fractions can I
2
different-sized fractional parts. For
discover using
) and explain why the
3
Fraction Strips?
example, in the fraction 6 , if the eighths
fractions are equivalent by
8
using a visual fraction model.
are taken in twos, then each pair of
eighths is a fourth. Sixth-eighthts then
can be seen as equivalent to
three-fourths. (Resource: Van de Walle)
"All the Jumps"
What is the
difference
between 2/1
and 2/2, 3/1 and
3/3?
3.NF.3b
9. Read and understand whole
Students need to understand how to
numbers as fractions, and
express whole number fractions on the
recognize fractions that are
number line when the unit interval is 1.
equivalent to the whole
Use a number line to help students notice
numbers. Examples:Express 3 in that the difference bewtween 2 and 2
1
2
45
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions



How can I
compare
fractions?
Assessments
for Learning
“Closest to 1/2”
“Comparing Fractions”
"A Piece of Yarn"
How can I
determine
length to the
nearest 1/4?
How can I
organize data
measured to the
half inch? To the
quarter inch?
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
the form of 3 ; recognize that
, or 3 and 3 , and that these fractions
1
6 = 6; locate 4 and 1 at the
1
4
is even greater and conctinue to grow as
the numbers go higher.
1
Differentiation e.g.
EL, SpEd, GATE
Resources
3
same point on a number line
diagram.
3.NF.3c
10. Represent and compare
Students can use fraction bars that show
common fractions with like
the same sized whole as models to
numerators or denominators
compare fractions.
and tell why one fraction is
They can also use number line to organize
greater than, less than, or
and compare fractions to determine the
equal to the other by using
relative size of the fractions, such as
concrete, pictorial models, and
more than 1 , exactly 1 or less than 1
2
2
2
number lines.
3.NF.3d . This type of reasoning can be repeated
with benchmark numbers such as 0 and
1.
Encourage students to write the results of
the comparisons with the symbols >, =, or
<, and justify the conclusions with a
model.
11. Use a standard ruler to
Students will need many opportunitites
measure items including details measuring the length of various objects in
about halves and quarter marks their environment so that they can
on the inch ruler; create a line
connect their understanding of fractions
plot to display their findings.
to measuring to one-half and one-quarter
3.MD.4 inch. For example, measure objects in
your desk to the nearest 1 or 1 of an
2
4
inch, display data collected on a line plot.
46
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions




Assessments
for Learning
How can I
display
fractional parts
of data in a
graph?
What estimation
strategies are
used in
measurement?
How can I
collect and
organize data?
“Jon and Charlie’s Run”
How are
fractions used in
problem-solving “Snow Day”
situations?
"Distances Swam"
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
12. Solve real-world problems that Students must experience fractions across
involve comparing fractions by
many constructs, such as the following
using visual fraction models
three categories of models: area (e.g., 1
3
and strategies based on
3
noticing equal numerators or
of a garden), length (e.g.,
of an inch),
4
denominators.
3.NF.3d and set or quantity (e.g., 1 of the class).
2
Partitioning and iterating are ways for
students to understand the meaning of
fractions, especially numerator and
denominator.
As they compare, students should reason
about the size of fractions and
contextualize their learning within
real-world applications.
Mid-point Check and Post
Assessment - engageNY,
Module 5 Tasks 1-4
47
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #5: Developing Understanding of Fractions
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
Gr 3_Unit 5_Mid & Post
Assessments.pdf
48
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #6: Representing and Interpreting Data
(Approx. # Days- )
Content Standards: 3.MD.3, 3.MD.4
In this unit students will represent and interpreting data to solve one-and two- step word problems.
Math Common Core State Standards- Mathematics:
Measurement and Data 3.MD
Represent and interpret data.
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.
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.
Standards for Mathematical Practice:
SMP 1 Make sense of problems and persevere in solving them
SMP 2 Reason abstractly and quantitatively
SMP 3 Construct viable argument and critique the reasoning of others
SMP 4 Model with mathematics
SMP 5 Use appropriate tools strategically
SMP 6 Attend to precision
SMP 7 Look for and make use of structure
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
ELD Standards to Support Unit:
Part I: interacting in Meaningful Ways
A. Collaborative
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
49
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience,
topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
2. Understanding cohesion
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
50
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #6: Representing and Interpreting Data
Essential
Questions
Essential
Questions are
thoughtprovoking,
open-ended
questions to be
used within daily
lessons that and
are therefore
connected to the
Sequence of
Learning
Outcomes.
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Assessments for Learning
address Diagnostic,
Formative, and
Summative assessments
used throughout the unit
to inform instruction
connected to the
Sequence of Learning
Outcomes.
Sequence of Learning Outcomes is
intentionally organized for student
success. Each outcome is not
necessarily intended to be taught
within one class session.
Note: These assessments
are suggested, not
required.
Mid-point Check and Post
Assessments- from
engageNY, Module 3, All
Tasks
Gr 3_Unit 3_Mid & Post
Assessments.pdf
Each Outcome begins with
Students will be able to…
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
General Strategy Support for Unit:
Differentiation
From the CA Mathematics Framework
Support for Unit:
Use of math journals
 “Instructional Strategies” chapter
for differentiation
provides research-based strategies for
and formative
teaching math, K-12
 “Supporting High Quality Common Core assessment (use
link below)
Instruction” chapter addresses the
https://www.teachi
development, implementation, and
ngchannel.org/vide
maintenance of high-quality,
os/math-journals
standards-based mathematics
instructional programs
Flexible grouping:
 Content
“Universal Design for Learning” from CAST,  Interest
the Center for Applied Special Technology  Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management
Plan (Must
Do/May Do)
 Grouping
o Content
o Rigor w/in
the concept
o Project-base
d learning
o Homework
Resources
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1 “What students Learn in Grade Three”
 p. 10-16 Operations and Algebraic Thinking and
Number and Operations in Base Ten domains
 p. 34-37 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 10-15, 24-25 Operations and Algebraic Thinking
domain
 p. 26-31 Number and Operations in Base Ten
domain
NC Unpacking Documents
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 7-17 Operations and Algebraic Thinking domain
 p. 18-20 Number and Operations in Base Ten
domain
Progressions for CCSS-M
 Narrative documents describing the progression
of a topic across a number of grade levels,
informed both by research on children's cognitive
development and by the logical structure of
mathematics.
 p. 2-3, 22-31 Operations and Algebraic Thinking
domain
 p. 11 Number and Operations in Base Ten domain
51
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #6: Representing and Interpreting Data
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
o
o







How to decide
which type of
graph is
appropriate to
use for which
type of data?
How can data
displayed be
used to inform?
To describe
events? To
describe
observations?
How to decide
what increment
scale to use for a
bar graph?
How to interpret
data in a graph?
How can graphs
be used to
organize data?
How can graphs
be used to
compare related
data?
How can we use
1. Draw a scaled picture and a
scaled bar graph to represent a
data set with several categories
(refer to Progressions
document Measurement and
Data, p.4).
3.MD.3
Measurement and Data
2. Use data from scaled bar
For example, draw a bar graph in which
3.MD.3
graphs to solve one- and
each square in the bar graph might
MAT.03.TE.1.000MD.H.23
two-step “how many more”
represent 5 pets (refer to Progressions
9 C1 T1
and “how many less” problems. document Measurement and Data, p.4).
3.MD.3
Resources
Grouping
Formative
Assessment
Anchor Activities:
 Content-related
 Tasks for early
finishers
o Game
o Investigation
o Partner
Activity
o Stations
Depth and
Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
o Complexity
http://scusd-math.wi
kispaces.com/home
52
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #6: Representing and Interpreting Data
Essential
Questions




graphs to solve
real-world
problems?
When and why
do we use rulers
to measure
things?
How might
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
"Estimating
Measurements"
3. Generate measurement data
by measuring lengths using
rulers marked with halves and
fourths of an inch.
3.MD.4
"Reading Survey"
Why are there
different types of
graphs?
How can data
displayed in
graphs
4. Make a line plot from the
generated measurement data
(see above), where the
horizontal scale is marked off in
appropriate units-whole
numbers, halves, or quarters.
3.MD.4
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
53
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #6: Representing and Interpreting Data
Essential
Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
Post Assessment engageNY, Module 6, All
Tasks
GR3_Unit 6_Post
Assessment.pdf
54
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #7: Geometric Figures and Problem Solving Involving Perimeters and Areas
(Approx. # Days- )
Content Standards: 3.G.1, 3.MD.8
In this unit students will categorize shapes based on their attributes and recognize that measurements of perimeter and area as attributes of plane figures.
Math Common State Content Standards- Mathematics:
Geometry 3.G
Reason with shapes and their attributes
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.
Measurement ad Data 3.MD
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
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.
Standards for Mathematical Practice:
SMP 1 Make sense of problems and persevere in solving them
SMP 2 Reason abstractly and quantitatively
SMP 3 Construct viable argument and critique the reasoning of others
SMP 4 Model with mathematics
SMP 5 Use appropriate tools strategically
SMP 6 Attend to precision
SMP 7 Look for and make use of structure
SMP 8 Look for and express regularity in repeated reasoning
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways
A. Collaborative
55
SCUSD Curriculum Map-Last Updated 12/02/14
Grade 3 Mathematics
1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics
2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia
3. Offering and supporting opinions and negotiating with others in communicative exchanges
4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)
B. Interpretive
5. Listening actively to spoken English in a range of social and academic contexts
6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language
8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience,
topic, and content area
C. Productive
9. Expressing information and ideas in formal oral presentations on academic topics
11. Supporting own opinions and evaluating others’ opinions in speaking and writing
12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas
Part II. Learning About How English Works
A. Structuring Cohesive Texts
1. Understanding text structure
2. Understanding cohesion
B. Expanding and Enriching Ideas
5. Modifying to add details
C. Connecting and Condensing Ideas
6. Connecting ideas
7. Condensing ideas
56
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #7: Problem Solving Involving Perimeters and Areas
Essential Questions
Essential Questions are
thought- provoking,
open-ended questions
to be used within daily
lessons that and are
therefore connected to
the Sequence of
Learning Outcomes.
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Assessments for
Learning address
Diagnostic, Formative,
and Summative
assessments used
throughout the unit to
inform instruction
connected to the
Sequence of Learning
Outcomes.
Sequence of Learning Outcomes is
intentionally organized for student
success. Each outcome is not
necessarily intended to be taught
within one class session.
Note: These
assessments are
suggested, not
required.
Mid-point Check and
Post Assessmentsfrom engageNY,
Module 3, All Tasks
Gr 3_Unit 3_Mid &
Post
Assessments.pdf
Each Outcome begins with
Students will be able to…
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
General Strategy Support for Unit:
Differentiation
From the CA Mathematics Framework
Support for Unit:
Use of math journals
 “Instructional Strategies” chapter
for differentiation
provides research-based strategies for
and formative
teaching math, K-12
 “Supporting High Quality Common Core assessment (use
link below)
Instruction” chapter addresses the
https://www.teachi
development, implementation, and
ngchannel.org/vide
maintenance of high-quality,
os/math-journals
standards-based mathematics
instructional programs
Flexible grouping:
 Content
“Universal Design for Learning” from CAST,  Interest
the Center for Applied Special Technology  Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management
Plan (Must
Do/May Do)
 Grouping
o Content
o Rigor w/in
the concept
o Project-base
d learning
o Homework
Resources
CCSS Support for the Unit:
CA Mathematics Framework “3rd Grade”
 p. 1 “What students Learn in Grade Three”
 p. 10-16 Operations and Algebraic Thinking and
Number and Operations in Base Ten domains
 p. 34-37 “Essential Learning for Next Grade”
KS Assoc. of Teachers of Mathematics FLIPBOOKS
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 10-15, 24-25 Operations and Algebraic Thinking
domain
 p. 26-31 Number and Operations in Base Ten
domain
NC Unpacking Documents
 Provide illustrated examples, instructional
strategies, additional resources/tools and
misconceptions by standard.
 p. 7-17 Operations and Algebraic Thinking domain
 p. 18-20 Number and Operations in Base Ten
domain
Progressions for CCSS-M
 Narrative documents describing the progression
of a topic across a number of grade levels,
informed both by research on children's cognitive
development and by the logical structure of
mathematics.
 p. 2-3, 22-31 Operations and Algebraic Thinking
domain
 p. 11 Number and Operations in Base Ten domain
57
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #7: Problem Solving Involving Perimeters and Areas
Essential Questions
Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
o
o






"Barons Shapes"
Do quadrilateals
have to look like
rectangles? How do "Sallys Shape Sort"
you know?
Do rectangles and
squares always look
the samw? How do
you know?
Do you think shapes
could be grouped
together in the
same family or
classification?
Explain.
Does the direction
that a shape is
facing change the
way it looks? Does it
change the shape’s
name?
Is it possible to find
more than one way "Guess the Rule"
for shapes to fit
together o make
another shape?
Explain.
What does it mean
to parttion a shape
Resources
Grouping
Formative
Assessment
1. Categorize and compare
Students in grade 2 have reasoned with
quadrilaterals versus other
shapes and their attribute. This standard Anchor Activities:
polygons by examining the
serves as a
 Content-related
properties of geometric figures. Students explain that:
 Tasks for early
3.G.1 1) a quadrilateral must be a close figure
finishers
with four straight sides,
o Game
2) notice the characteristics of the
o Investigation
angles,
o Partner
3) notice the relationship between
Activity
opposite sides
o Stations
2. Reason about decomposing
For example, two triangles can form a
and composing polygons to
quadrilateral;
make other polygons.
3.G.1
Depth and
Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
o Complexity
http://scusd-math.wi
kispaces.com/home
58
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #7: Problem Solving Involving Perimeters and Areas
Essential Questions



Assessments
for Learning
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
3. Explore the concept of
perimeter by measuring
perimeter of different size or
shape polygons and record the
perimeter using units, cm, m,
in, etc. Reason about different
size/shape polygons with the
same perimeter, but with
different side lengths.
3.MD.8
4. Solve word problems involving
perimeter of polygons(where
all side lengths are listed).
Students label the perimeter
with the correct unit.
3.MD.8
Students can walk around the perimeter of
the classroom, trace the perimeter of the
desks, or use rubber bands on a geo
board to represent the perimeter of the
geometric shape.
Students describe opposite sides of
rectangles and parallelograms have the
same lengths.
Differentiation e.g.
EL, SpEd, GATE
Resources
into parts?
How does
combining and
breaking apart
shapes affect the
perimeter and area?
How might finding
shapes within other
shapes help me in
life?
How do the
measure of lengths
change when the
unit of measure
changes?
"The Table"
Students discuss and justify faster ways to
find the perimeter without actually
counting or adding up all the lengths.
Give students the polygons with sides
already marked with unit lengths and
have students count the units lengths in
order to reason about how different
shapes can have the same perimeter.
Students reason about counting the
length-units and not the end-points to
get an accurate perimeter measurement.
59
Grade 3 Mathematics
SCUSD Curriculum Map-Last Updated 12/02/14
Unit #7: Problem Solving Involving Perimeters and Areas
Essential Questions

Assessments
for Learning
"Make a Garden"
Sequence of Learning Outcomes
3.OA.5-9, 3.NBT.3
Strategies for Teaching and Learning
Differentiation e.g.
EL, SpEd, GATE
Resources
5. Solve word problems involving Common error: students only add the unit
perimeter, where one or two of
lengths that are visible. Give students
the side lengths are missing.
opportunity to label all side lengths as a
3.MD.8 reminder.
3.MD.8

How are the
perimeter and area
of a shape related?
"Carpets"
6. Solve a variety of word
problems involving perimeter
and area where the polygons
have the same perimeter, but
different areas or polygons that
have the same area, but
different perimeters.
3.MD.8
60