SCUSD Curriculum Map-Last Updated 12/02/14 Grade 3 …scusd-math.wikispaces.com/file/view/Grade+3+CM+(Dec+2014)+New... · SMP. 1 Make sense of problems and persevere in solving them

SCUSD Curriculum Map-Last Updated 12/02/14 Grade 3 Mathematics

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Curriculum Map

Mathematics Grade 3

DRAFT Last Updated December 18, 2014 Sacramento City Unified School District


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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


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Grade 3 Year-at-a-Glance

District Benchmark 1

*Alignment TBD

Month Unit Content Standards

September Unit #1

Represent and Understand Multiplication and Division

3.OA.1 3.OA.2 3.OA.3 3.OA.4

October Unit #2

Place Value and Problem Solving with Units of Measure

3.NBT.1 3.NBT.2 3.MD.1 3.MD.2 3.OA.8


*Alignment TBD

November/ December

Unit #3 Problem Solving Using Multiplication and Division

3.OA.5 3.OA.6 3.OA.7 3.OA.8 3.OA.9 3.NBT.3

January/February Unit #4

Exploring Multiplication with Area

3.MD.5 3.MD.6 3.MD.7


*Alignment TBD March/April

Unit #5 Developing Understanding of Fractions

3.NF.1 3.NF.2 3.NF.3 3.G.2

3.MD.4

CAASPP (Smarter Balanced Summative Test)

May Unit #6

Representing and Interpreting Data 3.MD.3 3.MD.4

May/June Unit #7

Geometric Figures and Problem Solving Involving Perimeter and Area 3.G.1

3.MD.8


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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


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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


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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

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

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…

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 Support for Unit: Use of math journals

for differentiation and formative assessment (use link below) https://www.teachingchannel.org/videos/math-journals

Flexible grouping:

Content

Interest

Project/product

Level (Heterogeneous/ Homogeneous)

Tiered:

Independent Management Plan (Must Do/May Do)

Grouping o Content o Rigor w/in the

concept o Project-based

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


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 by the logical structure of mathematics.

p. 2-3, and 22-28 Operations and Algebraic Thinking domain

Videos from The Teaching Channel

Think Time and Collaborative Learning

Third Grade Math: A Complete Lesson

Catch and Release: Encourage Independence

Adjusting Lessons: Have a Plan B

http://scusd-math.wikispaces.com/file/view/CCGPS_Ice+Cream+Scoops_Performance+Task.pdf/509864888/CCGPS_Ice%20Cream%20Scoops_Performance%20Task.pdf

http://www.cde.ca.gov/ci/ma/cf/documents/aug2013instructstrat.pdf

http://www.cde.ca.gov/ci/ma/cf/documents/aug2013supportinghqccm.pdf


http://www.cast.org/

https://www.teachingchannel.org/videos/math-journals



http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

http://www.cde.ca.gov/ci/ma/cf/documents/aug2013gradethree.pdf

http://katm.org/wp/wp-content/uploads/flipbooks/3flipbookedited_2.pdf

http://maccss.ncdpi.wikispaces.net/Third+Grade

http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf

https://www.teachingchannel.org/videos/independent-and-group-work

https://www.teachingchannel.org/videos/classroom-daily-routines

https://www.teachingchannel.org/videos/effective-teaching-technique

https://www.teachingchannel.org/videos/teacher-backup-plans


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Essential Questions





Resources

How can I relate what I know about skip counting to multiply? What patterns can be used to find certain multiplication facts? How are addition and multiplication related? What is the

relationship between

factors and product?

NC Wikispace, 3rd Grade Tasks

1. Recognize multiplication as finding the total number of objects in a certain number of equal-sized groups. Provide students context (story problems) as they learn equal groupings.

3.OA.1

The standard defines multiplication of whole numbers a x b as finding the total number of objects in a groups of b objects.

Use the terms “number of objects in each group”(3 x __ = 18 and 18 ÷ 3 = __) or “number of groups” (__ x 6 = 18 and 18 ÷ 6 = __) with students.

Number bond can be used as a visual representation of this skip counting strategy.

Draw pictures to represent equal groups May use a variety of models (tile squares,

counters, linking cubes, beans, etc.) for students to manipulate equal groups

learning o Homework o Grouping o 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)

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”


From Illustrative

Mathematics:

“Fish Tanks”

“Markers in Boxes”

2. Interpret factors as the size of the group or the number of groups. Show with models “a number of groups of a certain number of object (or size)” when the language of “groups of” is presented with various terms (for example, “piles of,” “stacks of,” “rows of,” “cups of,” “teams of,” etc.).

3.OA.1

Use context to help students determine the factors.

Use number lines to show equal groups

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,


enVision, Topic 4:

Lesson 4-1 “Multiplication as Repeated Addition”

How can multiplication be represented? What is the


3. Represent multiplication with the array to show the relationship among all the numbers involved (factor x

Build rectangular arrays using “rows of.” Describe arrays in terms of equal groups

(by rows or by columns). For example, 4 x 5: “There are 4 rows of 5 chairs.” which


4-5 NC Unpacking, pg. 4

http://3-5cctask.ncdpi.wikispaces.net/3.OA.1-3.OA.4


http://www.engageny.org/resource/numbers-through-10-number-towers-number-path-number-bond

http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathCenter




http://maccss.ncdpi.wikispaces.net/file/view/Unpacking%203%20July%202013.pdf/443030266/Unpacking%203%20July%202013.pdf

http://www.engageny.org/resource/numbers-through-10-number-towers-number-path-number-bond

https://www.engageny.org/resource/grade-3-mathematics-module-1



http://www.illustrativemathematics.org/illustrations/1531














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Essential Questions





Resources

relarionship beween factors and product? What strategies can be used to find the factors or prodcuts?

factor = product). Use context so students will be able to visualize “rows/columns of” a particular group.

3.OA.1

is different from 5 rows of 4 chairs where the meaning and representation are different. The product is the same.

Partition arrays into smaller arrays (concept of decomposition)

Use tape diagrams

From engageny Downloadable Resources PDF, Module 1,


Video on Word Problems with tape Diagrams enVision, Topic 4:



Lesson 4-2 “Arrays and Multiplication”

How can division be represented?

How can I use what I know about subtraction, equal sharing, and forming equal groups to solve division problems? How are subtraction and division related?


From Illustrative

Mathematics:

“Two Interpretations of Division”

“Gifts from Grandma” Variation1

“Finding the unknown in a division equation”

4. Recognize division in two different situations – equal sharing (e.g., how many are in each group?), and determining how many groups (e.g., how many groups can you make?)

3.OA.2

Use the terms “number of objects in a group”(3 x __ = 18 and 18 ÷ 3 = __) or “number of groups” (__ x 6 = 18 and 18 ÷ 6 = __) with students rather than “partitive division” or “quotitive division.”

Use the array model to determine the unknown in division.

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:



Lesson 7-1 “Division as Sharing”

Lesson 7-2 “Division as Repeated Subtraction”

How can the same array model represent multiplication and division? How can I use the array model to explain


5. Model the relationship between multiplication and division by using a variety of methods, such as bar modeling, number line, arrays, etc.

3.OA.3

Model division as the unknown factor in multiplication in multiple ways (for example, bar modeling, number line, arrays, etc.).


7-9 NC Unpacking, pg. 5-6 From engageny Downloadable Resources PDF, Module 1,



http://www.engageny.org/resource/word-problems-with-tape-diagrams

























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Essential Questions





Resources

multiplication and division? How can I model division? How are multiplication and division alike and different?


Lesson from LearnZillion: “Solve Multiplication and Division Problems: Using a Diagram”

enVision, Topic 4:



Lesson 4-4 “Writing Multiplication Stories” enVision, Topic 7:



Lesson 7-5 “Writing Division Stories” enVision, Topic 8:



Lesson 8-6 “Making Sense of Multiplication and Division Equations”

Lesson 8-9 “Problem Solving: Draw a Picture and Write a Number Sentence”

How can I use the array model to explain multiplication and division?

How can I use known facts to find unknown facts?


From Illustrative

Mathematics:

“Analyzing Word Problems Involving Multiplication”

6. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

3.OA.3

Model problems using pictural representations and manipulatives.


7-9 NC Unpacking, pg. 5-6 From engageny Downloadable Resources PDF, Module 1,



https://learnzillion.com/lessons/54-solve-multiplication-and-division-problems-using-a-diagram

https://learnzillion.com/lessons/54-solve-multiplication-and-division-problems-using-a-diagram



https://www.illustrativemathematics.org/illustrations/365









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Essential Questions





Resources

enVision, Topic 4:



Lesson 4-5 “Problem Solving” enVision, Topic 5:


Interactive Learning, pp. 114-115 enVision, Topic 5:

Lesson 5-1 “2 and 5 as Factors” enVision, Topic 6:



Lesson 6-2 “3 as a Factor”


Lesson 6-4 “6 and 7 as Factors”


Lesson 6-7 “Multiplication Facts”

Lesson 6-8 “Multiplying to Find Combinations” enVision, Topic 7:



Lesson 7-6 “Problem Solving:Use Objects and Draw a Picture”

How are multiplication and division related? How can different strategies be helpful when solving


7. Determine the unknown whole number in a multiplication or division equation relating three whole numbers to make the equation true.

Use manipulatives, pictures, words, and/or equations to represent the problem and explain thinking process.


10-11, and 24 NC Unpacking, pg. 7 engageny Downloadable Resources PDF, Module 1, Topic









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Essential Questions





Resources

problems? 3.OA.4

B “Division as an Unknown Factor Problem”, pg. 1.B.1-1.B.35

enVision, Topic 7:



Lesson 7-4 “Problem Solving: Choose an Appropriate Equation”


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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.


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.


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


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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


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Unit #2: Place Value and Problems with Units of Measure

Essential

Questions

Assessments

for Learning


3.NBT.1-2,

3.MD.1-2, 3.OA.8

Strategies

for Teaching and Learning

Differentiation e.g.

EL,SpEd, GATE

Resources


Assessments for

Learning address

Diagnostic,

Formative, and

Summative

assessments used

throughout the unit


connected to the

Sequence of

Learning Outcomes.


Mid-point Check

and Post Assessments – from engageNY, Module 2 Tasks 1-5

Gr 3_Unit 2_Mid-Post Assessments.pdf

Sequence of Learning Outcomes is

intentionally organized for student

success. Each outcome is not

necessarily intended to be taught

within one class session.





“Universal Design for Learning” from CAST, the Center for Applied Special

Technology



Flexible grouping:

Content

Interest

Project/product


Tiered:




learning


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. 13-14 Operations and Algebraic domain


p. 24 Measurement and Data domain

NC Unpacking Documents


p. 13-14 Operations and Algebraic Thinking domain


p. 26-28 Measurement and Data domain Progressions for CCSS-M


p. 2-4, 11 Number and Operations in Base Ten domain

p. 2-4, 15-19 Measurement and Data domain

http://scusd-math.wikispaces.com/file/view/Gr+3_Unit+2_Mid-Post+Assessments.pdf/510131076/Gr%203_Unit%202_Mid-Post%20Assessments.pdf














http://ime.math.arizona.edu/progressions/



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Essential

Questions

Assessments

for Learning


3.NBT.1-2,

3.MD.1-2, 3.OA.8

Strategies



EL,SpEd, GATE

Resources

o Homework o Grouping o Formative


Content-related



Depth o Language of



http://scusd-math.wiki

spaces.com/home

p. 2-3, 27-28 Counting and Cardinality and Operations and Algebraic Thinking domains

What does “base ten” mean? What does “rounding” mean? When might you round to the nearest 10? When might you round to the nearest 100? What is an interval? How do you select an appropriate interval for a number line?

From NC Wikispace:

“Cafeteria Lunch Orders” 3.NBT.1 Task 1

“Comparing Heights” 3.NBT.1 Task 2

From Illustrative

Mathematics:

“Rounding to 50 or 500”

“Rounding to the Nearest Ten and Hundreds”

1. Use place value to round numbers to the nearest 10 on a number line.

3.NBT.1

Describe the distance of the two decade numbers (see KATM, p. 26-27).

Using a number line, plot decade numbers to identify the halfway point between two possible answers on a number line

Use a number line or a hundreds chart as tools to support students’ understanding of place value

CA Framework p. 15 Flipbook p.26-27 NC Unpacking, p. 19 enVision, Topic 1:

Math Background, pp. 2G-2H


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”

Lesson 1-5 “Rounding”

How can a number line help me round?

How do you select an appropriate interval for a number line?

From Illustrative Mathematics:

“Rounding to the Nearest Ten and Hundreds”

From NC Wikispace: “All About Rounding”

2. Use place value to round numbers to the nearest 100 on a number line.

3.NBT. 1

Students can use a number line or a hundreds chart as tools to support their 245 work with rounding.




Lesson 1-5 “Rounding”

Lesson 1-6 “More Rounding”

http://scusd-math.wikispaces.com/home


http://3-5cctask.ncdpi.wikispaces.net/3.NBT.1-3.NBT.3



















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Essential

Questions

Assessments

for Learning


3.NBT.1-2,

3.MD.1-2, 3.OA.8

Strategies



EL,SpEd, GATE

Resources

3.NBT.1 Task 3

In what kinds of situations is it appropriate to estimate? Why?

From NC Wikispace: “Toys for Us, Task

#2” 3.NBT.2 Task 2

3. Estimate to solve one-step addition and subtraction problems using rounding strategies.

3.NBT. 1

Prior to implementing rules for rounding students need to have opportunities to investigate place value. A strong understanding of place value is 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.




Lesson 1-7 “Ordering Numbers”

Lesson 1-8 “Problem Solving: Make an Organized List” (Missing in printed materials?)

In what kinds of situations is it appropriate to estimate? Why?


“Classroom Supplies”

4. Solve word problems involving three digit numbers using estimation to check for reasonableness in the solution.

Have students make estimations before solving the word problems. After students have solved the problems with the exact answer, have students

CA Framework p.13-15 Flipbook p. 19-21, 26-29 NC Unpacking, p. 14-15, 19-20












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Essential

Questions

Assessments

for Learning


3.NBT.1-2,

3.MD.1-2, 3.OA.8

Strategies



EL,SpEd, GATE

Resources

Why does place value play a significant role when using the properties of operations to solve problems?

From NC Wikispace:

“From 100 to 0”

3.NBT.2 Task 3

“Mrs. Snyder’s Game Board” 3.NBT.2 Task 1

Use strategies and algorithms based on place value, properties of operations, and/or the relationship 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.

explain how close their estimation was to the actual solution.

Have students solve problems with the unknown in all positions.

enVision, Topic 2:



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:



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”




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Essential

Questions

Assessments

for Learning


3.NBT.1-2,

3.MD.1-2, 3.OA.8

Strategies



EL,SpEd, GATE

Resources

Why is it useful to tell and write time to the nearest minute? What is an interval?

From NC Wikispace: “Morning

Schedule” 3.MD.1 Task 1

“Edna’s Busy Day,” 3.MD.1 Task 2

“Norman’s Number Line” 3.MD.1 Task 3

5. Tell, write, and measure lengths of time using analog and digital clocks. Solve real world problems involving elapsed time by representing the problems on a number line diagram.

3.MD.1

Relate clock to a number line when solving for elapsed time.

Make a schedule (for example, 15 minutes for breakfast, 10 minutes in the bathroom, 5 minutes to get dressed, etc.) to determine time elapsed by using a number line, clock, or numbers.

CA Framework p. 24 Flipbook p. 39-40 NC Unpacking, p. 27 enVision, Topic 12:


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”

When might you measure and estimate masses of objects in your everyday life? What is an interval in this situation?

From NC Wikispace: “Weighing Fruits”

3.MD.2 Task 1

6. Estimate, then measure weight in metric units (grams and kilograms).

3.MD.2

Connect the metric system to the base-ten place value system Give students opportunity to weigh

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.

CA Framework p. 24 Flipbook p. 41 NC Unpacking, p. 28-29 enVision, Topic 15:



Lesson 15-3 “Units of Mass”

Lesson 15-4 “Measuring Mass”

When might you measure and estimate liquid volumes in your everyday life? What is an interval in this situation?

From NC Wikispace: “Measuring Water”

3.MD.2 Task 2

7. Estimate, then measure liquid volume in metric units (liters).

3.MD.2

Give students opportunity to fill containers.

Students need opportunities to estimate before measuring (see KATM, p.40).




Lesson 15-1 “Metric Units of Capacity”

http://3-5cctask.ncdpi.wikispaces.net/3.MD.1-3.MD.2

















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Essential

Questions

Assessments

for Learning


3.NBT.1-2,

3.MD.1-2, 3.OA.8

Strategies



EL,SpEd, GATE

Resources

Lesson 15-2 “Measuring Capacity”


From NC Wikispace: 3.MD

8. Add and subtract to solve one-step word problems involving masses that are given in the same units by using drawings to represent the problem.

3.MD.2

Students should solve measurement problems with the unknown in all positions, while conserving units.




Lesson 15-5 “problem Solving: Draw a Picture”


From NC Wikispace: 3.MD

9. Add and subtract to solve one-step word problems involving volumes that are given in the same units by using drawings to represent the problem.

3.MD.2

Students should solve measurement problems with the unknown in all positions, while conserving units.




Lesson 15-5 “problem Solving: Draw a Picture”










20

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.



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



21



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




C. Connecting and Condensing Ideas 6. Connecting ideas 7. Condensing ideas


22

Unit #3: Problem Solving Using Multiplication and Division

Essential Questions


Sequence of Learning Outcomes 3.OA.5-9, 3.NBT.3



Resources


Assessments for

Learning address

Diagnostic,

Formative, and

Summative

assessments used

throughout the unit


connected to the


Outcomes.


Mid-point Check and

Post Assessments- from engageNY, Module 3, All Tasks

Gr 3_Unit 3_Mid & Post Assessments.pdf










“Universal Design for Learning” from CAST, the Center for Applied

Special Technology

Differentiation Support for Unit: Use of math journals for

differentiation and formative assessment (use link below) https://www.teachingchannel.org/videos/math-journals

Flexible grouping:

Content

Interest

Project/product


Tiered:




learning


p. 1 “What students Learn in Grade Three”

p. 10-16 Operations and Algebraic Thinking and Number and Operations in Base Ten domains



p. 10-15, 24-25 Operations and Algebraic Thinking domain

p. 26-31 Number and Operations in Base Ten domain NC Unpacking Documents



p. 18-20 Number and Operations in Base Ten domain Progressions for CCSS-M



p. 11 Number and Operations in Base Ten domain

http://scusd-math.wikispaces.com/file/view/Gr+3_Unit+3_Mid+%26+Post+Assessments.pdf/514360922/Gr%203_Unit%203_Mid%20%26%20Post%20Assessments.pdf

















23


Essential Questions





Resources

Why does the commutative property applies to some operations, but not to others?

How can I model multiplication?

When can you use multiplication and division in real life?

How is the commutative proprety of multiplication evident in an array model?

From NC Wikispace: 3.OA.3 Task 3: Raking Leaves

1. Understand and apply the commutative property of multiplication as a strategy to multiply when solving word problems. Students use the array, drawings, manipulatives, etc. to justify why the commutative property only applies to addition and multiplication, but not to subtraction or division.

3.OA.5

Students are learning and understanding the concept of commutative property; they do not need to use the formal terms.

Use the array model to represent the commutative property of multiplication.

Skip counting on the array model can be used to practice multiplication facts.

Spend time interpreting rows and columns by rotating array by 90˚.

o Homework o Grouping o Formative


Content-related



Depth o Language of the

Discipline o Patterns o Unanswered



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:



Lesson 4-3 “The Commutative property”

What is an associative property in multiplication?

How is the associative property of multiplication used in solving a problem?

From NC Wikispace:

3.OA.5 Task 1: Patterns on the Multiplication Chart

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,

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

CA Framework p. 10-11 Flipbook p. 12-15 NC Unpacking, p. 9-10 enVision, Topic 6:



Lesson 6-6 “Multipying with 3 Factors”


















24


Essential Questions





Resources

Grade 3-5, p.30). 3.OA.5

volume.” (NCTM Multiplication and Division, Grades 3-5, p.31)

How does decomposing numbers help you solve multiplication problems?

From Illustrative Mathematics: Valid Equalities? (Part 2)

3. Decompose and re-compose numbers to apply the associative property to solve multiplication word problems. Students solve 7 × 6 by decomposing the 6 as two 3s (2 × 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

Students use other methods (area model, partial products, calculator, etc.) to justify their reasoning from applying decomposition and the associative property.

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

How are multiplication and division related?

From NC Dept. of Public Instruction "Prove it!"

4. Use an area model to understand and apply the distributive property of multiplication(as a strategy) to multiply and divide. Students begin using the conventional order of operations (multiplication and division are done before addition and subtraction).

3.OA.5

Students need opportunities to continue to decompose numbers in order to apply the distributive property {for example, 32 x 7 = (30 + 2) x 7 = (30 x 7) + (2 x 7)} (refer to North Carolina’s Unpack Content, p. 9-10).

Students are learning and understanding the concept of distributive property; they do not 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 2 “Multiplication”

Section 1 “Properties of Multiplication” o Lesson 5, p.A11-13

enVision, Topic 6:



Lesson 6-1 “The Distributive Property”

http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/001/821/original/illustrative_mathematics_1821.pdf?1405998933





http://scusd-math.wikispaces.com/file/view/3.OA.5_Prove+it%21_Task+2.doc/512492128/3.OA.5_Prove%20it%21_Task%202.doc





25


Essential Questions





Resources

relationship between the distributive property and decomposition of numbers.

How does understanding the 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)?

How does decomposing numbers help you solve multiplication and division problems?

From NC Dept. of Public Instruction:

"Sharing Pencils"

5. Use an area model to apply the distributive property of multiplication over addition as a strategy to solve products they do not know (for example, 3 × 5 is 15, so 3 × 6 is 15 + 3 more is 18) to solve word problems.

3.OA.5

Students may decompose other factor pairs and use the area model/diagram to support their reasoning. Ask students if they see a pattern (refer to the Progression document K-5, Operations and Algebraic Thinking p.26).

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

What strategies can be used to solve multiplication problems?

What strategies can be used to solve


“Two Interpretations of Division”

6. Use the relationship between multiplication and division to solve division word problems as an unknown factor problem (48 ÷ 8 = ? 8 × ? = 48).

3.OA.6

Interpret the unknown in division using the array model.

Students solve word problems that involve unknown product, group size unknown, and number of 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”

http://scusd-math.wikispaces.com/file/view/3.OA.6_Sharing+Pencils_Task+1.doc/512492794/3.OA.6_Sharing%20Pencils_Task%201.doc











26


Essential Questions





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:



Lesson7-3 “Find Missing Numbers in a Multiplication Table”

enVision, Topic 8:



Lesson 8-1 “Relating Multiplication and Division”

Intervention/“Teamwork” Center Activity

Lesson 8-8 “Multiplication and Division Facts”

What patterns canbe used to find certain multiplication facts? Why is the multiplication table symmetric about its diagonal? What strategies can be used to learn

From Illustrative Mathematics “Finding the Unknown in a Division Equation”

7. Develop multiplication and division facts by studying patterns and relationships in multiplication facts and relating multiplication and division. Students record the patterns after using arrays, drawings, hundreds chart, manipulatives, etc. and justify their reasoning.

3.OA.7

Strategies for learning multiplication facts include:

Patterns

General strategies

Other strategies Strategies for learning division facts include:

Unknown factors

Related facts (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:










27


Essential Questions





Resources

multiplication facts? 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.

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”

How do the properties of operations enable you to solve problems?

What strategies can be used to solve multiplication problems?

From Illustrative Mathematics

“The Stamp Collection”

“The Class Trip” From NC Dept. of Public Instruction "Mario's Designs"

8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity by using tape diagrams.

3.OA.8

Students should have opportunities to assess the reasonableness of their answers using mental computation and estimation strategies including rounding.

Students should have opportunities to use visual representations, such as, part-part-whole, bar models, tape diagrams to solve problems (refer to CA Mathematics Framework, p.14)




Lesson 5-7 “Problem Solving: Two-Question Problems” enVision, Topic 6:



Lesson 6-9 “Problem Solving: Multiple-Step Problems” enVision, Topic 8:



Lesson 8-5 “Problem Solving: Multiple-Step Problems”

Why does place value play a significant role when using the properties of operations to solve problems?


Addition Patterns

Patterns in a Mulitiplication Table

Symmetry of the Addition Table

9. Identify arithmetic patterns and explain the patterns using properties of operations.

3.OA.9

For example, that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends (4 x 7 can be thought of as double 2 x 7).

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”




http://scusd-math.wikispaces.com/file/view/MAC2013-04+Mario%27s+Designs.pdf/513538188/MAC2013-04%20Mario%27s%20Designs.pdf













https://www.teachingchannel.org/videos/teaching-number-patterns


28


Essential Questions





Resources

Making a Ten o Lesson 1, p.A35-36 enVision, Topic 5:




Lesson 5-3 “Multiplying with 0 and 1”

Lesson 5-4 “Patterns for Facts”


How is place value related to multiples of ten?

How is multiplying by ten related to palce value?

What happens to a number when it is multiplied by ten?

From Illustrative Mathematics: How Many Colored

Pencils?

10. Use decomposition of factors of ten and properties of operations to multiply one-digit whole numbers by multiples of ten (10 – 90). Recognize and explain patterns when multiplying by multiples of ten.

3.NBT.3

Give students the opportunity to develop the conceptual understanding before teaching the standard algorithm. This skill will support students’ later learning of standard algorithm for multiplication of multi-digit numbers.

For example, 40 × 3 can be interpreted as 3 groups of 4 tens or 12 tens. Twelve tens equals 120 (refer to Mathematics Framework, p.16).

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:



Lesson 5-6 “Multipying by Multiples of 10”








29

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.



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



30

ELD Standards to Support Unit: Part I: interacting in Meaningful Ways


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. Connecting and Condensing Ideas 6. Connecting ideas

7. Condensing ideas


31

Unit #4: Multiplication and Area

Essential Questions


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



address Diagnostic,

Formative, and Summative

assessments used

throughout the unit to

inform instruction

connected to the Sequence

of Learning Outcomes.


Mid-point Check and Post

Assessments- from engageNY, Module 3, All Tasks











“Universal Design for Learning” from CAST, the Center for Applied Special Technology



Flexible grouping:

Content

Interest

Project/product


Tiered:


Grouping o Content o Rigor w/in

the concept o Project-base

d learning o Homework



p. 26-30 Measurement and Data domain



p. 45-49 Measurement and Data domain NC Unpacking Documents


p. 34-39 Measurement and Data domain Progressions for CCSS-M


p. 2-5, 16-19 K-5, Geometric Measurement domain

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

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”




















32


Essential Questions




Resources

multiplication facts?

o Grouping o Formative


Content-related

Tasks for early finishers o Game o Investigation o Partner

Activity o Stations


Depth o Language of



SCUSD Wikispace

o

Teaching Student-Centered Mathematics, Grades

3-5, Ch. 9 “Developing Measurement Concepts”

“Measuring Length,” p.257-265 enVision, Topic 14:



Why are square units commonly associated with finding area?

2. Color in a square from a grid (for example, centimeter grid) and reason about the side lengths as “a unit” and the space colored is “one square unit.”

3.MD.5a

Continue to have students color in squares and explain the number of colored squares is that number “square unit.”


𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 4 “Multiplication and Area”

Topic A: “Foundation for Understanding Area” enVision, Topic 14: Lesson 14-1 “Covering Regions”

Why is it important to not have gaps or overlaps when determining the area ofa figure?

From NC Dept. of Public Instruction: "Maggie’s Jelewry Box"

3. Describe and reason that an “area” or space to be colored or covered does not overlap or have no gaps is n unit squares.

3.MD.5b

Continue to give students an opportunity to shade in/color grids and explain the number of squares shaded in is n unit squares.



Topic A: “Foundation for Understanding Area” enVision, Topic 14:

Lesson 14-2 “Area and Units”

What symbols can be used to represent an

From NC Dept. of Public Instruction:

"Playgrounds"

4. Measure areas from grids by counting (or adding) the unit squares and describe that

CA Framework p. 26-27 Flipbook p. 47 NC Unpacking, p. 35





http://scusd-math.wikispaces.com/file/view/3.MD.5a+%26+5b+%26+6_Maggie%27s+Jelewry+Box_Task+2.doc/512499540/3.MD.5a%20%26%205b%20%26%206_Maggie%27s%20Jelewry%20Box_Task%202.doc




http://scusd-math.wikispaces.com/file/view/3.MD.6_Playgrounds_Task+2.doc/512499720/3.MD.6_Playgrounds_Task%202.doc





33


Essential Questions




Resources

unknown amount?

space as n unit squares. 3.MD.6



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



Lesson 14-11 “Selecting Appropriate Measurement Units and Tools”

What is tiling?

How does knowing the dimensions for a rectangle relate to area?


"The Square Counting Shortcut"

6. Find the area of any rectangles when given side lengths (cm, m, in, ft, etc.) by tiling it and counting all the tiles.

3.MD.7a

This an opportunity to remind students to connect back to Unit 1 and 3 when they created arrays to represent equal groups of rows and columns. However, the new learning is using units of measurement and understand the relationship among those different units.



Topic B: “Concepts of Area Measurement” enVision, Topic 14:

Lesson 14-4 “Area of Squares and Rectangles”










34


Essential Questions




Resources

Why is an area model a representation for multiplication?

What is the relationship between dimensions and factors?

How can area be determined without counting each square?

From NC Dept. of Public Instruction: "Gino’s New Room"

7. Find the area of any rectangle with given side lengths by adding every row or column, or by multiplying the side lengths. Reason that the total number 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

Students should see the progression from tiling and counting, to adding an equal number in every row or column (additive thinking), to multiplying equal groups (multiplicative thinking).



Topic B: “Concepts of Area Measurement” enVision, Topic 14:

Lesson 14-4 “Area of Squares and rectangles”

What strategies can be used to solve word problems?

From NC Dept. of Public Instruction: "All Areas"

8. Solve problems to find the areas of rectangles with different dimensions as they design a room or a playground.

3.MD.7b



Topic C: “Arithmetic Properties Using Area Models”

enVision, Topic 14:

Lesson 14-8 “Different Area, Same Perimeter”

Lesson 14-9 “Same Area, Different Perimeter”

Why is it important to understand that more than one

From NC Dept. of Public Instruction: "Antonio's Garden"

9. Solve problems to find the areas of complex figures (figures that an be decomposed into smaller rectangles, such as

Students decompose the “L-shaped” rooms to apply the distributive property to solve these problems (for example, 13 cm by 5 cm can be solved by finding 13 × 5 or


http://scusd-math.wikispaces.com/file/view/3.MD.6+%26+5_Gino%27s+New+Room_Task+1.doc/512499558/3.MD.6%20%26%205_Gino%27s%20New%20Room_Task%201.doc




http://scusd-math.wikispaces.com/file/view/3.MD.7_All+Areas_Task+1.doc/512499736/3.MD.7_All%20Areas_Task%201.doc




http://scusd-math.wikispaces.com/file/view/3.MD.5+%26+NF_Antonio%27s+Garden_Task+1.doc/512499504/3.MD.5%20%26%20NF_Antonio%27s%20Garden_Task%201.doc





35


Essential Questions




Resources

math operation may be needed to solve a problem?

How can knowledge of area be used to solve real-world problems?

From Illustrative Mathematics: "Three Hidden

Rectangles"

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.

enVision, Topic 14:

Lesson 14-7 “Area of Irregular Shapes”

How is the decomposition of a factor in an equation related to the distributive property of multiplication?

From NC Dept. of Public Instruction: "Micah & Nina

Rectangle"


"Finding th Area of Polygon"

10. Use area models to represent the distributive property.

3.MD.7c


Lesson 14-5 “Area and the Distributive Property”

Mid-Point Check and Post Assessments-engageNY, Module 4, All Tasks




http://scusd-math.wikispaces.com/file/view/3.MD.7acd_Micah+%26+Nina+Rectangle_Task+2.doc/512499752/3.MD.7acd_Micah%20%26%20Nina%20Rectangle_Task%202.doc

http://scusd-math.wikispaces.com/file/view/3.MD.7acd_Micah+%26+Nina+Rectangle_Task+2.doc/512499752/3.MD.7acd_Micah%20%26%20Nina%20Rectangle_Task%202.doc









36

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.


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.


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.


37

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










38




39

Unit #5: Developing Understanding of Fractions

Essential Questions




Resources



address Diagnostic,

Formative, and Summative

assessments used


inform instruction

connected to the Sequence

of Learning Outcomes.

















Flexible grouping:

Content

Interest

Project/product


Tiered:
















Progressions for CCSS-M




















40


Essential Questions




Resources



Content-related


Activity o Stations


Depth o Language of




What is a whole?

What does “equal parts” mean? What is a fraction?

How can I represent fractions of different sizes?

How are sixths related to the whole?

How can I use fractions to name parts of a whole?

What is a real-life example of using fractions?

“Naming the Whole for a

Fraction”

"Selling Bubble Gum"

"Rudy's Rectangle"

"Geometric Pictures of One Half"

"Representing Half of a

Circle"

1. Partition, or divide, a whole (line segments, rectangles, circles, etc.) into equal-sized parts. Orally describe each part as “halves, thirds, fourths, sixths, or eighths” (depending on the number of partitions. Count the number of equal-sized parts that make up the whole (“1 third, 2 thirds, 3 thirds and 3 thirds make a whole” – repeat with other fractional parts).

3.NF.1 Note: (Understanding that a fraction is a quantity formed by part of a whole is essential to number sense with fractions. Fractional parts are the building blocks for all fraction concepts, in the same sense that the number 1 is the basic building block of the whole numbers.)

Students should continue to build upon their 1st & 2nd grade prior knowledge /experience related to partitioning circles and rectangles into two, three, or four equal shares and use the words: halves, half of, thirds, a third of, fourth, fourth of, quarter of. They can further explore concepts of fractions using other concrete models such as pattern blocks.

Have students practice counting with fractions just as they counted with whole numbers.

Counting equalized parts will help them determine the number of parts it takes to make a whole and recognize fractions that are equivalent to whole numbers.

“Example of Instruction”: 3.NF.1 & 3.G.2 Common Misconception: Students may think that all shapes can

be divided the same way. Studets may not understand that when partitioning a whole shape, number line, or a set into unit fractions, the interval must be equal.

Possible Resources:

𝒆𝒏𝒈𝒂𝒈𝒆𝑵𝒀, Module 3 “Addition and Subtraction of Fractions”

Topic B: “Making Like Units Pictorially” o Lesson 3: “Add fractions with unlike units

using the strategy of creating equivalent fractions.

o Lesson 4: “Add fractions with sums between 1 and 2”

o Lesson 5: “Subtract fractions with unlike units using the strategy of creating equivalent fractions”

o Lesson 6: “Subtract fractions from numbers between 1 and 2”

Mathematics International, Unit 10: “Addition and Subtraction of Fractions

Section 2: “Addition and Subtraction of Fractions” o Lesson 5, p.B24 o Lesson 6, p.B24

Teaching Student-Centered Mathematics, Grades 3-5, Ch. 6 “Fraction Computation”

“Addition and Subtraction,” p.162-167





http://scusd-math.wikispaces.com/file/view/3.NF.1_Selling+Bubble+Gum_Task+4.doc/512495644/3.NF.1_Selling%20Bubble%20Gum_Task%204.doc

http://scusd-math.wikispaces.com/file/view/3.NF.1_Rudy%27s+Rectangle_Task+2.doc/512495512/3.NF.1_Rudy%27s%20Rectangle_Task%202.doc





http://www.engageny.org/resource/common-core-video-series-grade-3-module-5-mathematics-example-of-instruction


41


Essential Questions




Resources

How can I use pattern blocks to name fractions?

How can I use pattern blocks to represent fractions?

What are the important features of a unit of fraction?

Why is the denominator important to the unit fractions?

"Equal Shares" "Making a Scarf"

2. Use fraction bars and geometric shapes to partition

the whole into b

1 where b

represents the number of equal-sized parts. Understand and describe each fractional part of a whole is called a unit fraction. Read, count, and label unit fractions using words and

numbers b

1 .

3.NF.1

Students will need many opportunites to analyze and discuss fractional parts using concrete models to develop familiarity and understanding of fractions.

Students need to recognize and represent that the numerator is the top number (term) of a fraction and that it represents the number of equal-sized parts of a whole.

Students can reason about fractional parts using decomposition strategy and/or

number bond representation (e.g., 6

4 is

the same as 6

1 and 6

3 , 6

2 and 6

2 , or

6

3 and6

1 ).

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

http://scusd-math.wikispaces.com/file/view/MAC2013-03+Equal+Shares.pdf/512400596/MAC2013-03%20Equal%20Shares.pdf

http://scusd-math.wikispaces.com/file/view/3.NF.1_Making+a+Scarf_Task+3.doc/512495742/3.NF.1_Making%20a%20Scarf_Task%203.doc


42


Essential Questions




Resources

equal-sized parts. Common Misconception:

Students see the numbers in fractions as two unrelated whole numbers separated by a line.

Why is the size of the whole important?

What is the relationship between a unit fraction and a unit of 1?

3. Understand that the size of a fractional part is relative to the size of a whole.

3.NF.1

Students need to recognize that 2

1 of the

liquid in a small bottle could be less liquid than

3

1 of the liquid in a larger bottle, but

3

1 of a ribbon is longer than 8

1 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.

How can I compare fractions?

How can I compare fractions when they have the same numerators?

How can I compare fractions when

"Sharing Pie" 4. Represent and compare common fractions with like numerators or denominators and tell why one fraction is greater than, less than, or equal to the other by using concrete and pictorial models.

3.NF.3d

Students can use fraction bars that show the same sized whole as models to compare fractions.

They can also use Venn diagrams to organize and compare fractions to determine the relative size of the fractions, such as more than

2

1 , exactly

2

1 or less than 2

1 .

Encourage students to write the results of the comparisons with the symbols >, =, or <, and justify the conclusions with a model.

Common Misconception:

http://scusd-math.wikispaces.com/file/view/3.NF.3ab_Sharing+Pie_Task+1.doc/512500066/3.NF.3ab_Sharing%20Pie_Task%201.doc


43


Essential Questions




Resources

they have the same denominators?

When we compare two fractions, how do we know which has the greater value?

Students may not understand fractions can be greater than 1.

When we compare two fractions, how do we know which has the greater value?

Why is the denominator important to the unit fractions?

"Comparing Fractions" 5. Understand and explain the concept that the larger the denominator, the smaller the size of the piece.

3.NF.1

Students should understand that decomposing into more equal shares equals smaller shares, and that equal shares of identical wholes need not have the same shape.

How are tenths related to the whole?

How can I represent fractions of different lengths?

“Locating Fractions Less than One on the Number Line”

“Locating Fractions Greater

than One on the Number Line”

“Find 1”

6. Use number lines to understand that the whole is the unit interval, measured by length from one number to another number. Using the understanding of consecutive whole numbers, create unit fractions on number lines, focusing on halves, thirds,

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.

http://scusd-math.wikispaces.com/file/view/3.NF.3d_Comparing+Fractions_Task+3.doc/512500126/3.NF.3d_Comparing%20Fractions_Task%203.doc









44


Essential Questions




Resources

How is the odd and even pattern with unit of fractions on a number line similar to units of 1 on a number line?

fourths, sixths, and eighths. Whole numbers on a number line:

Unit fractions on a number line:

3.NF.2

Students need to know how to plot fractions on a number line, by using the

meaning of the fraction (e.g., to plot 6

4

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 count the hash mark at zero as the first unit fraction.

"Placing Fractions on a Number Line"

7. Understand and show that two fractions as equivalent (equal) if they are the same size, (though not necessarily the same shape) or the same point on a number line.

Having students count equalized parts will help them determine the number of parts it takes to make a whole and recognize fractions that are equivalent to whole numbers.

http://scusd-math.wikispaces.com/file/view/3.NF.3_Placing+Fractions+on+a+Number+Line_Task+5.doc/512500032/3.NF.3_Placing%20Fractions%20on%20a%20Number%20Line_Task%205.doc

http://scusd-math.wikispaces.com/file/view/3.NF.3_Placing+Fractions+on+a+Number+Line_Task+5.doc/512500032/3.NF.3_Placing%20Fractions%20on%20a%20Number%20Line_Task%205.doc


45


Essential Questions




Resources

3.NF.3a

What equivalent groups of fractions can I discover using Fraction Strips?

"Halves, Thirds, and Sixths"

8. Create simple equivalent

fractions, (e.g., 2

1 = 4

2 , 6

4 =

3

2 ) and explain why the

fractions are equivalent by using a visual fraction model.

3.NF.3b

Stduents need to understand that two equivalent fractions are two ways of describing the same amount by using different-sized fractional parts. For

example, in the fraction 8

6 , if the eighths

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)

What is the difference between 2/1 and 2/2, 3/1 and 3/3?

"All the Jumps"

9. Read and understand whole numbers as fractions, and recognize fractions that are equivalent to the whole numbers. Examples:Express 3 in

Students need to understand how to express whole number fractions on the number line when the unit interval is 1. Use a number line to help students notice

that the difference bewtween 1

2 and 2

2


http://scusd-math.wikispaces.com/file/view/3.NF.2_All+the+Jumps_Task+5.doc/512500392/3.NF.2_All%20the%20Jumps_Task%205.doc


46


Essential Questions




Resources

the form of 1

3 ; recognize that

1

6 = 6; locate 4

4 and 1 at the

same point on a number line diagram.

3.NF.3c

, or 1

3 and 3

3 , and that these fractions

is even greater and conctinue to grow as the numbers go higher.

How can I compare fractions?

“Closest to 1/2” “Comparing Fractions”

10. Represent and compare common fractions with like numerators or denominators and tell why one fraction is greater than, less than, or equal to the other by using concrete, pictorial models, and number lines.

3.NF.3d

Students can use fraction bars that show the same sized whole as models to compare fractions.

They can also use number line to organize and compare fractions to determine the relative size of the fractions, such as

more than 2

1 , exactly 2

1 or less than 2

1

. 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.

How can I determine length to the nearest 1/4?

How can I organize data measured to the half inch? To the quarter inch?

"A Piece of Yarn" 11. Use a standard ruler to measure items including details about halves and quarter marks on the inch ruler; create a line plot to display their findings.

3.MD.4

Students will need many opportunitites measuring the length of various objects in their environment so that they can connect their understanding of fractions to measuring to one-half and one-quarter inch. For example, measure objects in

your desk to the nearest 2

1 or 4

1 of an

inch, display data collected on a line plot.



http://scusd-math.wikispaces.com/file/view/3.NF.2_A+Piece+of+Yarn_Task+2.doc/512500362/3.NF.2_A%20Piece%20of%20Yarn_Task%202.doc


47


Essential Questions




Resources

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?

How are fractions used in problem-solving situations?

“Jon and Charlie’s Run” “Snow Day” "Distances Swam"

12. Solve real-world problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.

3.NF.3d

Students must experience fractions across many constructs, such as the following

three categories of models: area (e.g., 3

1

of a garden), length (e.g., 4

3 of an inch),

and set or quantity (e.g., 2

1 of the class).

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



http://scusd-math.wikispaces.com/file/view/3.NF.3_Distances+Swam_Task+4.doc/512499994/3.NF.3_Distances%20Swam_Task%204.doc


48


Essential Questions




Resources





49

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:


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



B. Interpretive 5. Listening actively to spoken English in a range of social and academic contexts



50

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







51

Unit #6: Representing and Interpreting Data

Essential Questions




Resources



address Diagnostic,

Formative, and

Summative assessments

used throughout the unit


connected to the


Outcomes.

















Flexible grouping:

Content

Interest

Project/product


Tiered:




































52


Essential Questions




Resources



Content-related


Activity o Stations


Depth o Language of




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?

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

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

Measurement and Data 3.MD.3 MAT.03.TE.1.000MD.H.239 C1 T1

2. Use data from scaled bar graphs to solve one- and two-step “how many more” and “how many less” problems.

3.MD.3

For example, draw a bar graph in which each square in the bar graph might represent 5 pets (refer to Progressions document Measurement and Data, p.4).




53


Essential Questions




Resources

graphs to solve real-world problems?

When and why do we use rulers to measure things?

How might

"Estimating Measurements"

3. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.

3.MD.4

Why are there different types of graphs?

How can data displayed in graphs

"Reading Survey" 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

http://scusd-math.wikispaces.com/file/view/3.MD.4_Estimating+Measurements_Task+3.doc/512499242/3.MD.4_Estimating%20Measurements_Task%203.doc

http://scusd-math.wikispaces.com/file/view/3.MD.4_Estimating+Measurements_Task+3.doc/512499242/3.MD.4_Estimating%20Measurements_Task%203.doc

http://scusd-math.wikispaces.com/file/view/3.MD.4_reading+Survey_Task+1.doc/512499300/3.MD.4_reading%20Survey_Task%201.doc


54


Essential Questions




Resources

Post Assessment - engageNY, Module 6, All Tasks

GR3_Unit 6_Post Assessment.pdf

http://scusd-math.wikispaces.com/file/view/GR3_Unit+6_Post+Assessment.pdf/512534346/GR3_Unit%206_Post%20Assessment.pdf

http://scusd-math.wikispaces.com/file/view/GR3_Unit+6_Post+Assessment.pdf/512534346/GR3_Unit%206_Post%20Assessment.pdf


55

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


A. Collaborative



56

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







57

Unit #7: Problem Solving Involving Perimeters and Areas

Essential Questions Assessments for Learning



Resources


Assessments for

Learning address

Diagnostic, Formative,

and Summative

assessments used


inform instruction

connected to the


Outcomes.


Mid-point Check and

Post Assessments- from engageNY, Module 3, All Tasks














Flexible grouping:

Content

Interest

Project/product


Tiered:





































58





Resources



Content-related


Activity o Stations


Depth o Language of




Do quadrilateals have to look like rectangles? How do 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?

"Barons Shapes" "Sallys Shape Sort"

1. Categorize and compare quadrilaterals versus other polygons by examining the properties of geometric figures.

3.G.1

Students in grade 2 have reasoned with shapes and their attribute. This standard serves as a

Students explain that: 1) a quadrilateral must be a close figure

with four straight sides, 2) notice the characteristics of the

angles, 3) notice the relationship between

opposite sides

Is it possible to find more than one way for shapes to fit together o make another shape? Explain.

What does it mean to parttion a shape

"Guess the Rule"

2. Reason about decomposing and composing polygons to make other polygons.

3.G.1

For example, two triangles can form a quadrilateral;



http://scusd-math.wikispaces.com/file/view/3.G.1_Barons+Shapes_Task+1.doc/512498448/3.G.1_Barons%20Shapes_Task%201.doc

http://scusd-math.wikispaces.com/file/view/3.G.1_Sallys+Shape+Sort_Task+2.doc/512498466/3.G.1_Sallys%20Shape%20Sort_Task%202.doc

http://scusd-math.wikispaces.com/file/view/MAC2013-04+Guess+The+Rule.pdf/513539518/MAC2013-04%20Guess%20The%20Rule.pdf


59





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?

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

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.

How do the measure of lengths change when the unit of measure changes?

"The Table"

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 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.

http://scusd-math.wikispaces.com/file/view/3.MD.8_The+Table_Task+4.doc/512499922/3.MD.8_The%20Table_Task%204.doc


60





Resources

"Make a Garden" 5. Solve word problems involving perimeter, where one or two of the side lengths are missing.

3.MD.8

Common error: students only add the unit lengths that are visible. Give students opportunity to label all side lengths as a 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

http://scusd-math.wikispaces.com/file/view/3.MD.8_Make+a+Garden_Task+3.doc/512499866/3.MD.8_Make%20a%20Garden_Task%203.doc

http://www.engageny.org/resource/grade-3-math-instruction-focus-standard-3md8

http://scusd-math.wikispaces.com/file/view/3.MD.8_Carpets_Task+2.doc/512521364/3.MD.8_Carpets_Task%202.doc