DRAFT Curriculum Map

Grade 3

Vision for Assessment and InstructionAs a community of learners, we strive to implement a rigorous thinking curriculum that utilizes an inquiry-based,

formative assessment process in order to provide opportunities for students to develop academic maturity as disciplinary thinkers.

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This document was created to support instructional design and delivery of Grade 2 mathematics using enVision Math from Pearson as a resource.

Math Grade 3: Year-at-a-Glance

Month UnitsContent

Standards

September**envisions Benchmark Topic 1-3

Unit #1Place Value and Problem Solving with Addition and Subtraction

(Topics 1-3) In this unit, students will use place value understanding, properties of addition and subtraction, and estimation strategies to solve problems involving addition and subtraction.

3.NBT.13.NBT.23.OA.8

Sept/Oct-Dec

Unit #2Represent, Understand, and Problem Solve with Multiplication and Division

(Topics: 4, 7, 5, 6, 8)In this unit, students will develop understanding of, interpreting,

representing, and solving problems involving multiplication and division.

3.OA.1 3.OA.6 3.OA.2 3.OA.7 3.OA.3 3.OA.8 3.OA.4 3.OA.9

3.OA.5 3.NBT.3

Jan-Feb

Unit #3Developing Understanding of Fractions

(Topics: 9-10)In this unit, students will develop understanding of fractions as numbers.

3.NF.13.NF.23.NF.33.G.2

3.MD.4

March- April

Unit #4Measurement and Data(Topics: 12, 15, 13, 14)

In this unit, students will read, write, measure, and solve word problems involving addition and subtraction of time intervals; work with metric units of capacity and mass; and understand the concept of perimeter and area

measurements.

3.MD.1 3.MD.53.MD.2 3.MD.6

3.MD.7 3.MD.8 3.G.2

May

Unit #5Representing and Interpreting Data

(Topic 16)In this unit, students will draw, read, and analyze scaled picture graphs and

bar graphs that represent a data set and use those graphs to solve word problems.

3.MD.33.MD.4

June

Unit #6Geometric Figures and Problem Solving Involving Perimeter and Area

(Topic 11)In this unit, students will categorize shapes based on their attributes and

recognize that measurements of perimeter and area as attributes of plane figures.

3.G.13. MD 7a & 7d

3.MD.8

Grade 3 1

Grade 3 2

Grade 3

Unit 1: Place Value and Problem Solving with Addition and Subtraction(Approx. 2-3 weeks*)

(*Do enVision Benchmark to decide how long to spend on these Supporting Standardsneeded for Unit 2. enVision Benchmark answer key)

In this unit, students will use place value understanding, properties of addition and subtraction, and estimation strategies to solve problems involving addition and subtraction.

Over-Arching Essential Questions for Unit 1: How does understanding place value help you round whole numbers? How does place value and properties of operations help you add and subtract?

In this unit students will: Use place value to round whole numbers to the nearest 10 or 100. Add and subtract within 1000 using addition and subtraction methods/strategies developed in

grade two.

Culminating Task: Check and Post Assessments – from engageNY

, Module 2 Tasks 1-5 Gr 3_Unit 2_Mid-Post Assessments.pdf

Standards

Common Core State Standards-Mathematics: (Supporting Standards)Number and Operations in Base Ten 3.NBTUse 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.OASolve 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.

Standards for Mathematical Practice:SMP 1 Make sense of problems and persevere in solving them. Students use the concept of rounding and place value understanding to solve addition and subtraction word problems. They may use concrete manipulatives, pictorial representations, and/or mental mathematics to conceptualize and solve a problem.

SMP 2 Reason abstractly and quantitatively. Students reason abstractly and quantitatively as they translate word problem situations into equations and use the equations to answer questions about those situations.

SMP 3 Construct viable arguments and critique the reasoning of others. As students participate in investigating patterns on the hundreds charts they construct arguments to explain why

SMP 4 Model with mathematics. Students represent problem situations in multiple ways using numbers, words (mathematical language), objects, and math drawings. They

Grade 3 3

the pattern makes sense. Students also listen to others’ explanations, decide if they make sense and ask appropriate questions.

use models to represent both equations and story problems and can explain their thinking. They evaluate their results in the context of the situation and reflect on whether the results make sense.

SMP 5 Use appropriate tools strategically. Students may use a number line and/or the hundreds chart to visualize the placement of numbers and find the halfway point when rounding, and place-value blocks to solve problems.

SMP 6 Attend to precision. Students communicate clearly, using grade-level-appropriate vocabulary accurately and precise explanations and reasoning to explain their processes and solutions. Students consider if their answers are reasonable and check their work to ensure the accuracy of solution.

SMP 7 Look for and make use of structure. Students use patterns in counting sequences of whole numbers on a number line, mental math strategies based on patterns (making ten, fact families, doubles), and the structure of place value to solve problems.

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

A. Collaborative1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and

academic topics2. Interacting with others in written English in various communicative forms (print, communicative technology, and

multimedia3. Offering and supporting opinions and negotiating with others in communicative exchanges4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)

B. Interpretive5. Listening actively to spoken English in a range of social and academic contexts6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed

explicitly and implicitly through language7. 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 area8. 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 areaC. Productive

9. Expressing information and ideas in formal oral presentations on academic topics11. Supporting own opinions and evaluating others’ opinions in speaking and writing12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas

Part II. Learning About How English WorksA. Structuring Cohesive Texts

1. Understanding text structure2. Understanding cohesion

B. Expanding and Enriching Ideas5. Modifying to add details

C. Connecting and Condensing Ideas6. Connecting ideas7. Condensing ideas

Social and Emotional Learning Standards for Mathematical Practice: SMP. 1 Make sense of problems and persevere in solving themSMP. 2 Reason abstractly and quantitativelySMP. 3 Construct viable argument and critique the reasoning of othersSMP. 4 Model with mathematics

Grade 3 4

SMP. 6 Attend to precisionSMP. 7 Look for and make use of structureSMP. 8 Look for and express regularity in repeated reasoningSEL Competencies:

Self-awarenessSelf-managementSocial awarenessRelationship skillsResponsible decision making

Grade 3 5

Unit 1: Place Value and Problem Solving with Addition and Subtraction(Approx. 2-3 weeks)

Math:Standards 3.NBT.1, 3.NBT.2, 3.NBT.3, 3.OA.8

Essential QuestionsAssessments for Learning

Note: These assessments are suggested, not required, and can be used as lessons.

1. How can you use place value understanding to

represent numbers? How does making an organized list help you solve

addition and subtraction problems? 3.NBT.1

1. enVision, Quick Check Master 1-1, 1-7

2. What is a number line? What is an interval? How can we use a number line to represent

numbers? 3.NBT. 1

2. enVision, Quick Check Master 1-3

3. How can we use place value to round numbers to the nearest 10?How can we use place value to round numbers to the nearest 10?

3.NBT.1

3. enVision, Quick Check Master 1-4

4. How can we use place value to round numbers to

the nearest 100? How can a number line help me round? How do you select an appropriate interval for a

number line?

3.NBT.1

4. enVision, Quick Check Master 1-6

From NC Wikispace: “Comparing Heights” 3.NBT.1 Task 2. “All About Rounding”3.NBT.1 Task 3. “Cafeteria Lunch Orders” 3.NBT.1 Task 1

From Illustrative Mathematics: “Rounding to the Nearest Ten and

Hundreds”

. “Rounding to 50 or 500”From NC Wikispace: “All About Rounding”3.NBT.1 Task 3

5. In what kinds of situations is it appropriate to

estimate? Why? Why does place value play a significant role when

using the properties of operations to solve addition and subtraction word problems?

How can models be used to solve problems

5. From Illustrative Mathematics:. “Classroom Supplies”From NC Wikispace: “From 100 to 0” 3.NBT.2 Task 3 “Mrs. Snyder’s Game Board” 3.NBT.2 Task 1

Grade 3 6

involving addition and subtraction? What mental strategies can be used to add and

subtract numbers reasonably quickly and accurately?

3.NBT.2 & 3.OA.8Sequence of Learning OutcomesStudents will be able to…in order to… Resources:

1. Students will use place value to read and write 3 digit numbers.

enVision, Topic 1: “Numeration”Lessons 1-1, 1-7

Strategies for Teaching and Learning: 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 development of number sense and the subsequent work that involves rounding numbers.

Use and draw place value blocks (base ten blocks). Make an organized list.

2. Students will be able to place numbers on a number line.

enVision, Topic 1: “Numeration”Lessons 1-2, 1-3

Strategies for Teaching and Learning: Use a number line as tools to support students’ understanding of place value.

3. Students will be able to use place value to round numbers to the nearest 10 on a number line. 3.NBT.1

enVision, Topic 1: “Numeration”Lessons 1-4, 1-5

Strategies for Teaching and Learning: 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.

4. Use place value to round numbers to the nearest 100 on a number line. 3.NBT. 1

NOTE: Students will learn WHEN and WHY to round numbers and extend their understanding of place value to include whole numbers with four digits.

enVision, Topic 1: “Numeration”Lessons 1-5, 1-6From NC Wikispace: “Cafeteria Lunch Orders” 3.NBT.1 Task 1From Illustrative Mathematics: “Rounding to 50 or 500”

Strategies for Teaching and Learning: 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 hundred number chart as tools to support students’ understanding of place

value.5. Solve math problems involving three digit numbers using estimation to check for reasonableness in the solution. 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

enVision, Topic 2: “Number Sense: Addition and Subtraction”Lessons 2-1, 2-2, 2.3, 2.4, 2.5, 2.6, 2.7enVision, Topic 3: “Using Place Value to Add and Subtract”Lessons 3-1, 3-2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9,

Grade 3 7

3.10, 3-11, 3-12, 3-13NOTE: The content of this standard 3.NBT.2 is

a review of all the Addition and Subtraction methods/strategies used in solving all 12 problem types (12) from grade 2. Now in grade three, students will use some of those methods to generalize to larger numbers.

"Choose Three Ways" is a handout for recording multiple methods when problem-solving.

Strategies for Teaching and Learning: * Use and draw place value blocks (base ten blocks). Make an organized list. Using a number line. A hundred number chart as tools to support students’ understanding of place value. Mental strategies that support the development of addition and subtraction fluency in addition to

the understanding of place value include:o Counting ono Making tenso Decomposing a number leading to a teno Related factso Relationship between addition and subtractiono Equivalent but easier or known sumso Doubleso Doubles plus one

Additional Resources Differentiation (e.g. Special Education, EL, GATE)

enVisions, Topic 1: “Math Background” pp.2G-2HenVision, Topic 2: “Math Bacjkground” pp. 27A-27B

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

CCSS Support for the Unit:CA Mathematics Framework “3rd Grade” p. 1-5 “What students Learn in Grade Three”

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

Flexible grouping:

ContentInterestProject/productLevel (Heterogeneous/ Homogeneous)

Tiered: Independent Management Plan (Must

Do/May Do) Grouping

Grade 3 8

p. 135-146 Number and Operations in Base Ten domain p. 10-14 Operations and Algebraic Thinking p. 2734-2937 “Essential Learning for Next Grade”

KS Assoc. of Teachers of Mathematics FLIPBOOKS Scroll down to 3rd grade to view the pdf version. Provide illustrated examples, instructional strategies, additional resources/tools and misconceptions by standard. p. 13 Operations and Algebraic domain p. 43 Number and Operations in Base Ten domain

NC Unpacking Documents Scroll down to “3rd grade Unpacking

Document”. Provide illustrated examples, instructional strategies, additional resources/tools and misconceptions by standard. p. 13-14 Operations and Algebraic Thinking domain p. 18-19 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. 2-4, 11 Number and Operations in Base Ten domain p. 2-3, 27-28 Counting and Cardinality and Operations and Algebraic Thinking domains

enVisions, Topic 1: “Math Background” pp.2G-2HTeaching Student-Centered Mathematics Developmentally Appropriate Instruction for Grades 3-5 *

Ch. 8 “Exploring Number and Operation Sense”, pages 100-107.

Ch. 9 “Helping Children Master the Basic Facts”, pages 127 – 137.

Ch.10 “Developing Whole-Number Place Value Concepts” , pages 151-170.

Ch. 11 “Building Strategies for Whole-Number Computation”, pages 171-180.

o Contento Rigor w/in the concepto Project-based learningo Homeworko Groupingo Formative Assessment

Anchor Activities:

Content-relatedTasks for early finishers

o Gameo Investigationo Partner Activityo Stations

Depth and Complexity Prompts/Icons:Deptho Language of the Disciplineo Patternso Unanswered Questionso Ruleso Trendso Big Ideaso Complexity

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

Click here for: "Differentiation Resources" - SCUSD Wikispaces

Grade 3 9

Unit 2: Represent, Understand, and Problem Solving with Multiplication and Division(Approx. 12 weeks))

In this unit, students will develop understanding of, interpreting, representing, and solving problems involving multiplication and division.

Over-Arching Essential Questions for Unit 2: How does understanding the properties and relationships between multiplication and division help

solve problems involving the four operations?

In this unit students will: Develop understanding of multiplication and it’s properties Develop understanding of division and it’s properties Develop strategies for multiplication & division Identify relationships between multiplication & division

Culminating Task: Unit 1 Post Assessment modified from GA DOE “Ice Cream Scoops,” Part II “Multiplication and Division” only, pp. 156-162 and/ or Mid-point Check and Post Assessments- from engageNY, Module 3, All Tasks Gr 3_Unit 3_Mid & Post Assessments.pdf

StandardsCommon Core State Standards-Mathematics: (Major Standards)Operations and Algebraic Thinking 3.OARepresent 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 equations8x?=48,5=□÷3,6x6=?.

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.

Grade 3 10

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.NBTUse 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.

ELD Standards to Support Unit:Part I: Interacting in Meaningful WaysA. Collaborative1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic

topics2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia3. Offering and supporting opinions and negotiating with others in communicative exchanges4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)B. Interpretive5. Listening actively to spoken English in a range of social and academic contexts6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly

and implicitly through language7. 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 area8. 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 areaC. 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 ideasPart II. Learning About How English WorksA. Structuring Cohesive Texts

1. Understanding text structure2. Understanding cohesion

B. Expanding and Enriching Ideas 5. Modifying to add detailsC. Connecting and Condensing Ideas 6.Connecting ideas 7.Condensing ideas

Standards for Mathematical Practice:SMP. 1 Make sense of problems and persevere in solving themSMP. 2 Reason abstractly and quantitativelySMP. 3 Construct viable argument and critique the reasoning of othersSMP. 4 Model with mathematics

SELSelf-awarenessSelf-managementSocial awarenessRelationship skills

Grade 3 11

SMP. 5 Use appropriate tools strategicallySMP. 6 Attend to precisionSMP. 7 Look for and make use of structureSMP. 8 Look for and express regularity in repeated reasoning

Responsible decision making

Unit 2: Represent, Understand, and Problem Solving with Multiplication and Division(Approx. 12 weeks*)

* This Unit needs more lessons than what enVision provides. Look at “Resource” column for additional lessons.)Math:

Standards 3.OA.1-4, 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8, 3.OA.9, 3.NBT.3

Essential Questions:Assessments for Learning

Note: These assessments are suggested, not required, and can be used as lessons.

1. 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?

1. NC Wikispace, 3 rd Grade Tasks

2. What is the relationship between factors and products?

2. From Illustrative Mathematics: “Fish Tanks” “Markers in Boxes”

3. How can multiplication be represented? What strategies can be used to find the

factors or products?

3. NC Wikispace, 3 rd Grade Tasks

4. 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?

4. NC Wikispace, 3 rd Grade Tasks

From Illustrative Mathematics: “Two Interpretations of Division” “Gifts from Grandma” Variation1 “Finding the unknown in a division equation”

5. How can the same array model represent

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

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

different?

5. NC Wikispace, 3 rd Grade Tasks

6. How can I use the array model to explain

multiplication and division? How can I use known facts to find unknown

6. NC Wikispace, 3 rd Grade Tasks

From Illustrative Mathematics:“Analyzing Word Problems Involving Multiplication”

Grade 3 12

facts?7.

How multiplication and division related How can different strategies be helpful when

solving problems?

7. NC Wikispace, 3 rd Grade Tasks

8. How can I model multiplication? When can you use multiplication and

division in real life? How is the commutative property of

multiplication evident in an array model, but not in subtraction or division?

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

9. What is an associative property in

multiplication? How is the associative property of

multiplication used in solving a problem?

9. From NC Wikispace: 3.OA.5 Task 1: Patterns on the Multiplication

Chart 3.OA.5 Task 2: Prove It!

10. How does decomposing numbers help you solve multiplication problems?

10. From Illustrative Mathematics:Valid Equalities? (Part 2)

11. How are multiplication and division related?11. From NC Dept. of Public Instruction "Prove it!"

12. How does using an area model help

understand multiplication and division? How does the model (array) help us think

about the different ways to decompose a number(factors or products) to solve multiplication and division problems?

12. From NC Dept. of Public Instruction:"Sharing Pencils"

13. What strategies can be used to solve

multiplication problems? What strategies can be used to solve real-

world division problems?

13. From Illustrative Mathematics: “Two Interpretations of Division”

14. What patterns can be used to find certain

multiplication facts? Why is the multiplication table symmetric

about its diagonal? What strategies can be used to learn

multiplication facts?

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

15. How do the properties of operations

enable you to solve problems? What strategies can be used to solve

multiplication problems?

15. From Illustrative Mathematics “The Stamp Collection” “The Class Trip”

From NC Dept. of Public InstructionGrade 3 13

"Mario's Designs"

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

From Illustrative Mathematics: Addition Patterns Patterns in a Mulitiplication Table Symmetry of the Addition Table Making a Ten

17. 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?

17. From Illustrative Mathematics:How Many Colored Pencils?

Sequence of Learning OutcomesStudents will be able to…in order to…

Resources:

1. 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

enVision, Topic 4: “Meanings of Multiplication”Lessons 4-1, 4-3, 4-4, 4-5

Strategies for Teaching and Learning: 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 groups2. 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

enVision, Topic 5: “Multiplication Facts: Use Patterns” Lessons 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7enVision, Topic 6: “Multiplication Facts: Use Known Facts” Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9CA Mathematics Framework “3 rd Grade” pg. 9 chartFlipbook from KS Assoc. of Teacher of Mathematics,

pg. 4-5NC Unpacking, pg. 4From engageny Downloadable Resources PDF,

Module 1, Topic A “Mulitplcation and the Meaning of the Factors”, pg. 1.A.1-1.A.40

Strategies for Teaching and Learning: Use context to help students determine the factors. Use number lines to show equal groups

Grade 3 14

3. Represent multiplication with the array to show the relationship among all the numbers involved (factor x factor = product). Use context so students will be able to visualize “rows/columns of” a particular group. 3.OA.1

enVision, Topic 4: “Meanings of Multiplication”Lessons 4-2CA Mathematics Framework “3 rd Grade” pg. 9 chartFlipbook from KS Assoc. of Teacher of Mathematics,

pg. 4-5NC Unpacking, pg. 4From 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

Strategies for Teaching and Learning: 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 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

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

enVision, Topic 7: “Meanings of Division”Lessons 7-1, 7-2, 7-3, 7-5, 7-6CA Mathematics Framework “3 rd Grade” pg. 9 chartFlipbook from KS Assoc. of Teacher of Mathematics,

pg. 6NC Unpacking, pg. 4From engageny Downloadable Resources PDF, Module 1, Topic B “Division as an Unknown Factor Problem”, pg. 1.B.1-1.B.35

Strategies for Teaching and Learning: 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.

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

enVision, Topic 8: “Division Facts”Lessons 8-1, 8-2, 8-3, 8-4, 8-6, 8-7, 8-8CA Mathematics Framework “3 rd Grade” pg. 9

chartFlipbook from KS Assoc. of Teacher of

Mathematics, pg. 7-9NC Unpacking, pg. 5-6From 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.35Lesson from LearnZillion: “Solve Multiplication

and Division Problems: Using a Diagram”

Grade 3 15

Strategies for Teaching and Learning:Model division as the unknown factor in multiplication in multiple ways (for example, bar modeling,

number line, arrays, etc.).6. Use multiplication and division within 100 to

solve word problems in situations involving equal groups, arrays, and measurement quantities. 3.OA.3

enVision, Topic 8: “Division Facts”Lessons 8-5, 8-9CA Mathematics Framework “3 rd Grade” pg. 9

chartFlipbook from KS Assoc. of Teacher of

Mathematics, pg. 7-9NC Unpacking, pg. 5-6From 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.35Strategies for Teaching and Learning:Model problems using pictorial representations and manipulatives.7. Determine the unknown whole number in a

multiplication or division equation relating three whole numbers to make the equation true. 3.OA.4

enVision, Topic 7: “Meanings of Division”Lessons 7-4CA Mathematics Framework “3 rd Grade” pg. 9

chartFlipbook from KS Assoc. of Teacher of

Mathematics, pg. 10-11, and 24NC Unpacking, pg. 7

engageny Downloadable Resources PDF, Module 1, Topic B “Division as an Unknown Factor Problem”, pg. 1.B.1-1.B.35

Strategies for Teaching and Learning:Use manipulatives, pictures, words, and/or equations to represent the problem and explain thinking

process8. Understand and apply the commutative

property of multiplication as a strategy to multiply when solving word problems. 3.OA.5

enVision, Topic 4: “Meanings of Multiplication”Taught in 4-3 so use Quick Check 4-3 p.103A &

“Differentiated Instruction” On-Level Center Activity p. 103B

Mathematics International, Unit 1 “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.66engageNY, Module 3 “Multiplication and

Division with Units of 0, 1, 6-9, and 10”

Grade 3 16

Topic 1, Lesson 1CA Framework p. 10-11 Flipbook p. 12-15NC Unpacking, p. 9-10

Strategies for Teaching and Learning: 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. Skip counting on the array model can be used to practice multiplication facts. Spend time interpreting rows and columns by rotating array by 90˚.9. Understand and apply the associative property of multiplication as a strategy to multiply when solving word problems.3.OA.5

enVision, Topic 6: “Multiplication Facts”Taught in 6-6 so use Quick Check 6-6 p.153A &

“Differentiated Instruction” On-Level Center Activity p. 153B

Mathematics International, Unit 1 “Multiplication”

Section 1, “Properties of Multiplication”Lesson 2, p.A8CA Framework p. 10-11 Flipbook p. 12-15NC Unpacking, p. 9-10

Strategies for Teaching and Learning: Have 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, Grade 3-5, p.30).

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

10. Decompose and re-compose numbers to apply the associative property to solve multiplication word problems. 3.OA.5

enVision, Topic 6: “Multiplication Facts”Taught in topic 6 so use “Math Background”

p.154A as a model, then see Strategies belowMathematics International, Unit 1

“Multiplication” Section 1, “Properties of Multiplication”Lesson 2, p. A8

Strategies for Teaching and Learning: 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).

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

11. 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

enVision, Topic 6: “Multiplication Facts”Taught in 6-7 so use Quick Check 6-7 p.155A

Strategies for Teaching and Learning: Students need opportunities to continue to decompose numbers in order to apply the distributive

Grade 3 17

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 relationship between the distributive property and decomposition of numbers.

12. 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

Teaching Student-Centered Mathematics: Grades 3-5 “The Distributive Property,” p.66

o “Slice It Up” activity 2.27 “Strategies for Multiplication Facts”“If You Didn’t Know” activity 3.9, p.92 & 98-99

Strategies for Teaching and Learning: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).

13. Use the relationship between multiplication and division to solve division word problems as an unknown factor problem (48 ÷ 8 = ? 8 × ? = 48). 3.OA.6

Taught in envision, Topic 7 Lesson 7-3 & 8 Lessons 8-1, 8-8

Mathematics International, Unit 3 “Division” Section 1 “Calculations for Finding How Many

for 1 Person”o Lesson 1, p.A25-27o Lesson 2, p.A28

Section 2, “Calculations for fidning the Number of People We Can Divide Something Into”

o Lesson 1, p.A29=31o Lesson 2, p.A31-32o Lesson 3, p.A33

Strategies for Teaching and Learning: 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.14. Develop multiplication and division Taught in envision, Topic 8 Lessons 8-2, 8-3, 8-4

Grade 3 18

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

Mathematics International, Unit 3 “Division” “Power Builder,” p.A36 “Mastery Problems, p.A37

Strategies for Teaching and Learning: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) 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.15. 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

enVision, Topic 5: Taught in lesson 5-7 so use Quick Check 5-7 p.131A

Math Background, pp. 113A-113B Interactive Learning, pp. 114-115enVision, Topic 6: Taught in lesson 6-9 so use

Quick Check -9 p.161A Math Background, pp. 137A-137B Interactive Learning, pp. 138-139enVision, Topic 8: Taught in lesson 8-5 so use

Quick Check 8-5 p.201A & Enrichment Master p.201B

Math Background, pp. 187A-187B Interactive Learning, pp. 188-189CA Framework p. 13-14 Flipbook p. 19-21NC Unpacking, p. 14-15

Strategies for Teaching and Learning: 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)16. Identify arithmetic patterns and

explain the patterns using properties of operations. 3.OA.9

enVision, Topic 5: Taught in lesson 5-2, 5-3, 5-4, 5-5 so use Quick Check 5-1 p.119A

Math Background, pp. 113A-113B Interactive Learning, pp. 114-115CA Framework p. 14-15 Flipbook p. 22-23NC Unpacking, p. 16-18

“Discover Number Patterns with Skip Counting” Grade 3 19

Video from the Teaching Channel

Mathematics International, Unit 3 “Division” Section 3 “Calculations for Finding Times as

Much”o Lesson 1, p.A35-36

Strategies for Teaching and Learning:Students need paper or white boards to model: 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).

17. 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

enVision, Topic 5: Taught in lesson 5-6 Math Background, pp. 113A-113BInteractive Learning, pp. 114-115CA Framework p. 15-16 Flipbook p. 30NC Unpacking, p. 21

Mathematics International, Unit 9 “Multiplication Algorithm,” Part 1

Section 1 “Multiplication by 10 and 100”o Lesson 1, p.A91-92o Lesson 2, p.A92

Section 2, “Mulitplication of 2-Digit by 1-Digit Numbers”

o Lesson 1, p.A93-95o Lesson 2, p.A96o Lesson 3, p.A97o Lesson 4, p.A98

Strategies for Teaching and Learning: 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).

Additional Resources Differentiation (e.g. Special Education, EL, GATE)

CA Mathematics Framework “3 rd Grade” pg. 9 chartFlipbook from KS Assoc. of Tchr of Mathematics, pg.

4-5NC Unpacking, pg. 4Video from engageny Number bondFrom 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

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

Grade 3 20

Do) Grouping

o Contento Rigor w/in the concepto Project-based learningo Homeworko Groupingo Formative Assessment

Anchor Activities: Content-related Tasks for early finishers

o Gameo Investigationo Partner Activityo Stations

Depth and Complexity Prompts/Icons: Depth

o Language of the Disciplineo Patternso Unanswered Questionso Ruleso Trendso Big Ideaso Complexity

From GA DOE, Differentiation via Math Centers (Tubs)

Grade 3 21

Unit 3: Developing Understanding of Fractions(about 8 weeks)

In this unit, students will develop understanding of fractions as numbers.

Over-Arching Essential Questions for Unit 2: What is a fraction? How can I use fractions to name parts of a whole?

In this unit students will: Develop understanding of a fraction 1/b as the quality formed by 1 part when the whole is portioned into

b equal parts Develop understanding of a fraction a/b as the quality formed by a parts of size 1/b Understanding and representing fractions on a number line Explain how two fractions are equal Compare fractions by their size

Culminating Task Mid-point Check and Post Assessments- from engageNY, Module 5 Tasks 1-4 Gr 3_Unit 5_Mid & Post Assessments.pdfStandardsCommon Core State Standards-Mathematics:Number and Operations -- Fractions 3.NFDevelop 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.

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

Grade 3 22

A. Collaborative1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and

academic topics2. Interacting with others in written English in various communicative forms (print, communicative technology, and

multimedia3. Offering and supporting opinions and negotiating with others in communicative exchanges4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)

B. Interpretive5. Listening actively to spoken English in a range of social and academic contexts6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed

explicitly and implicitly through language7. 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 area8. 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 areaC. Productive

9. Expressing information and ideas in formal oral presentations on academic topics11. Supporting own opinions and evaluating others’ opinions in speaking and writing12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas

Part II. Learning About How English WorksA. Structuring Cohesive Texts

1. Understanding text structure2. Understanding cohesion

B. Expanding and Enriching Ideas5. Modifying to add details

C. Connecting and Condensing Ideas6. Connecting ideas7. Condensing ideas

Standards for Mathematical PracticeSMP. 2 Reason abstractly and quantitativelySMP. 3 Construct viable argument and critique the reasoning of othersSMP. 4 Model with mathematicsSMP. 5 Use appropriate tools strategicallySMP. 8 Look for and express regularity in repeated reasoning

SEL Competencies:Self-awarenessSelf-managementSocial awarenessRelationship skillsResponsible decision making

Unit 3: Developing Understanding of Fractions (Topics 9-10)Standards: 3.NF1, 3.NF2, 3.NF.3

Essential Questions: Assessments for LearningNote: These assessments are suggested, not required, and can

be used as lessons.

1. What is a whole? What does equal parts mean? How can I represent fractions of different

sizes?

1. “Naming the Whole for a Fraction”"Geometric Pictures of One Half""Representing Half of a Circle""Selling Bubble Gum"

2. What are the important features of a unit of

fraction? Why is the denominator important to the unit

2. "Equal Shares""Making a Scarf"

Grade 3 23

fractions?3.

Why is the size of the whole important? What is the relationship between a unit

fraction and a unit of 1?

3. enVision, Quick Check 9-1

4. How can I represent fractions of different

lengths? How can the numbers 0 and 1 on a number

line help you compare fractions?

“Locating Fractions Less than One on the Number Line”

“Locating Fractions Greater than One on the Number Line”

“Find 1” 5.

How can I compare fractions? How can I compare fractions when they have

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

the same denominators? When we compare two fractions, how do we

know which has the greater value?

5. "Sharing Pie" "Comparing Fractions" “Closest to 1/2” illustrative math “Comparing Fractions”

6. What are equivalent fractions? What equivalent groups of fractions can I

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

discover using a number line?

6. "Halves, Thirds, and Sixths"

7. How can we represent whole numbers as

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

3/1 and 3/3?

7. "All the Jumps"

8. How are fractions used in problem Solving situations?

8. "Distances Swam"

Sequence of Learning OutcomesStudents will be able to…in order to…

Resources:Note: enVision, Topic 9, Lessons 9-3, 9-4 address 4th

grade standards. Recommended to skip.1. Partition, or divide, a whole (line segments,

rectangles, circles, etc.) into equal-sized parts and 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” …). 3.NF.1

enVision, Topic 9: “Understanding Fractions” Math Background, pp. 217A-217B Interactive Learning, pp. 290-291Lesson 9-1engageNY , Module 5 “Fracions as Numbers on the

Number Line” Topic A: “Partitioning a Whole into Equal

Parts” Topic B: “Unit Fractions and Their Relation to

the Whole” Topic C: “Comparing Unit Fractions and Specify

Grade 3 24

the Whole” Topic D: “Fractions on the Number Line” Topic E: “Equivalent Fractions” Topic F: “Comparison, Order, and Size of

Fractions”Mathematics International, Unit 14: “Fractions” Section B: “Meaning of fractions and their

representation”o Lesson 1-3, p.B43-46o Lesson “Using Mathematics”, p.B47-49

Teaching Student-Centered Mathematics, Grades 3-5, Ch. 5 “Exploring Fraction Concepts,” p. 131-155

CA Framework p. 16-23, 30-32 Flipbook p. 32-37, 54-55NC Unpacking, p. 21-25, 45

Strategies for Teaching and Learning: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. Students may not understand that when

partitioning a whole shape, number line, or a set into unit fractions, the interval must be equal.2. Use fraction bars and geometric shapes to

partition the whole into 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 . 3.NF.1

enVision, Topic 9: “Understanding Fractions” Lesson 9-2

CA Framework p. 16-23, 30-32 Flipbook p. 32-37, 54-55NC Unpacking, p. 21-25, 45

Strategies for Teaching and Learning: Students will need many opportunities to analyze and discuss fractional parts using concrete models

to develop familiarity and understanding of fractions. Students need to practice recognizing and representing 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

Grade 3 25

b1

b1

representation (e.g., is the same as and , and , or and ). Students to practice writing the denominator as the bottom number (term) of a fraction and that it

represents the total number of equal-sized parts. Common Misconception: Students see the numbers in fractions as two unrelated whole numbers separated by a line.

3. Understand that the size of a fractional part is relative to the size of a whole. 3.NF.1

enVision, Topic 9: “Understanding Fractions”Lesson 9-8CA Framework p. 16-23 Flipbook p. 32-37NC Unpacking, p. 21-25

Strategies for Teaching and Learning:

(Use real-world objects) Students need to recognize that of the liquid in a small bottle could be less liquid than of

the liquid in a larger bottle, but of a ribbon is longer than 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. 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, fourths, sixths, and eighths.

3.NF.2Whole numbers on a number line:

Unit fractions on a number line:

enVision, Topic 9: “Understanding Fractions” Lesson 9-5, 9-6, 9-7

CA Framework p. 16-23 Flipbook p. 32-37NC Unpacking, p. 21-25

Strategies for Teaching and Learning: Divide a shape into equal parts and represent 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.

Students should plot fractions on a number line, by using the meaning of the fraction (e.g., to plot

on a number line, there are 6 equal parts with 4 copies of one of the 6 equal parts). Common Misconception:

Grade 3 26

64

61

63

62

62

63

61

21

31

31

81

64

Students do not count correctly on the number line. For example, students may count the hash mark at zero as the first unit fraction

5. Understand and explain the concept that the

larger the denominator, the smaller the size of the piece. 3.NF.1

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

enVision, Topic 10: “Fraction Comparison and Equivalence” Math Background, pp. 241A-241B Interactive Learning, pp. 242-243 Lesson 10-1, 10-2, 10-3, 10-4

CA Framework p. 16-23 Flipbook p. 32-37NC Unpacking, p. 21-25

Strategies for Teaching and Learning: Students should practice decomposing fraction bars or shapes into equal shares to visual the pieces

getting smaller as the denominator gets larger. 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 , exactly or less than . Encourage students to write the results of the comparisons with the symbols >, =, or <, and justify the

conclusions with a model.Common Misconception:Students may not understand fractions can be greater than 1

6.Create simple equivalent fractions, (e.g., = ,

= ) and explain why the fractions are equivalent by using a visual fraction model.

3.NF.3b

6. enVision, Topic 10: “Fraction Comparison…”Lesson 10-5, 10.6

CA Framework p. 16-23 Flipbook p. 32-37NC Unpacking, p. 21-25

Strategies for Teaching and Learning:Students need to use fraction strips and number lines 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 , if the eighths are taken in twos, then each pair of eighths is a fourth. Sixth-eighths then can be seen as equivalent to three-fourths. (Resource: Van de Walle)7. Read and understand whole numbers as fractions, and recognize fractions that are equivalent to the whole numbers. Examples: Express 3 in the form of

; recognize that = 6; locate and 1 at the same

enVision, Topic 10: “Fraction Comparison…”Lesson 10-7CA Framework p. 16-23 Flipbook p. 32-37NC Unpacking, p. 21-25

Grade 3 27

21

21

21

21

42

64

32

86

13

16

44

point on a number line diagram. 3.NF.3cStrategies for Teaching and Learning:Students need to use fraction strips and number lines 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

between and , or and , and that these fractions is even greater and continue to grow as the numbers go higher.8. 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

enVision, Topic 10: “Fraction Comparison…”Lesson 10-8“Jon and Charlie’s Run”“Snow Day”

Strategies for Teaching and Learning:Have models available for student use such as fraction strips and number lines(scratch paper available

to create their own.) so students can experience fractions across many constructs, such as the

following three categories of models: area (e.g., of a garden), length (e.g., of an inch), and set or

quantity (e.g., of the class). Partitioning and iterating are ways for students to understand the meaning of fractions, especially numerator and denominator.

Additional Resources Differentiation (e.g. Special Education, EL, GATE)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 Learni n g ” from CAST, the Center for Applied Special Technology

Use of math journals for differentiation and formative assessment (use link below) https://www.teachingchannel.org/videos/math-journalsFlexible grouping: Content Interest Project/product Level (Heterogeneous/ Homogeneous)Tiered: Independent Management Plan (Must Do/May

Do) Grouping

o Contento Rigor w/in the concepto Project-based learningo Homeworko Groupingo Formative Assessment

Anchor Activities: Content-related Tasks for early finishers

o Gameo Investigationo Partner Activity

Grade 3 28

12

22

13

33

31

43

21

o StationsDepth and Complexity Prompts/Icons: Depth

o Language of the Disciplineo Patternso Unanswered Questionso Ruleso Trendso Big Ideaso Complexity

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

Grade 3 29

Unit #4Measurement and Data

(about 6-8 weeks)In this unit, students will

Over-Arching Essential Questions for Unit 1:See (Topics: 12, 15, 13, 14)

In this unit students will:

Culminating Task:

Standards

Math Common Core State Standards- Mathematics:3.MD.1 3.MD.53.MD.2 3.MD.6 3.MD.7 3.G.2

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

A. Collaborative1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and

academic topics2. Interacting with others in written English in various communicative forms (print, communicative technology, and

multimedia3. Offering and supporting opinions and negotiating with others in communicative exchanges4. Adapting language choices to various contexts (based on task, purpose, audience, and text type)

B. Interpretive5. Listening actively to spoken English in a range of social and academic contexts6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed

explicitly and implicitly through language8. 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. Productive9. Expressing information and ideas in formal oral presentations on academic topics11. Supporting own opinions and evaluating others’ opinions in speaking and writing12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas

Part II. Learning About How English WorksA. Structuring Cohesive Texts

1. Understanding text structure2. Understanding cohesion

B. Expanding and Enriching Ideas5. Modifying to add details

C. Connecting and Condensing Ideas6. Connecting ideas7. Condensing ideas

Standards for Mathematical Practice: SEL Competencies:

Grade 3 30

SMP 1 Make sense of problems and persevere in solving themSMP 2 Reason abstractly and quantitativelySMP 3 Construct viable argument and critique the reasoning of othersSMP 4 Model with mathematicsSMP 5 Use appropriate tools strategicallySMP 6 Attend to precisionSMP 7 Look for and make use of structure

Self-awarenessSelf-managementSocial awarenessRelationship skillsResponsible decision making

Grade 3 31