DRAFT Curriculum Map

Grade 4

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.

_________________________________________________________________________________________This document was created to support instructional design and delivery of Grade 4 mathematics using enVision Math

from Pearson as a resource.

4TH GRADE MATH: Year-at-a-Glance

Month UnitsContent

Standards

September/

October/November

Unit 1Operations and Algebraic Thinking with Number Sense

Students use multi-stepped problems with four operations with real world applications, using pattern studies. Pattern studies include

generating patterns given a certain rule and identifying the features. Students explore place value relationships comparing multi-digit base

ten numbers and rounding.

enVisions Topics 1-4

4.OA.14.OA.24.OA.34.OA.5

4.NBT.14.NBT.24.NBT.3

November/

December/ January/ February

Unit TwoNumber Sense in Base Ten

With Multiplication and Division

Students solve multi-stepped problems within four operations, including remainders. Students use equations, rectangular arrays and/or other

models to represent multiplication and division. Multiple strategies for multiplication are emphasized as students use rounding and estimation

to attend to precision, as they develop fluency with one and two digit factors and four digit dividends with one divisor.

enVisions Topics 5-10

4.OA.A.34.NBT.B.54.NBT.A.34.NBT.B.54.NBT.B.6

March/April

Unit ThreeNumbers and Operations with Fractions

Using models, students are able to recognize, generate and compare equivalent fractions. Students will compare fractions with different

numerators and denominators. Students will be able to factor pairs for a whole number to 100 and identify prime and composite numbers to 100.

Students add and subtract fractions and mixed numbers with like denominators and are able to decompose and compose fractions using

models and real world applications, they will understand that denominators of 10 and 100 using decimal notation, comparing to

hundredths and tenths and applying this concept to money.

enVisions Topics 11-13

4.OA.B.44.NF.A.14.NF.A.2

4.NF.B.3a4.NF.B.3b4.NF.B.3c4.NF.B.3d4.NF.B.4a4.NF.B.4b4.NF.B.4c4.NF.C.54.NF.C.64.NF.C.74.MD.A.2

MayUnit Four

Measurement and Data

Know relative sizes of measurements within one system and express

4.MD.A.14.MD.A.24.MD.A.34.MD.B.4

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4TH GRADE MATH: Year-at-a-Glance

Month UnitsContent

Standardsmeasurements of a larger unit in terms of a smaller unit. Students will

use four operations to solve word problems involving distances, intervals, liquid volumes, mass and money, including fractions and

decimals. Students apply their understanding of perimeter and area to real world problems and create simple line plots to represent data in

fractional units.

enVisions Topics 14 & 15

June

Unit FiveGeometry

Students create and explore points, line, planes, line segments, rays and angles. Students will classify two dimensional figures based on lines.

Students recognize special two dimensional shapes and lines of symmetry. Students understand angles and unit angles and can measure and solve addition and subtraction problems to find unknown angles in

the real world.

envisions Topic 16

4.MD.C.5a4.MD.C.5b4.MD.C.64.MD.C.74.G.A.14.G.A.24.G.A.3

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Unit 1: Operations and Algebraic Thinking with Number SenseTOPICS 1 – 4

(Approx. 10 weeks)In this unit, students solve multi-stepped problems with real world applications using the four operations.

Students will develop an understanding of multiplication and division. Pattern studies include generating patterns given a certain rule and identifying the features. Students will explore place value relationships

comparing multi-digit base ten numbers and rounding.

Over-Arching Essential Questions for Unit 1: How are the four operations related to each other? What are different ways to model multiplication and division? How can patterns be used to solve problems? How is place value used to read, write, and compare numbers?

In this unit students will: Students will explore the inverse relationship between multiplication and division.

Students will use patterns and properties to determine products and quotients.

Students will use tables to organize number patterns

Students will represent larger numbers through the concept of place value

Students will use place value to order, compare, and round whole numbers.

Students will develop estimating skills

Students will add and subtract fluently using the standard algorithm

Culminating Task -

Standards

Common Core State Standards- MathematicsOperations and Algebraic Thinking 4.OAUse the four operations with whole numbers to solve problems.

1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations

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with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Generate and analyze patterns.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not

explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Number and Operations in Base Ten1

Generalize place value understanding for multi-digit whole numbers.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place

to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two

multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

3. Use place value understanding to round multi-digit whole numbers to any place.¹Students need the opportunity to practice adding and subtracting multi-digit whole numbers to build fluency for numbers up to 1,000,000 throughout the school year.

Standards for Mathematical Practice:SMP 1 Make sense of problems and persevere in solving them. Students may explain problems to themselves and makes several attempts at solving them. Concrete objects or pictures may help to conceptualize concepts and assist in finding solutions. Discussions about solution methods will lead to other approaches.

SMP 2 Reason abstractly and quantitatively. Students will use reasoning skills when determining equations from mathematical situations. When working with place value concepts, student will reason when representing or rounding numbers.

SMP 3 Construct viable arguments and critique the reasoning of others. Students construct arguments using objects, pictures, or drawing. Students may think aloud and engage in conversation about intended solution paths.

SMP 4 Model with mathematics. Students may represent mathematical situations in multiple ways such as writing equations to describe problems.

SMP 5 Use appropriate tools strategically. Students may use various tools, (including estimation) such as tables to organize numbers, number lines to order and compare, and hundreds charts for exploring patterns.

SMP 6 Attend to precision Students may use number lines when ordering and comparing numbers. Clear precise language is used when communicating ideas.

SMP 7 Look for and make use of structure Students may use patterns and multiples to determine products and quotients. Arrays and properties of operations may be used to explain calculations.

SMP 8 Look for and express regularity in repeated reasoning. Students may look for repetitive actions in computations to make generalizations.

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

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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 LearningSEL Competencies:

Self-awarenessSelf-managementSocial awarenessRelationship skillsResponsible decision making

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Unit I: Operations and Algebraic Thinking with Number SenseTopics 1-4

4.OA.1, 4.OA.2, 4.OA.3, 4.OA.5, 4.NBT.1, 4.NBT.2, 4.NBT.3

Essential Questions: Assessments for for Learning/Tasks1. How is repeated addition related to equal

groups and multiplication?enVision, Quick Check Master 1-1

2. How can I use what I know about multiples to solve multiplication problems??

enVision, Quick Check Master 1-2

3. How can I use properties to solve multiplication problems?

enVision, Quick Check Master 1-3enVision, Quick Check Master 1-4

4. How can I use multiplication facts to find comparisons?

enVision, Quick Check Master 1-5

5. How can I use pictures and drawings to solve division problems?

enVision, Quick Check Master 1-6

6. Why does knowing fair shares and equal groups help you explain multiplication and division problems?

enVision, Quick Check Master 1-7

7. How can I use multiplication facts to help me solve division problems?

enVision, Quick Check Master 1-8enVision, Quick Check Master 1-9

8. How can I use pictures and drawings to solve multiplication problems?

enVision, Quick Check Master 1-10

9. What is a pattern? envision, Quick Check Master 2-1envision, Quick Check Master 2-2

10. What is a rule? envision, Quick Check Master 2-3envision, Quick Check Master 2-4

11. How can tables be used to determine relationships between numbers?

envision, Quick Check Master 2-5

12. Is there one “right way” to solve a problem? envision, Quick Check Master 2-6

Additional questions to be added to complete Unit 1

Additional assessments/tasks to be added to complete Unit 1

13.

[13.]

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[14.]

[15.]

[16.]

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

Resources:

1. Recognize relationship between multiplication and repeated addition of equal groups used in arrays and comparisons.

4.OA.1

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-1

Strategies for Teaching and Learning: Students can use numbers, words, pictures, physical objects, or equations to represent the problem. Avoid telling students that when multiplying, the answer is always bigger – as this will create a

misconception carrying into fractions (refer to “Common Misconception” from Mathematics Framework, pp.10-11).

Present tape or bar diagrams to help students visualize the multiplication problems.

2. Use patterns to determine products with given factors.

4.OA.5

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-2

Strategies for Teaching and Learning:To develop the concept of generating and analyzing patters, students could examine a sequence of dot designs in which each design has 4 more dots than the previous one and then reason about how the dots are organized in the design to determine the total number of dots in the 100th design.

3. Use multiplication properties to simplify problems.

4.OA.3

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lessons: 1-3, 1-4

NOTE: These lessons provide foundational support for 4.OA.3 and do not meet the standard in its entirety.

Strategies for Teaching and Learning:Students can use numbers, words, pictures, physical objects, or equations to represent the problem

4. Visualize, interpret, and represent multiplication equations as multiplicative comparisons and represent verbal statements of multiplicative comparisons as multiplication equations.

4.OA.1

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-5

Strategies for Teaching and Learning:7

Students need opportunities to identify and verbalize all three quantities involved: which quantity is being multiplied, which number tells how many times, and which number is the product.

5. Visualize, interpret and represent division problems and solve by using and creating models.

4.OA.2

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-6

Strategies for Teaching and Learning:Students need many opportunities to solve contextual problems. A tape/bar diagram can help students visualize and solve multiplication and division word problems. Tape diagrams are useful for connecting what is happening in the problem with an equation that represents the problem. (ICA Framework, pg. 8)

6. Apply knowledge of multiplicative comparison to multiply or divide to solve word problems.

4.OA.1, 4.OA.2

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-7

Strategies for Teaching and Learning:Students need many opportunities to solve contextual problems. A tape/bar diagram can help students visualize and solve multiplication and division word problems. Tape diagrams are useful for connecting what is happening in the problem with an equation that represents the problem. (ICA Framework, pg. 8)

7. Identify and use multiplication facts related to division facts to solve division problems.

4.OA.3

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-8, 1-9

NOTE: These lessons provide foundational support for 4.OA.3 and do not meet the standard in its entirety.

Strategies for Teaching and Learning:Students need opportunities to clarify the difference between 6 more than a number (additive) and 6 times a number (multiplicative). For example, using 18 and 6, a question could be “How much more is 18 than 6?” Thinking multiplicatively, the answer is 3; however, thinking additively, the answer is 12 (adapted from KATM 2012, 4th Grade Flipbook).

8. Use models and draw pictures to solve multiplication situations and to write equations.

4.OA.2

enVision, Topic 1: “Multiplication and Division: Meanings and Facts” Lesson: 1-10

Strategies for Teaching and Learning:Students can use numbers, words, pictures, physical objects, or equations to represent the problem

9. Identify and extend patterns involving shapes, numbers, or operations.

4.OA.5

enVision, Topic 2: “Generate and Analyze Patterns” Lessons: 2-1, 2-2

Strategies for Teaching and Learning:

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A pattern is a sequence that repeats or evolves in a predictable process over and over. A rule dictates what that process will look like. This type of investigation will reinforce students’ fact knowledge and develop their fluency with

operations. Students could examine a sequence of dot designs where each design has 4 more dots than the

previous one: “Double Plus One” (Illustrative Mathematics 2013) and “Patterns that Grow”10. Find and use rules to extend tables of ordered

and number pairs.4.OA.5

enVision, Topic 2: “Generate and Analyze Patterns” Lessons: 2-3, 2-4

Strategies for Teaching and Learning: A pattern is a sequence that repeats or evolves in a predictable process over and over. A rule dictates what that process will look like.

11. Extend patterns (tile or cube towers) and use tables to determine pattern or rule.

4.OA.5

enVision, Topic 2: “Generate and Analyze Patterns” Lesson: 2-5

Strategies for Teaching and Learning:

12. Use multiple strategies to solve multistep word problems.

4.OA.3

enVision, Topic 2: “Generate and Analyze Patterns” Lesson: 2-6

Strategies for Teaching and Learning:

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Strategies for Teaching and Learning:

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Strategies for Teaching and Learning:

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Strategies for Teaching and Learning:

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Strategies for Teaching and Learning:

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Strategies for Teaching and Learning:

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

General Strategy Support for Unit: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

CA Mathematics Frameworks “ Grade 4” p. 1-5 “What Students Learn in Grade 4” p. 6-13 Operations and Algebraic Thinking p. 14-22 Number and Operations in Base Ten

Kansas Association of Teachers of Mathematics (KATM) 4 th Flipbook , Provides illustrated examples, instructional strategies, additional resources/tools and misconceptions by standard.

p. 11-25 Operations and Algebraic Thinking p. 34-39 Number and Operations in Base Ten

North Carolina Unpacked Standards 4 th Grade Provides illustrated examples, instructional strategies, additional resources/tools and misconceptions by standard.

p. 5-12 Operations and Algebraic Thinking p. 18-25 Number and Operations in Base Ten

Progressions Documents for the CCSSMNarrative documents describing the progression of a topic across a number of grade levels, informed both y research on children’s cognitive development and by the logical structure of mathematics.

K-5, Operations and Thinking p. 2-3, 29-31, 33, 36-39K-5, Number and Operations in Base Ten p. 2-4, 12-14

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

Flexible grouping:1. Content2. Interest3. Project/product4. 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:1. Content-related2. Tasks for early finishers

1. Game2. Investigation3. Partner Activity4. Stations

Depth and Complexity Prompts/Icons:1. Depth

o Language of the Disciplineo Patternso Unanswered Questionso Ruleso Trends

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

o Big Ideaso Complexity

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