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Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

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In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. 85% or more time spent in instruction in each grade Kindergarten, 1, and 2 align exclusively to the major work of the grade. 75% or more time spent in instruction in each grade 3, 4, and 5 align exclusively to the major work of the grade. Supporting Content - informaiont that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

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The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with

longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025.

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Mathematical Practices

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning

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To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

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The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical Practice

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Standards for Mathematical Practicehttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of Mathematics

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The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students. Additional Instructional Support

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The curriculum maps continue to provide references to envision lessons that support covered standards. Since this resource was developed for previous TN State Standards, it was necessary to evaluate and provide additional resources to support teachers and students. The 2016-17 Curriculum Maps include the addition of the open resource curriculum that can be found at engageny.org. The curriculum and resources developed by Great Minds for engage ny have consistently been rated as “exemplifying quality” by districts and organizations across the country, meaning they are highly aligned to college and career standards and instructional shifts.

How to Use the Mathematics Curriculum Maps

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TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards the supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work It is the teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

Content

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Weekly and daily objectives/learning targets should be included in you plans. These can be found under the column titled content. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation. In order to assit with planning, a list of fluency activities have been included for each lesson. It is

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expected that fluency practice will be a part of daily instruction. (Note: Fluency practice is NOT intended to be speed drills, but rather an intentional sequence to support student automaticity. Conceptual Understanding MUST underpin the work of fluency.)Grade 4 Quarter 1 Overview

Module 1: Place Value, Rounding, and Algorithms for Addition and SubtractionModule 2: Metric Unit Conversions and Problem Solving with Metric MeasurementModule 3: Multi-digit Multiplication and Division

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Overview In this Grade 4 Module 1, students extend their work with whole numbers. They begin with large numbers using familiar units (hundreds and thousands) and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart (4.NBT.1). They recognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand, million, billion). 1 The place value chart is fundamental to Topic A. Building upon their previous knowledge of bundling, students learn that 10 hundreds can be composed into 1 thousand, and therefore, 30 hundreds can be composed into 3 thousands because a digit’s value is 10 times what it would be one place to its right ( 4.NBT.1). Students learn to recognize that in a number such as 7,777, each 7 has a value that is 10 times the value of its neighbor to the immediate right. One thousand can be

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decomposed into 10 hundreds; therefore 7 thousands can be decomposed into 70 hundreds.

Similarly, multiplying by 10 shifts digits one place to the left, and dividing by 10 shifts digits one place to the right. Shelby County Schools 2016/2017

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3,000 = 10. 300 3,000 ÷ 10 = 300

In Topic B, students use place value as a basis for comparing whole numbers. Although this is not a new concept, it becomes more complex as the numbers become larger. For example, it becomes clear that 34,156 is 3 thousands greater than 31,156.

34,156 > 31,156

Comparison leads directly into rounding, where their skill with isolating units is applied and extended. Rounding to the nearest ten and hundred was mastered with three-digit numbers in Grade 3. Now, Grade 4 students moving into Topic C learn to round to any place value (4.NBT.3), initially using the vertical number line

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though ultimately moving away from the visual model altogether. Topic C also includes word problems where students apply rounding to real life situations.

In Grade 4, students become fluent with the standard algorithms for addition and subtraction. In Topics D and E, students focus on single like-unit calculations (ones with ones, thousands with thousands, etc.), at times requiring the composition of greater units when adding (10 hundreds are composed into 1 thousand) and decomposition into smaller units when subtracting (1 thousand is decomposed into 10 hundreds) (4.NBT.4). Throughout these topics, students apply their algorithmic knowledge to solve word problems. Students also use a variable to represent the unknown quantity. The module culminates with multi-step word problems in Topic F (4.OA.3). Tape diagrams are used throughout the topic to model additive compare problems like the one exemplified below. These diagrams facilitate deeper comprehension and serve as a way to support the reasonableness of an answer.

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A goat produces 5,212 gallons of milk a year.A cow produces 17,279 gallons of milk a year.

How much more milk does a goat need to produce to make the same amount of milk as a cow?

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17,279 – 5,212 = ________A goat needs to produce _______ more gallons of milk a year.

The Mid-Module Assessment follows Topic C. The End-of-Module Assessment follows Topic F.

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In order to explore the process of working with mixed units, Module 2 focuses on length, mass, and capacity in the metric system1 where place value serves as a natural guide for moving between larger and smaller units. In Topic A, students review place value concepts while building fluency with decomposing, or converting from larger to smaller units (4.MD.1). They learn the relative sizes of measurement units, building off prior knowledge of grams and kilograms from Grade 3 (3.MD.2) and meters and centimeters from Grade 2 (2.MD.3). Conversions between the units are recorded in a two-column table. Single-step problems involving addition and subtraction of metric units provide an opportunity to practice mental math calculations as well as the addition and subtraction algorithms established in Module 1. Students reason by choosing to convert between mixed and single units before or after the computation (4.MD.2). Connecting their familiarity with both metric units and place value, the module moves swiftly through each unit of conversion, spending only one day on each type. This initial understanding of unit conversions allows for further application and practice, such as multiplying and dividing metric units, throughout subsequent modules.

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In Module 3, students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends.

Students begin in Topic A by investigating the formulas for area and perimeter. They then solve multiplicative comparison problems including the language of times as much as with a focus on problems using area and perimeter as a context (e.g., “A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?”). Students create diagrams to represent these problems as well as write equations with symbols for the unknown quantities (4.OA.1). This is foundational for understanding multiplication as scaling in Grade 5 and sets the stage for proportional reasoning in Grade 6. This Grade 4 module, beginning with area and

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perimeter, allows for new and interesting word problems as students learn to calculate with larger numbers and interpret more complex problems (4.OA.2, 4.OA.3, 4.MD.3).

In Topic B, students use place value disks to multiply single-digit numbers by multiples of 10, 100, and 1,000 and two-digit multiples of 10 by two-digit multiples of 10 (4.NBT.5). Reasoning between arrays and written numerical work allows students to see the role of place value units in multiplication (as pictured below). Students also practice the language of units to prepare them for multiplication of a single-digit factor by a factor with up to four digits and multiplication of two two-digit factors.

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In preparation for two-digit by two-digit multiplication, students practice the new complexity of multiplying two two-digit multiples of 10. For example, students have multiplied 20 by 10 on the place value chart and know that it shifts the value one place to the left, 10 × 20 = 200. To multiply 20 by 30, the associative property allows for simply tripling the product, 3 × (10 × 20), or multiplying the units, 3 tens × 2 tens = 6 hundreds (alternatively, (3

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× 10) × (2 × 10) = (3 × 2) × (10 × 10)). Introducing this early in the module allows students to practice during fluency so that, by the time it is embedded within the two-digit by two-digit multiplication in Topic H, understanding and skill are in place.

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Building on their work in Topic B, students begin in Topic C decomposing numbers into base ten units in order to find products of single-digit by multi-digit numbers. Students use the distributive property and multiply using place value disks to model. Practice with place value disks is used for two-, three-, and four-digit by one-

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digit multiplication problems with recordings as partial products. Students bridge partial products to the recording of multiplication via the standard algorithm. 1 Finally, the partial products method, the standard algorithm, and the area model are compared and connected by the distributive property (4.NBT.5).

1,423 x 3

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Topic D gives students the opportunity to apply their new multiplication skills to solve multi-step word problems (4.OA.3, 4.NBT.5) and multiplicative comparison problems (4.OA.2). Students write equations from statements within the problems (4.OA.1) and use a combination of addition, subtraction, and multiplication to

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solve.

In Topic E, students synthesize their Grade 3 knowledge of division types (group size unknown and number of groups unknown) with their new, deeper understanding of place value.

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Overview recap

Focus Grade Level Standard Type of Rigor Foundational Standards

4.OA.1 Conceptual 3.OA.1, 3.OA.3

4.OA.2 Procedural Skill and Fluency 3.OA.3

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4.OA.3 Procedural Skill and Fluency 3.OA.8, 4.NBT.3, 4.NBT.6

4.OA.4 Conceptual 3.OA.7

4.NBT.1 Conceptual 2.NBT.1

4.NBT.2 Application 4.NBT.1

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4.NBT.3 Conceptual 3.NBT.1, 4.NBT.1, 4.NBT.2

4.NBT.4 Procedural Skill and Fluency 3.NBT.2, 4.NBT.1

4.NBT.5 Procedural Skill and Fluency 2.NBT.1, 3.OA.1, 3.OA.2, 3.OA.B, 3.NBT.A.3, 3.OA.5, 3.OA.7, 4.NBT.1

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4.NBT.6 Procedural Skill and Fluency, Conceptual 3.OA.1, 3.OA.2, 3.OA.B, 2.NBT.1, 3.OA.5, 3.OA.7, 4.NBT.1, 4.NBT.6

4.MD.1 Procedural Skill and Fluency 3.MD.2, 3.OA.7

4.MD.2 Procedural Skill and Fluency 4.MD.1, 4.NF.5, 4.NF.6

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4.MD.3 Application 3.MD.8, 3.OA.4

Fluency

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NCTM Position

Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

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Fluency is designed to promote automaticity by engaging students in daily practice. Automaticity is critical so that students avoid using lower-level skills when they are addressing higher-level problems. The automaticity prepares students with the computational foundation to enable deep understanding in flexible ways. Therefore, it is recommended that students participate in fluency practice daily using the resources provided in the curriculum maps. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.

The fluency standard for 4th grade listed below should be incorporated throughout your instruction over the course of the school year. The engage ny lessons include

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fluency exercises that can be used in conjunction with building conceptual understanding.

4.NBT.B.4 Add/Subtract within 1,000,000

Note: Fluency is only one of the three required aspects of rigor. Each of these components have equal importance in a mathematics curriculum.

References:

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https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS

Module 1 Place Value, Rounding, and Algorithms for Addition and Subtraction (Allow 5 weeks for instruction, review and assessment)

Domain: Operations and Algebraic ThinkingCluster: 4.OA.A Use the four operations with whole numbers to solve problems.

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

Domain: Numbers and operations in Base TenCluster: 4.NBT.A Generalize place value understanding for multi-digit whole numbers.

4.NBT.A.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.

4.NBT.A.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.

4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Enduring Understandings Our number system is based on groups

of ten. In our numeration system, the value of a

digit is determined by its position. Basic facts and place value patterns can

be used to find products when one factor is a multiple of 10, 100, or 1,000.

Rounding is a process for finding the multiple of 10, 100, etc. closest to a given number.

The base ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value.

Essential Questions Is place value important when comparing

and ordering numbers? How can you estimate a product by

rounding? What are some ways to represent

numbers in the thousands and millions? How do you round numbers?

Objectives/Learning TargetsTopic ALesson 1: I can Interpret a multiplication equation as a comparison. (4.NBT.1, 4.NBT.2, 4.OA.1)

Lesson 2: I can recognize a digit represents 10 times the value of what it represents in the place to its right. (4.NBT.1, 4.NBT.2, 4.OA.1)

Lesson 3: I can name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units. (4.NBT.1, 4.NBT.2, 4.OA.1)

Lesson 4: I can read and write multi-digit numbers using base ten numerals, number names, and expanded form. (4.NBT.1, 4.NBT.2, 4.OA.1)

Allow the first two days to develop classroom math routines and habits that will contribute to student’s future success in mathematics. Please refer to the First Week Lesson Guide for suggestions/examples of Number Talks, Quick Writes, Accountable Talk Moves/Stems, and Mathematical Discussions/Math Messages, which are designed to allow students to develop expertise with the eight Mathematical Practices early in the school year.

engageny Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction

Topic A: Place Value of Multi-Digit Whole NumbersLesson 1Lesson 2Lesson 3Lesson 4

Videos:

Model Numbers Understand the Relationship Between

Place and Value Read and Write Numbers in Numeric

Form Read and Write Numbers in Word

Form Read and Write Numbers in Expanded

Form

VocabularyMillions, ten millions, hundred millions, ten thousands, hundred thousands, variables

Familiar Terms and Symbols=, <, >, addend, algorithm, bundling, making, renaming, changing, exchanging, regrouping, trading compose, decompose, difference, digit, endpoint, equation, estimate, expanded form, expression, halfway, number line, number sentence, place value, rounding, standard form, sum, tape diagram, unbundling, breaking, renaming, changing, regrouping, trading, word form

Fluency Practice:Please see engageNY full module download for suggested fluency pacing and activities.

Lesson 1Sprint: Multiply and divide by 10Multiply and divide by 10Place Value

Lesson 2Skip CountingMultiply by 10Place Value

Lesson 3Sprint: Multiply by 3Place Value and ValueBase Ten Units

Lesson 4Skip CountingPlace ValueNumbers expressed in Different Base Units

Objectives/Learning TargetsTopic BLesson 5: I can compare numbers based on meanings of the digits using >, <, or = to

Topic B: Comparing Multi-Digit Whole NumbersLesson 5Lesson 6

Fluency Practice:Lesson 5Sprint: Multiply by 4Unit Skip CountingPlace Value

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RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of grade-level skills and concepts. These resources were chosen as an accompaniment to

modules taught within this quarter. Incorporated materials may assist educators with grouping, enrichment, remediation, and differentiation.NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

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Textbook ResourcesengageNY Mathematics Modulesenvision Math

TN Core/CCSSTN Math StandardsAchieve the Core

VideosNCTM Common Core VideosLearnZillionCCSS Video Series

Children’s LiteratureThe Reading NookMath and Literature:

Interactive ManipulativesInteractive Contenthttp://www.eduplace.com/

Additional SitesEdutoolbox (Formerly TNCORE)Singapore Math

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A Match Made in the ClassroomMath for Kids-Best Children’s BooksScholastic: Books and Programs to Improve Elementary Math

Illuminations Resources for Teaching Math Interactive Sites for EducatorsMath Playground: Common Core StandardsThinking Blocks: Computer and iPad based gamesPARCC GamesIXL Math Virtual Manipulatives

Math-Play-ComScholastic Math Study Jams

Other

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Illustrated Mathematics Dictionary for Kids

Other:Use this guide as you prepare to teach a module for additional guidance in planning, pacing, and suggestions for omissions.Pacing and Preparation Guide (Omissions)

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