Shelby County Schools’ mathematics instructional maps are ...



IntroductionIn 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 ready90% of students will graduate on time100% of our students who graduate college or career ready will enroll in a post-secondary opportunityIn 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. 457200223012000The 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. -571500457200Throughout 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. 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:The TN Mathematics StandardsThe Tennessee Mathematics Standards: 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 Standards for Mathematical Practice 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 Curriculum MapsThis map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The map is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides suggested sequencing, pacing, time frames, and aligned resources. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.The map is meant to support effective planning and instruction to rigorous standards. It is not meant to replace teacher planning, prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, text(s), task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgment aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade level specific standards, including purposeful support of literacy and language learning across the content areas. Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades K-5 in 2010-2011. ?The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. ?We now have new standards, therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials.?The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. ?Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., EngageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.How to Use the MapsOverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide specific examples of student work.Tennessee State StandardsTN 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. ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, performance in the major work of the grade). Support for the development of these lesson objectives 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 clearly communicating and making objectives measureable leads to greater student mastery.Instructional ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. At the end of each module you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation. Vocabulary and FluencyThe inclusion of vocabulary serves as a resource for teacher planning, and for building a common language across K-12 mathematics. One of the goals for CCSS is to create a common language, and the expectation is that teachers will embed this language throughout their daily lessons. In order to aid your planning, we have included a list of fluency activities for each lesson. It is expected that fluency practice will be a part of your 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 OverviewModule 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 DivisionOverview 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 decomposed into 10 hundreds; therefore 7 thousands can be decomposed into 70 hundreds. 64008003492500Similarly, multiplying by 10 shifts digits one place to the left, and dividing by 10 shifts digits one place to the right. 3,000 = 10. 300 3,000 ÷ 10 = 300In 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 > 31,156Comparison 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 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.A goat produces 5,212 gallons of milk a year.A cow produces 17,279 gallons of milk a year.342900014541500How much more milk does a goat need to produce to make the same amount of milk as a cow?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.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.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 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).1143000706120In 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.457200097726500In 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 × 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.2971800-635Building 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-digit multiplication problems with recordings as partial products. Students bridge partial products to the recording of multiplication via the standard algorithm. 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 3160020014732000Topic 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 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.Overview recapFocus Grade Level StandardType of RigorFoundational Standards4.OA.1Conceptual3.OA.1, 3.OA.34.OA.2Procedural Skill and Fluency3.OA.34.OA.3Procedural Skill and Fluency3.OA.8, 4.NBT.3, 4.NBT.64.OA.4Conceptual3.OA.74.NBT.1Conceptual2.NBT.14.NBT.2Application4.NBT.14.NBT.3Conceptual3.NBT.1, 4.NBT.1, 4.NBT.24.NBT.4Procedural Skill and Fluency3.NBT.2, 4.NBT.14.NBT.5Procedural Skill and Fluency2.NBT.1, 3.OA.1, 3.OA.2, 3.OA.B, 3.NBT.A.3, 3.OA.5, 3.OA.7, 4.NBT.14.NBT.6Procedural Skill and Fluency, Conceptual3.OA.1, 3.OA.2, 3.OA.B, 2.NBT.1, 3.OA.5, 3.OA.7, 4.NBT.1, 4.NBT.64.MD.1Procedural Skill and Fluency3.MD.2, 3.OA.74.MD.2Procedural Skill and Fluency4.MD.1, 4.NF.5, 4.NF.64.MD.3Application3.MD.8, 3.OA.4Fluency 0158750NCTM PositionProcedural 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.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 engageny lessons include fluency exercises that can be used in conjunction with building conceptual understanding. 4.NBT.B.4 Add/Subtract within 1,000,000Note: Fluency is only one of the three required aspects of rigor. Each of these components have equal importance in a mathematics curriculum. References: STATE STANDARDSCONTENTRESOURCES & TASKSCONNECTIONSModule 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 UnderstandingsOur 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 QuestionsIs 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 Targets Topic 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 SubtractionTopic A: Place Value of Multi-Digit Whole NumbersLesson 1Lesson 2Lesson 3Lesson 4Videos: HYPERLINK "" Model NumbersUnderstand the Relationship Between Place and ValueRead and Write Numbers in Numeric FormRead and Write Numbers in Word FormRead and Write Numbers in Expanded FormVocabularyMillions, 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 1 Sprint: Multiply and divide by 10Multiply and divide by 10Place ValueLesson 2Skip CountingMultiply by 10Place ValueLesson 3Sprint: Multiply by 3Place Value and ValueBase Ten UnitsLesson 4Skip CountingPlace ValueNumbers expressed in Different Base UnitsObjectives/Learning Targets Topic BLesson 5: I can compare numbers based on meanings of the digits using >, <, or = to record the comparison. (4.NBT.2)Lesson 6: I can find 1, 10, and 100 thousand more and less than a given number. (4.NBT.2)Topic B: Comparing Multi-Digit Whole NumbersLesson 5Lesson 6Fluency Practice:Lesson 5Sprint: Multiply by 4Unit Skip CountingPlace ValueLesson 6Unit Skip CountingRename the UnitsCompare NumbersObjectives/Learning Targets Topic CLesson 7: I can round multi-digit numbers to the thousands place using the vertical number line. (4.NBT.3)Lesson 8: I can round multi-digit numbers to any place using the vertical number line. (4.NBT.3)Lesson 9: I can use place value understanding to round multi-digit numbers to any place value. (4.NBT.3)Lesson 10: I can use place value understanding to round multi-digit numbers to any place value using real world applications. (4.NBT.3)Topic C: Rounding Multi-digit Whole NumbersLesson 7Lesson 8Lesson 9Lesson 10Mid-Module AssessmentVideos:Round Numbers Using a Number lineRound in Real Life SituationsVideo Rounding on Vertical Number Line Understand the Relationship Between Place and ValueFluency Practice:Lesson 7Change Place ValueNumber PatternsFind the MidpointLesson 8Sprint: Find the Halfway PointRename the UnitsLesson 9Multiply by TenRound to Different Place ValuesLesson 10Sprint: Round to the Nearest 10,000Multiply by 10Objectives/Learning Targets Topic DLesson 11: I can use place value understanding to fluently add multi-digit whole numbers using the standard addition algorithm, and apply the algorithm to solve word problems using tape diagrams. (4.OA.3, 4.NBT.4, 4.NBT.1, 4.NBT.2)Lesson 12: I can solve multi-step word problems using the standard addition algorithm modeled with tape diagrams, and assess the reasonableness of answers using rounding. (4.OA.3, 4.NBT.4, 4.NBT.1, 4.NBT.2Topic D: Multi-Digit Whole Number AdditionLesson 11Lesson 12Fluency Practice:Lesson 11Round to Different Place ValuesMultiply by 10Add Common UnitsLesson 12Round to Different Place ValuesFind the sumObjectives/Learning Targets Topic ELesson 13: I can use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson 14: I can use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson 15: I can use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams. Lesson 16: I can solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding. Topic E: Multi-Digit Whole Number SubtractionLesson 13Lesson 14Lesson 15Lesson 16Videos:Subtract Using Number LineSubtract Using Standard AlgorithmFluency Practice:Lesson 13Find the SumSubtract Common UnitsLesson 14Base Ten Thousand UnitsFind the DifferenceConvert UnitsLesson 15Place ValueFind the DifferenceConvert UnitsLesson 16Sprint: Convert Meters and Centimeters to CentimetersCompare NumbersObjectives/Learning Targets Topic FLesson 17: I can solve additive compare word problems modeled with tape diagrams. Lesson 18: I can solve multi-step word problems modeled with tape diagrams, and assess the reasonableness of answers using rounding. Lesson 19: I can create and solve multi-step word problems from given tape diagrams and equations. Topic F: Addition and Subtraction Word ProblemsLesson 17Lesson 18Lesson 19End-of Module AssessmentVideos:Subtract Using Number LineSubtract Using Standard AlgorithmFluency:Lesson 17Change Place ValueConvert UnitsLesson 18Number PatternsConvert UnitsLesson 19Sprint: Convert Meters to Kilometers and MetersTask Bank:Number and Operations in Base TenA Question of NumbersCoordinating I-Ready Lessons:Use Place Value to Round NumbersRounding to the Nearest 10, 100, or 1,000enVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum)ThousandsMillionsComparing and Ordering Whole NumbersRounding Whole Numbers2-4: Addition: Adding Whole Numbers2-5: Subtracting: Whole NumbersLiterature Connections Sir Cumference and All the King’s Tens by Cindy NeuschwanderCount to a Million by Jerry Pallotta How Much is a Million by David M. Schwartz Earth Day-Hooray! By Stuart J. Murphy A Place for Zero by Angeline LoPresti 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)Module 2 Unit Conversions and Problem solving with Metric Measurement(Allow 1 week for introduction and instruction: Continue measurement work through fluency, and within Science and Social Studies interdependencies)Domain: Measurement and DataCluster: 4.MD.A: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36)…4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.Enduring UnderstandingsMeasurement compares a unit to the object being measured.The length of any object can be a measurement unit for length, but a standard unit, such as an inch, is always the same length. The smaller the unit used, the more units are needed to equal a given length. Centimeters, decimeters, meters, and kilometers are standard units for measuring length in the Metric System and they are related to each other.Essential QuestionsHow can you estimate and measure length?How do you measure an object in inches?How do you measure to a fraction of an inch?How can you estimate and measure length?Objectives/Learning Targets Topic A Lesson 1: I can express metric length measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric length. (4.MD.1, 4.MD.2)Lesson 2: I can express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass. (4. MD.1, 4.M.2)Lesson 3: I can express metric capacity measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric capacity. (4.MD.1, 4.MD.2)engageny Module 1: Unit Conversions and problem Solving with Metric MeasurementTopic A: Metric Unit conversionsLesson 1Lesson 2 HYPERLINK "" Lesson 3VocabularyConvert (express a measurement in a different unit; rename units) Kilometer, Mass, Milliliter, Mixed Units Familiar Terms and Symbols=, <, >, Algorithm, Capacity, Distance, Equivalent, Kilogram (kg), gram (g), Larger or smaller unit, Length, Liter (L) , Measurement, Meter (m), centimeter (cm), Mixed units. Simplifying strategy, Table, Times as much as, Weight Fluency Practice:Please see engageNY full module download for suggested fluency pacing and activities. Lesson 1Convert UnitsMeter and Centimeter Number BondsLesson 2Convert UnitsUnit CountingAdd and Subtract Meters and CentimetersLesson 3Convert Units Unit Counting Add and Subtract Meters and Centimeters Literature Connections How Tall, How Short, How Far Away by David Adler, How Long or How Wide by Brian Cleary, Millions to Measure by David Schwartz 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)Topic BLesson 4: I can know and relate metric units to place value units in order to express measurements in different units (4. MD.1, 4.M.2)Lesson 5: I can use addition and subtraction to solve multi-step word problems involving length, mass, and capacity (4. MD.1, 4.M.2) Topic B: Application of Metric Unit Conversions HYPERLINK "" Lesson 4 HYPERLINK "" Lesson 5End of Module AssessmentTasks:Who is the Tallest?Movin ‘n GroovinCoordinating I-Ready Lessons:Express Measurements in Larger UnitsenVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum)16-1: Measurement: UsingCustomary Units of Length16-5: Measurement: UsingMetric Units of Lengths16-7: Measurement: Units ofMassTasks:Who is the Tallest?Movin ‘n GroovinCoordinating I-Ready Lessons:Express Measurements in Larger UnitsenVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum)16-1: Measurement: UsingCustomary Units of Length16-5: Measurement: UsingMetric Units of Lengths16-7: Measurement: Units ofMassFluency Practice:Lesson 4Perimeter and Area Add and Subtract Meters and Centimeters Add and Subtract M and CMConvert Units Unit CountingLesson 5Sprint: Convert Kilograms to Grams Write in Kilograms and Grams Sprint Convert Kilograms and Grams Convert Units Unit Counting Module 3 Multi-Digit Multiplication and Division(Allow 3 weeks for instruction, review and assessment)Domain: Operations and Algebraic ThinkingCluster: 4.OA.1 Use the Four Operations with whole numbers to solve problems 4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 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. 4.OA.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 4.OA.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: Operations and Algebraic ThinkingCluster: 4.OA. Gain Familiarity with factors and multiples4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.Domain: Numbers and Operations in Base TenCluster: Use place value understanding and properties of operations to perform multi-digit arithmetic 4.NBT.5 Multiply a whole number of up to four digits by a one digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.6 Find whole-number quotients and remainders with up to four dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Domain: Measurement and DataCluster: Solve Problems involving measurement and conversion of measurements from a larger unit to a smaller unit.4.MD.3 Apply the area and perimeter formula for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing he area formula as a multiplication equation with an unknown factor.Enduring UnderstandingsThere is more than one way to do a mental calculation. Techniques involve changing the numbers or the expression so the calculation is easy to do mentally. Partial products can be added together to find the product. The standard algorithm for multiplying a 3-digit number by one digit is just an extension to the hundreds place of the algorithm for multiplying 2-digit by one digit. . Essential QuestionsWhat place-value patterns can be seen when you multiply 1-digit numbers by multiples of 10 and 100? What are some ways to multiply mentally? How can you use rounding to estimate when you multiply? How do you know if your answer is reasonable? How do you multiply a 2-digit number by a 1-digit number? How do you multiply a 3-digit number by a 1-digit number? Objectives/Learning Targets Topic ALesson 1: Investigate and use the formulas for area and perimeter of rectangles (4.OA.1, 4.OA.2, 4.MD.3, 4.OA.3)Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas. (4.OA.1, 4.OA.2, 4.MD.3, 4.OA.3)Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi-step real world problems. (4.OA.1, 4.OA.2, 4.MD.3, 4.OA.3)engageny Module 3: Multi-Digit Multiplication and DivisionTopic A: Multiplicative Comparison word ProblemsLesson 1Lesson 2Lesson 3Videos: Grade 4 Module 3 Lesson 1Grade 4 Module 3 Lesson 2Grade 4 Module 3 Lesson 3VocabularyAssociative property, composite number, distributive property, divisible, divisor, formula, long division, partial product, prime number, remainderFamiliar Terms and SymbolsAlgorithm, Area, Area model, Array, bundling, grouping, reaming, changing, compare, distribute, divide, division, equation, factors, mixed units, multiple, multiply, multiplication, perimeter, place value, product, quotient, rectangular array, rows, columns, __times as many__as ____Fluency Practice:Please see engageNY full module download for suggested fluency pacing and activities. Lesson 1Perimeter and AreaMultiply Number by ItselfGroup CountFind the Unknown FactorLesson 2Multiply a Number by ItselfRename the UnitFind the Area and PerimeterLesson 3Sprint: Missing Products and FactorsFind the Area and PerimeterObjectives/Learning Targets Topic BLesson 4: Interpret and represent patterns when multiplying by 10, 100, and 1,000 by single digits recognizing patterns. (4.NBT.5, 4.OA.1, 4.OA.2, 4.NBT.1) Lesson 5: Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns. (4.NBT.5, 4.OA.1, 4.OA.2, 4.NBT.1) Lesson 6: Multiply two digit multiples of 10 by two digit multiples of 10 with the area model. (4.NBT.5, 4.OA.1, 4.OA.2, 4.NBT.1) Topic B: Multiplication by 10, 100, 1,000Lesson 4Lesson 5Lesson 6Videos:Grade 4 Module 3 Lesson 4Grade 4 Module 3 Lesson 5Grade 4 Module 3 Lesson 6Fluency Practice:Lesson 4Rename the UnitGroup Count by Multiples of 10 and 100Find the Area and PerimeterLesson 5Group Count by Multiples of 10 and 100Multiply UnitsGroup 6Multiply by Different UnitsTake Out the 10, 100, or 1,000Multiply by Multiples of 10, 100,1,000Objectives/Learning Targets Topic CLesson 7: Use place value disks to represent two-digit by one-digit multiplication. (4.NBT.5, 4.OA.2, 4.NBT.1) Lesson 8: Extend the use of place value disks to represent three- and four-digit by one-digit multiplication. (4.NBT.5, 4.OA.2, 4.NBT.1) Lesson 9 or 10: Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm. (4.NBT.5, 4.OA.2, 4.NBT.1) Lesson 11: Connect the area model and the partial products method to the standard algorithm. (4.NBT.5, 4.OA.2, 4.NBT.1) Topic C: Multiplication of up to Four Digits by single digit numbersLesson 7Lesson 8Lesson 9 or 10Lesson 11Videos:Grade 4 Module 3 Lesson 7Grade 4 Module 3 Lesson 8Grade 4 Module 3 Lesson 9Grade 4 Module 3 Lesson 10Grade 4 Module 3 Lesson 11Fluency PracticeLesson 7Sprint: Multiply Multiples of 10, 100, and 1,000Multiply MentallyLesson 8Expanded FormMultiply MentallyMultiplying Using DisksLesson 9 or 10Expanded FormMultiply MentallyMultiplying Using DisksRepresent Expanded FormMultiply Using Partial ProductsLesson 11Multiply MentallyMultiply in Three different WaysObjectives/Learning Targets Topic DLesson 12: Solve two-step word problems, including multiplicative comparison (4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5)Lesson 13: Use multiplication, addition, or subtraction to solve multi-step word problems (4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5)Topic D: Multiplication Word ProblemsLesson 12Lesson 13Mid-Module AssessmentVideos:Grade 4 Module 3 Lesson 12Grade 4 Module 3 Lesson 13Fluency Practice:Lesson 12Multiply MentallyMultiply in Three different WaysLesson 13Sprint: Mental MultiplicationMultiply using the Standard AlgorithmObjectives/Learning Targets Topic ELesson 14: Solve division word problems with remainders(4.NBT.6, 4.OA.3)*Module 3 continues in Quarter 2*Topic E: Division of Tens and Ones with Successive RemaindersLesson 14Video:Grade 4 Module 3 Lesson 14Fluency Practice:Lesson 14Group Count to DivideNumber Sentences in an ArrayDivide with RemaindersTasks:Multiplication Task ArcsCoordinating I-Ready Lessons:Multiplying two-digit numbers by one digit numbersMultiplying two-digit numbers by two-digit numbersReview Multiplying two-digit numbers by one digit numbersMultiplying by two-digit numbersenVision Resource: (enVision may be used to support the needs of your students, but should not be used independently of the mathematics curriculum)7-4: Multiplying 2 Digit Numbers by Multiples of107-5: Multiplying 2 Digit by 2 Digit NumbersLiterature Connections Amanda Bean’s Amazing Dreams by Cindy Neuschwander Multiplying Menace by Pam Calvert Safari Park by Stuart J. Murphy (Finding Unknowns) 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)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: - 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) - These Khan Academy lessons are aligned to RIT scores.Textbook ResourcesengageNY Mathematics Modulesenvision MathTN Core/CCSSTN Math StandardsAchieve the CoreVideosNCTM Common Core VideosLearnZillionCCSS Video SeriesChildren’s Literature The Reading Nook HYPERLINK "" Math and Literature:A Match Made in the ClassroomMath for Kids-Best Children’s BooksScholastic: Books and Programs to Improve Elementary MathInteractive ManipulativesInteractive Content Resources for Teaching Math Interactive Sites for Educators Math Playground: Common Core StandardsThinking Blocks: Computer and iPad based games PARCC GamesIXL Math Virtual ManipulativesAdditional SitesEdutoolbox (Formerly TNCORE)Singapore Math Math-Play-Com Scholastic Math Study Jams OtherIllustrated Mathematics Dictionary for KidsOther: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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