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 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.Mathematical Practice StandardsMathematical Practice Standards 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.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. -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: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 2 Quarter 1 OverviewModule 1: Sums and Differences to 100Module 2: Addition and Subtraction of Length UnitsModule 3: Place Value, Counting, and Compaison of Numbers to 1,000Overview Module 1: 1143000868680Level 2: Count onLevel 3: Make an easier problem00Level 2: Count onLevel 3: Make an easier problemModule 1 sets the foundation for students to master sums and differences to 20 (2.OA.2). Students subsequently apply these skills to fluently add one-digit to two-digit numbers at least through 100 using place value understanding, properties of operations, and the relationship between addition and subtraction (2.NBT.5). In Grade 1, students worked extensively with numbers to gain fluency with sums and differences within 10 (1.OA.5) and became proficient in counting on (a Level 2 strategy). They also began to make easier problems to add and subtract within 20 and 100 by making ten and taking from ten (Level 3 strategies) (1.OA.6, 1.NBT.4–6). In Module 1, students advance from Grade 1’s subtraction of a multiple of ten to a new complexity, subtracting single-digit numbers from both multiples of ten (e.g., 40 – 9) and from any two-digit number within 100 (e.g., 41 – 9). 11874506985 40 – 9 = 31 / \30 1010 – 9 = 130 + 1 = 3100 40 – 9 = 31 / \30 1010 – 9 = 130 + 1 = 3133528006985 41 – 9 = 32 / \31 1010 – 9 = 131 + 1 = 3200 41 – 9 = 32 / \31 1010 – 9 = 131 + 1 = 32Topic A’s two lessons are devoted solely to the important practice of fluency, the first lesson working within 20 and the second extending the same fluencies to numbers within 100. Topic A reactivates students’ Kindergarten and Grade 1 learning as they energetically practice the following prerequisite skills for Level 3 decomposition and composition methods: decompositions of numbers within ten (e.g., 0 + 7, 1 + 6, 2 + 5, and 3 + 4, all equal seven).partners to ten(e.g., 10 and 0, 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5, and “I know 8 needs 2 to make ten”).tens plus sums (e.g., 10 + 9, 10 + 8).For example, students quickly remember make ten facts. They then immediately use those facts to solve problems with larger numbers (e.g., “I know 8 needs 2 to make 10, so 58 needs 2 to make 6 tens or sixty!”). Lessons 1 and 2 include Sprints that bring back automaticity with the tens plus sums, which are foundational for adding within 100 and expanded form (e.g., “I know 10 + 8 = 18, so 40 + 8 = 48”). Topic B takes Grade 1’s work to a new level of fluency as students make easier problems to add and subtract within 100 by using the number system’s base ten structure. The topic begins with students using place value understanding to solve problems by adding and subtracting like units (e.g., “I know 8 – 5 = 3, so 87 – 50 = 37 because 8 tens – 5 tens = 3 tens. I know 78 – 5, too, because 8 ones – 5 ones = 3 ones. I used the same easier problem, 8 – 5 = 3, just with ones instead of tens!”). Students then practice making ten within 20 before generalizing that strategy to numbers within 100 (e.g., “I know 9 + 6 = 15, so 79 + 6 = 85, and 89 + 6 = 95”). The preceding lessons segue beautifully into the new concepts of Topic B, subtracting single-digit numbers from two-digit numbers greater than 20. In Lesson 6, students use the familiar take from ten strategy to subtract single-digit numbers from multiples of ten (e.g., 60 – 8, as shown below). In Lesson 7, students practice taking from ten within 20 when there is the complexity of some ones in the total (e.g., 13 – 8, as shown below). In Lesson 8, they then subtract single-digit numbers from 2-digit numbers within 100 when there are also some ones (e.g., 63 – 8, as shown below). 343535145415Decompose and Subtract From Ten 63 – 8 = 55 /\53 10 10 – 8 = 2 53 + 2 = 55 60 – 8 = 52 / \50 1010 – 8 = 250 + 2 = 52 13 – 8 = 5 / \3 10 10 – 8 = 2 3 + 2 = 5Lesson 6Lesson 8Lesson 7Decompose and Subtract From Ten 63 – 8 = 55 /\53 10 10 – 8 = 2 53 + 2 = 55 60 – 8 = 52 / \50 1010 – 8 = 250 + 2 = 52 13 – 8 = 5 / \3 10 10 – 8 = 2 3 + 2 = 5Lesson 6Lesson 8Lesson 7 692785010223500These strategies deepen place value understandings in preparation for Module 3 and the application of those understandings to addition and subtraction in Modules 4 and 5. Listen to how the language of make ten and take from ten is foundational to the work of later modules: Module 3: “I have 10 tens, so I can make a hundred. It’s just like I can make a ten when I have 10 ones.” Module 5: “When I solve 263 – 48, I take a ten from 6 tens to make 5 tens and 13 ones. Now, I am ready to subtract in the ones place” (pictured to the right).Note that mastery of sums and differences within 100 is not to be expected in Module 1 but rather by Module 8. Because the amount of practice required by each student to achieve mastery prior to Grade 3 will vary, a motivating, differentiated fluency program needs to be established in these first 2 weeks to set the tone for the year. In Grade 2 Module 1, Application Problems begin in Topic B. They contextualize learning as students apply strategies to solving simple add to, take from, put together/take apart problem types using the Read-Draw-Write, or RDW, process (2.OA.1). Application Problems may precede the Concept Development to act as the lead-in, allowing students to discover through problem-solving the logic and usefulness of a strategy before it is formally presented. Or, problems may follow the Concept Development so that students connect and apply new learning to real-world situations. At the beginning of Grade 2, problem-solving may begin more as a guided activity, with the goal being to move students to independent problem-solving, wherein they reason through the relationships embedded within the problem and choose an appropriate strategy to solve (MP.5). Module 2: In this 12-day Grade 2 module, students engage in activities designed to deepen their conceptual understanding of measurement and to relate addition and subtraction to length. Their work in Module 2 is exclusively with metric units in order to support place value concepts. Customary units are introduced in Module 7. Topic A opens with students exploring concepts related to the centimeter ruler. In the first lesson, they are guided to connect measurement with physical units as they find the total number of length units by laying multiple copies of centimeter cubes (physical units) end to end along various objects. Through this, students discover that to get an accurate measurement, there must be no gaps or overlaps between consecutive length units. Next, students measure by iterating with one physical unit, using the mark and advance technique, also known as mark and move forward. Students then repeat the process by laying both multiple copies and a single cube along a centimeter ruler. This helps students create a mental benchmark for the centimeter. It also helps them realize that the distance between 0 and 1 on the ruler indicates the amount of space already covered. Hence 0, not 1, marks the beginning of the total length. Students use this understanding to create their own centimeter rulers using a centimeter cube and the mark and advance technique. Topic A ends with students using their unit rulers to measure lengths (2.MD.1), thereby connecting measurement with a ruler. Students build skill in measuring using centimeter rulers and meter sticks in Topic B. They learn to see that a length unit is not a cube, or a portion of a ruler (which has width), but is a segment of a line. By measuring a variety of objects, students build a bank of known measurements or benchmark lengths, such as a doorknob being a meter from the floor, or the width of a finger being a centimeter. Then, students learn to estimate length using knowledge of previously measured objects and benchmarks. This enables students to internalize the mental rulers of a centimeter or meter, empowering them to mentally iterate units relevant to measuring a given length (2.MD.3). The knowledge and experience signal that students are determining which tool is appropriate to make certain measurements (2.MD.1).In Topic C, students measure and compare to determine how much longer one object is than another (2.MD.4). They also measure objects twice using different length units, both standard and non-standard, thereby developing their understanding of how the total measurement relates to the size of the length unit (2.MD.2). Repeated experience and explicit comparisons help students recognize that the smaller the length unit, the larger the number of units, and the larger the length unit, the smaller the number of units.The module culminates as students relate addition and subtraction to length. They apply their conceptual understanding to choose appropriate tools and strategies, such as the ruler as a number line, benchmarks for estimation, and tape diagrams for comparison, to solve word problems (2.MD.5, 2.MD.6). The problems progress from concrete (i.e., measuring objects and using the ruler as a number line to add and subtract) to abstract (e.g., representing lengths with tape diagrams to solve start unknown and two-step problems).Module 3: In Module 2, students added and subtracted measurement units within 100 (2.MD.5, 2.MD.6), a meaningful application of their work from Module 1 (2.NBT.5) and a powerful bridge to the base ten units of Grade 2. In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana―1 hundred, 2 hundred, 3 hundred, etc. (2.NBT.1). A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones (2.NBT.1). The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart (2.NBT.3). Furthermore, in this module instruction includes a great deal of counting: by ones, tens, and hundreds (2.NBT.2). Counting up using the centimeter tape or a classroom number line shows movement from left to right as the numbers increase. Counting up on the place value chart shows movement from right to left as the numbers increase. For example, as 10 ones are renamed as 1 ten, the larger unit is housed in the place directly to the left. The goal is for students to move back and forth fluidly between these two models, the number line and the place value chart, using them to either to rename units and compare numbers (2.NBT.4). In this module, the place value story has advanced. Along with changing 10 ones for 1 ten, students now also change 10 tens for 1 hundred. This changing leads to the use of counting strategies to solve word problems (2.OA.1). In the next module, this change leads to mental math and the formal algorithms for addition and subtraction. Comparison extends into finding 100 more and 100 less, 10 more and 10 less, etc. Just as in Grade 1, more and less translate into formal addition and subtraction at the onset of Module 4 (2.NBT.8). How is this module’s learning foundational to later grades? Understanding 3 tens or 3 units of 10 leads to an understanding of 3 fours or 3 units or groups of four (Grade 3 OA standards), 3 fourths or 3 units of one-fourth (Grade 3 NF standards). Learning that 12 tens = 120 leads to an understanding of 12 tenths = 1.2, 4 thirds = 4/3 = 1 1/3, or even 4 threes = 12. Counting up and down by ones, tens, and hundreds with both the number line and place value chart is essential from Grade 3 forward for rounding and mental math (Grade 3 NBT standards) to meaningful understanding of all operations with base ten whole numbers (Grade 4 NBT standards) and to understanding place value’s extension into decimal fractions and operations (Grade 5 NBT standards).Focus Grade Level StandardType of RigorFoundational Standards2.OA.A.1Conceptual Understanding & Application1.NBT.C.4, 1.NBT.C.5, 1.NBT.C.6, 1.OA.A.12.OA.B.2Procedural Skill & Fluency1.OA.C.62.NBT.A.5Procedural Skill & Fluency1.NBT.C4, 1.NBT.C.5, 1.NBT.C.6, 2.OA.B.22.MD.A.1Conceptual Understanding & Application1.MD.A.22.MD.A.2Conceptual Understanding & Application2.MD.A.1, 2.MD.A.32.MD.A.3Conceptual Understanding2.MD.A.12.MD.A.4Application2.MD.A.32.MD.B.5Conceptual Understanding & Application2.MD.A.42.MD.B.6Conceptual UnderstandingIntroductory Skill2.NBT.A.1Conceptual Understanding1.NBT.B.2, 2.NBT.A.22.NBT.A.2Procedural Skill & FluencyIntroductory Skill2.NBT.A.3Procedural Skill & Fluency2.NBT.A.12.NBT.A.4Conceptual Understanding2.NBT.A.104279900Fluency NCTM 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 2nd 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. 2.OA.B.2 Fluently add and subtract within 20 using mental strategies. 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Note: Fluency is only one of the three required aspects of rigor. Each of these components have equal importance in a mathematics curriculum. References: STATE STANDARDSCONTENTINSTRUCTIONAL RESOURCESVOCABULARY/FLUENCYSums and Differences to 100 (Allow approximately 2 ? weeks for instruction, review and assessment) Domain: Operations and Algebraic ThinkingCluster 2.OA.A: Represent and solve problems involving addition and subtraction. 2.OA.A.1 Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.Cluster 2.OA.B: Add and subtract within 20 2.OA.B.2 Fluently add and subtract within 20 using mental strategies.Domain: Numbers Base TenCluster: Use place value understanding and properties of operations to add and subtract. 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Enduring UnderstandingsAddition and subtraction are relatedStrategies can by applied to solve addition/subtraction problemsEssential QuestionsHow can we write related addition and subtraction facts?What strategy do you use when you add/subtract? Why?Objectives/Learning TargetsLesson 1: I can practice making ten and adding to ten. (2.OA.B.2)Lesson 2: I can practice making the next ten and adding to a multiple of ten. (2.OA.B.2)Teachers should begin the year with grade level appropriate standards and content. Instruction may be differentiated to meet student needs in core, Tier 1 instruction and additional support may be provided in tiered, supplemental intervention. 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/example 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 Module1: Sums and Differences to 100Topic A: Foundations for Fluency with Sums and Differences within 100Lesson 1Lesson 2Vocabulary:Make a tenFamiliar Terms and Symbols:Addend, a ten, count on, expression, like units, make ten and take from ten, number sentence, number bond, one part, partners to 10, say ten counting, ten plus facts, totalFluency Practice: Please see engageny full module download for suggested fluency pacing and activities.Lesson 1: Ten Frame Flash Happy Counting the Say Ten Way Sprint: Add a Ten and Some Ones Target Practice: Within 10 Pairs to Ten with Number BondsLesson 2: The Value of Tens and Ones Happy Counting the Say Ten Way Sprint: Add a Ten and Some Ones Target Practice: Within 10 Make the Next TenObjectives/Learning TargetsLesson 3: I can add and subtract like units (2. OA. A.1, 2.OA.B.2)Lesson 4: I can make a ten to add within 20. (2. OA. A.1, 2.OA.B.2, 2.NBT. 5)Lesson 5: I can make a ten to add within 100. (2. OA. A.1, 2.OA.B.2, 2.NBT. 5)Lesson 6: I can subtract single-digit numbers from multiples of 10 within 100. (2. OA. A.1, 2.OA.B.2, 2.NBT. 5)Lesson 7: I can take from ten within 20. (2. OA. A.1, 2.OA.B.2, 2.NBT. 5)Lesson 8: I can take from ten within 100. (2. OA. A.1, 2.OA.B.2, 2.NBT. 5)Topic B: Initiating Fluency with Addition and Subtraction Within 100Lesson 3Lesson 4Lesson 5Lesson 6Lesson 7Lesson 8 HYPERLINK "" End of Module AssessmentFor supporting resources see the following enVision lessons:2-1 Adding 0,1,22-6 Making 10 to add 92-7 Making 10 to add 83-1 Subtracting 0,1,23-3 Thinking Addition to 10 to SubtractLesson 3: Sprint: Related FactsLesson 4: Draw Tens and Ones Make Ten Make the Next Ten within 100 Take Out OneLesson 5: Happy Counting: Say Ten Way Put Together/Take Apart Make the Next Ten Within 100Lesson 6: One or Two Less Take from Ten Take Out TenLesson 7: Take Out Ten and SubtractLesson 8: Take from a Ten or Take from the ones Take Out Ten and SubtractTasks:Addie's EquationBuilding Towards FluencyAdditional Resources:Learn Zillion ResourcesAdd and Subtract Within 100 to Solve Word Problems (2.OA.A.1)Solve Addition and Subtraction Word Problems by Drawing Models (2.OA.A.1)Use Mental Strategies to Add and Subtract Within 20 (2.OA.B.2)Add and Subtract Within 20 (2.OA.B.2)Add and Subtract Within 100 Using Place Value Strategies, Hundreds Charts and Properties of Operation (2.NBT.B.5) I-Ready Lessons:Subtraction in Comparison SituationsSubtraction in Part-Part-Whole SituationsAddition and Subtraction Fact FamiliesReview Addition and Subtraction Fact FamiliesRelating Addition and Subtraction FactsOther: 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)Addition and Subtraction of Lengths Units (Allow approximately 2 weeks for instruction, review and assessment)Domain: Measurement and DataCluster 2.MD.A: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks and measuring tapes. 2.MD.A.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.A.2 Measure the length of an object twice using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen 2.MD.A.3 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD. A.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Cluster 2.MD.D: Relate addition and subtraction to length 2.MD.D.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rules) and equations with a symbol for the unknown number to represent the problem. 2.MD.D.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0,1,2,…, and represent whole-number sums and differences within 100 on a number line diagramEnduring UnderstandingsAttributes are measureable.The lengths of objects are measurable in different units.Measurements need the same unit of measure in order to be compared.Essential QuestionsHow can you tell which attributes of an object can be measured?What objects can be used to approximate standard units of inches, feet, yards, centimeters and meters?How can you compare measurements?Objectives/Learning TargetsLesson 1: I can connect measurement with physical units by using multiple copies of the same physical unit to measure. (2.MD.A.1)Lesson 2: I can use iteration with one physical unit to measure. (2.MD.A.1)Lesson 3: I can apply concepts to create unit rulers and measure lengths using unit rulers. (2.MD.A.1) HYPERLINK "" Engageny Module 2: Addition and Subtraction of Lengths UnitsTopic A: Understand Concepts About the RulerLesson 1Lesson 2Lesson 3For supporting resources see the following enVision lessons:13-3 Measuring Length Using Nonstandard Units13-4a InchesVocabularyBenchmark, endpoint, estimate, hash mark, meter, meter stick or strip, number line, overlap, rulerFamiliar Terms and Symbols:Centimeter, combine, compare, difference, height, length, length unitFluency Practice: Please see engageny full module download for suggested fluency pacing and activities.Lesson 1: Happy Counting 20-40 Two More Sprint: Before, Between, AfterLesson 2: Say Ten Counting Say Ten Counting to the Next Ten Make Ten to AddLesson 3: Happy Counting 40-60 Making 10 by Identifying the Missing Part Sprint: Making 10Objectives/Learning TargetsLesson 4: I can measure various objects using centimeter rulers and meter sticks. (2.MD.A.1, 2.MD.A.3)Lesson 5: I can develop estimation strategies by applying prior knowledge of length and using mental benchmarks. (2.MD.A.1, 2.MD.A.3)Topic B: Measure and Estimate Length Using Different Measurement ToolsLesson 4Lesson 5For supporting resources see the following enVision lessons: 13-5 Centimeters and Meters13-5a CentimetersFluency Practice: Lesson 4: Related Facts on a Ruler Sprint: Related FactsLesson 5: Break Apart by Tens and Ones Take Out a PartObjectives/Learning TargetsLesson 6: I can measure and compare lengths using centimeters and meters. (2.MD.A.1, 2.MD.A.2, 2.MD.A.4)Topic C: Measure and Compare Lengths Using Different Length UnitsLesson 6Omit Lesson 7For supporting resources see the following enVision lessons: 13-6C Comparing LengthsFluency Practice: Lesson 6: Happy Counting Sprint: Find the Longer LengthObjectives/Learning TargetsLesson 8: I can solve addition and subtraction word problems using the ruler as a number line. (2.MD.B.5, 2.MD.B.6)Lesson 9: I can measure lengths of string using measurement tools, and use tape diagrams to represent and compare the lengths. (2.MD.B.5, 2.MD.B.6)Lesson 10: I can apply conceptual understanding of measurement by solving two-step word problems. (2.MD.B.5, 2.MD.B.6)Topic D: Relate Addition and Subtraction to LengthLesson 8Lesson 9Lesson 10End of Module AssessmentFor supporting resources see the following enVision lessons: 13-6B Adding and Subtracting MeasurementFluency Practice: Lesson 8: How Many More to Make a Meter? Sprint: Making a MeterLesson 9: Adding Multiples of 10 to Numbers Happy Counting by CentimetersLesson 10: Subtracting Multiples of 10 from Numbers Take From Ten Relate Subtraction to Addition Sprint: Relate Subtraction to AdditionTasks: Determining LengthHow Big is A Foot Frog and Toad on the Number LineAdditional Resources:LearnZillion: Exploring Standard Units of LengthLearnZillion: Relating Addition and Subtraction Strategies to LengthI-Ready Lessons:Using a Ruler: InchesUsing a Ruler: CentimetersMeasuring Lengths with a RulerUnderstand Measurement with Different UnitsCompare lengthsSolve Problems Involving LengthOther: 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)Place Value, Counting, and Comparison of Numbers to 1,000(Allow approximately 4 1/2 week for instruction, review and assessment)Domain: Numbers and Operations Base TenCluster 2.NBT.A: Understand place value. 2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the special cases. 2.NBT.A.2 Count within 1000; skip count by 5s, 10s, and 100s. 2.NBT.A.3 Read and write numbers to 1000 using base ten numerals, number names, and expanded form 2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundred, tens, and ones digits, using symbols to record the results of comparisons.Enduring UnderstandingsThe placement of any number written in standard form has a meaning.Numbers can be compared using greater than, less than, and equal to.Our number system is based on groups of tens.Essential QuestionsHow do you know the value of a number?How can you find the number that is one before or one after another number, or the number between two other numbers?How can you find the number that is ten/100 before or below another number?How does understanding place value help you compare three digit numbers?Objectives/Learning Targets: Lesson 1: I can bundle and count ones, tens, and hundreds to 1,000. (2.NBT.A.1)Lesson 2: I can count up and down between 100 and 220 using ones and tens. (2.NBT.A.2) (Note: Use analog clock to proved a context for skip-counting by 5’s)Lesson 3: I can count up and down between 90 and 1,000 using ones, tens, and hundreds. (2.NBT.A.2) (Note: Use analog clock to proved a context for skip-counting by 5’s)Engageny Module 3: Place Value, Counting, and Comparison of Numbers to 1,000Topic A: Forming Base Ten Units of Ten, a Hundred, and a ThousandLesson 1Topic B: Understanding Place Value Units of One, Ten and a HundredLesson 2Lesson 3For supporting resources see the following enVision lessons: 4-1 Models for Tens4-2 Models for Tens and Ones17-6a Skip Counting by 5, 10, 100 to 1,000VocabularyBase ten numerals, expanded form, hundreds place, one thousand, place value or number disk, standard form, unit form, word formFamiliar Terms and Symbols=, <,>, altogether, bundling, grouping, how many more/less, how much more/less, more than, less than, number sentence, ones place, place value, renaming, changing, tens place, units of ones, hundreds, one thousandFluency Practice: Please see engageny full module download for suggested fluency pacing and activities.Lesson 1: Meter Strip Subtraction Skip Count Up and Down by Fives Happy Counting Skip-count by TensLesson 2: Meter Strip Subtraction Measure and Compare Skip-count Up and Down by Fives on the Clock Counting with Ones, Tens, and HundredsLesson 3: Sprint: differences to 10 with Teen NumbersMixed Counting with Ones, Tens, and Hundreds from 0 to 1000Objectives/Learning Targets: Lesson 4: I can count up to 1,000 on the place value chart. (2.NBT.A.3)Lesson 5: I can write base ten three-digit number in unit form; show the value of each digit. (2.NBT.A.3)Lesson 6: I can write base ten numbers in expanded form. (2.NBT.A.3)Lesson 7: I can write, read, and relate base ten numbers in all forms. (2.NBT.A.3)Topic C: Three-Digit Numbers in Unit, Standard, Expanded and Word FormsLesson 4Lesson 5Lesson 6Lesson 7For supporting resources see the following enVision lessons: 4-3 Reading and Writing Numbers4-8 Number Patterns on a Hundred Chart17-5 Patterns with Numbers on a Hundreds ChartFluency Practice: Lesson 4: Sprint: Adding to the Teens Exchange to Get to 50 Lesson 5: Exchange to Get 100 Meter Strip Addition: Using Two-Digit Numbers with Totals in the Ones Place that are Less Than or Equal to 12Lesson 6: Meter Strip Addition: Using Two-Digit Numbers with Totals in the Ones that are Greater than 12 Unit Form Counting from 398-405 Think 10 to Add 9Lesson 7: Write Numbers in Expanded Form Sprint: Expanded Form Skip-Count up and down $10 Between 45-125 Objectives/Learning Targets: Lesson 8: I can count the total value of $1, $10, and $100 bills up to $1,000. (2.NBT.A.2)Lesson 9: I can count from $10 to $1,000 on the place value chart and the empty number line. (2.NBT.A.2)Lesson 10: I can explore $1,000. How many $10 bills can we change for a thousand dollar bill? .(2.NBT.A.2)Topic D: Modeling Base Ten Numbers Within 1,000 with MoneyLesson 8Lesson 9Lesson 10Mid Module AssessmentFor supporting resources see the following enVision lessons: 4-8 Number Patterns on a Hundred Chart17-5 Patterns with Numbers on a Hundred ChartFluency Practice: Lesson 8: Mixed Counting with Ones, Tens, and HundredsLesson 9: Count and Change Coins Mixed Counting with Ones, Tens and Hundreds Skip-count by twos beginning at 394Lesson 10: Count and Change Coins Sprint: More Expanded Form Skip-count by TensObjectives/Learning Targets: Lesson 11: I can count the total value of ones, tens, and hundreds with place value disks. (2.NBT.A. 1, 2.NBT.A.3)Lesson 12: I can change 10 ones for 1 ten, 10 tens for 1 hundred, and 10 hundreds for 1 thousand. (2.NBT.A. 1, 2.NBT.A.3)Lesson 13: I can read and write numbers within 1,000 after modeling with place value disks. (2.NBT.A. 1, 2.NBT.A.3)Lesson 14: I can model numbers with more than 9 ones or 9 tens; write in expanded, unit, standard, and word forms. (2.NBT.A. 1, 2.NBT.A.3)Lesson 15: I can explore a situation with more than 9 groups of ten. (2.NBT.A. 1, 2.NBT.A.3)Topic E: Modeling Numbers Within 1,000 with Place Value DisksLesson 11Lesson 12Lesson 13Lesson 14Lesson 15For supporting resources see the following enVision lessons: 17-2 Counting Hundreds, Tens, and Ones17-3 Reading and Writing Numbers to 1,00017-4 Changing Numbers by Hundreds and TensFluency Practice: Lesson 11: Rekenrek Counting: Numbers in Unit Form Sprint: Addition and Subtraction to 10Lesson 12: 10 More/10 Less Sprint: Sums to 10 with Ten NumbersLesson 13: Sprint: Sprint-Place Value Counting to 100 100 More/100 Less How Many Tens/How Many HundredsLesson 14: Sprint: Review of Subtraction in the Teens Happy Counting Up and Down by Ones Crossing 100Lesson 15: Sprint: Expanded Notation Compare NumbersObjectives/Learning Targets: Lesson 16: I can compare two three-digit numbers using <,>, and =. (2.NBT.A.4)Lesson 17: I can compare two three-digit numbers using <,>, and = when there are more than 9 ones or 9 tens. (2.NBT.A.4)Lesson 18: I can order numbers in different form. (2.NBT.A.4)Topic F: Comparing Two Three-Digit NumbersLesson 16Lesson 17Lesson 18For supporting resources see the following enVision lessons: 17-6 Comparing Numbers17-7 Before, After, and Between17-8 Ordering NumbersFluency Practice: Lesson 16: Sprint: Sums Crossing Ten Lesson 17: Sprint: Sums Crossing Ten (Sums and Differences to 20)Lesson 18: Sprint: Sums Crossing Ten (Sums and Differences to 20)Objectives/Learning Targets: Lesson 19: I can model and use language to tell about 1 more and 1 less, 10 more and 10 less, and 100 more and 100 less. (2.NBT.A.2)Lesson 20: I can model 1 more and 1 less, 10 more and 10 less, and 100 more and 100 less when changing the hundreds place. (2.NBT.A.2)Lesson 21: I can complete a pattern counting up and down. (2.NBT.A.2)Topic G: Finding 1,10, and 100 More or Less than a NumberLesson 19Lesson 20Lesson 21End of Module AssessmentFor supporting resources see the following enVision lessons: 17-4 Changing Numbers by Hundreds and Tens17-9 Problem Solving: Look for a PatternFluency Practice: Lesson 19: Sprint: Differences Lesson 20: Sprint: Differences Lesson 21: Sprint: Differences Tasks:Boxes and Cartons of PencilsBundling and UnbundlingCounting StampsThe Largest Number GameAdditional Resources:LearnZillion: Understanding Three Digit NumbersLearnZillion: Expressing and Comparing Three Digit NumbersRelating Skip Counting to Mental Addition and SubtractionI-Ready Lessons:Place Value: Hundreds, Tens, OnesPlace Value to 1,000Place Value and Writing Numbers in Standard FormCounting by TensCounting by 5sGrouping Objects by 2s, 5s to 100Number Words 0-120Comparing and Ordering Numbers 1,000Other: 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 ResourcesEngage NY/Eureka Math Teacher SupportenVision MathenVision Common Core Addendum LessonsTN /CCSSTNReady Math StandardsAchieve the CoreTN EdutoolboxVideosMaking math fun with place value gamesKids Math TVLearnZillionTN Early Grades Math ToolkitChildren’s Literature Children's Literature on Number SenseChildren's Literature on Addition and SubtractionChildren's Literature on MoneyChildren's Literature on Counting Higher than 10Marilyn Burns Math Literature List 2nd GradeInteractive ManipulativesBase TenBase Ten BlocksAddition ChartAdditional SitesMath DictionaryInverse relationship of addition and subtractionAddition MachineAlien AdditionAdding DoublesWrite a subtraction sentence based on the pictureAdd three or more one-digit numbersBalance addition equations one-digitPopup Addition GamePopup Subtraction GameRead and Write NumbersIllustrative Mathematics 2nd GradeOther 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)Homework Help: Grade 2- Module 1: Sums and Differences to 100 TN Early Grades Math ToolkitParent Roadmap: Supporting Your Child in First Grade Mathematics ................
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