CCLS Mathematics Grade 3 Curriculum Guide

MOUNT VERNON CITY SCHOOL DISTRICT CCLS Mathematics Grade 3 Curriculum Guide THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GRADE 3 MATHEMATICS CURRICULUM IN MOUNT VERNON. 2015-2016

Mount Vernon City School District Board of Education Adriane Saunders President Serigne Gningue Vice President Board Trustees Charmaine Fearon Rosemarie Jarosz Micah J.B. McOwen Omar McDowell Darcy Miller Wanda White Lesly Zamor Superintendent of Schools Dr. Kenneth Hamilton Deputy Superintendent Dr. Jeff Gorman Assistant Superintendent of Business Ken Silver Assistant Superintendent of Human Resources Denise Gagne-Kurpiewski Administrator of Mathematics and Science (K-12) Dr. Satish Jagnandan 2

TABLE OF CONTENTS I. COVER..... 1 II. MVCSD BOARD OF EDUCATION..... 2 III. TABLE OF CONTENTS..... 3 IV. IMPORTANT DATES..... 4 V. VISION STATEMENT..... 5 VI. PHILOSOPHY OF MATHEMATICS CURRICULUM. 6 VII. NYS GRADE 3 COMMON CORE LEARNING STANDARDS..7 VIII. MVCSD GRADE 3 MATHEMATICS PACING GUIDE...14 IX. WORD WALL... 34 X. SETUP OF A MATHEMATICS CLASSROOM... 35 XI. ELEMENTARY GRADING POLICY... 36 XII. SAMPLE NOTEBOOK RUBRIC... 37 XIII. CLASSROOM AESTHETICS... 38 XIV. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON... 39 3

IMPORTANT DATES 2015-16 REPORT CARD 10 WEEK PERIOD MARKING PERIOD MARKING PERIOD BEGINS MP 1 September 8, 2015 MP 2 November 16, 2015 MP 3 February 1, 2016 MP 4 April 18, 2016 INTERIM PROGRESS REPORTS October 9, 2015 December 18, 2015 March 11, 2016 May 20, 2016 MARKING PERIOD ENDS November 13, 2015 January 29, 2016 April 15, 2016 June 23, 2016 DURATION REPORT CARD DISTRIBUTION 10 weeks Week of Nov. 23, 2015 10 weeks Week of February 8, 2016 9 weeks Week of April 25, 2016 10 weeks Last Day of School June 23, 2016 The Parent Notification Policy states Parent(s) / guardian(s) or adult students are to be notified, in writing, at any time during a grading period when it is apparent - that the student may fail or is performing unsatisfactorily in any course or grade level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during the grading period when it becomes evident that the student's conduct or effort grades are unsatisfactory. 4

VISION STATEMENT True success comes from co-accountability and co-responsibility. In a coherent instructional system, everyone is responsible for student learning and student achievement. The question we need to constantly ask ourselves is, "How are our students doing?" The starting point for an accountability system is a set of standards and benchmarks for student achievement. Standards work best when they are well defined and clearly communicated to students, teachers, administrators, and parents. The focus of a standards-based education system is to provide common goals and a shared vision of what it means to be educated. The purposes of a periodic assessment system are to diagnose student learning needs, guide instruction and align professional development at all levels of the system. The primary purpose of this Instructional Guide is to provide teachers and administrators with a tool for determining what to teach and assess. More specifically, the Instructional Guide provides a "road map" and timeline for teaching and assessing the Common Core Learning Standards. I ask for your support in ensuring that this tool is utilized so students are able to benefit from a standards-based system where curriculum, instruction, and assessment are aligned. In this system, curriculum, instruction, and assessment are tightly interwoven to support student learning and ensure ALL students have equal access to a rigorous curriculum. We must all accept responsibility for closing the achievement gap and improving student achievement for all of our students. Dr. Satish Jagnandan Administrator for Mathematics and Science (K-12) 5

PHILOSOPHY OF MATHEMATICS CURRICULUM The Mount Vernon City School District recognizes that the understanding of mathematics is necessary for students to compete in today s technological society. A developmentally appropriate mathematics curriculum will incorporate a strong conceptual knowledge of mathematics through the use of concrete experiences. To assist students in the understanding and application of mathematical concepts, the mathematics curriculum will provide learning experiences which promote communication, reasoning, and problem solving skills. Students will be better able to develop an understanding for the power of mathematics in our world today. Students will only become successful in mathematics if they see mathematics as a whole, not as isolated skills and facts. As we develop mathematics curriculum based upon the standards, attention must be given to both content and process strands. Likewise, as teachers develop their instructional plans and their assessment techniques, they also must give attention to the integration of process and content. To do otherwise would produce students who have temporary knowledge and who are unable to apply mathematics in realistic settings. Curriculum, instruction, and assessment are intricately related and must be designed with this in mind. All three domains must address conceptual understanding, procedural fluency, and problem solving. If this is accomplished, school districts will produce students who will 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique 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. 6

New York State P-12 Common Core Learning Standards for Mathematics Mathematics - Grade 3: Introduction In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes. 1. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. 2. Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. 3. Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. 4. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique 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. 7

Grade 3 Overview Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Understand properties of multiplication and the relationship between multiplication and division. Multiply and divide within 100. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Number and Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations Fractions Develop understanding of fractions as numbers. Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Represent and interpret data. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Geometry Reason with shapes and their attributes. Operations & Algebraic Thinking 3.OA Represent and solve problems involving multiplication and division. 1. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7. 2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8. 3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 1 4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = _ 3, 6 6 =? Understand properties of multiplication and the relationship between multiplication and division. 5. Apply properties of operations as strategies to multiply and divide. 2 Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) 6. Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100. 7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and explain patterns in arithmetic. 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3 8

9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 1 See Glossary, Table 2. 2 Students need not use formal terms for these properties. 3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order. Number & Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. 1 1. Use place value understanding to round whole numbers to the nearest 10 or 100. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10 90 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. 1 A range of algorithms may be used. Number & Operations Fractions¹ 3.NF Develop understanding of fractions as numbers. 1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 1 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8. 9

Measurement & Data 3.MD Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. 2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. 2 Represent and interpret data. 3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve oneand two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 5. Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 7. Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 1 Excludes compound units such as cm3 and finding the geometric volume of a container. 2 Excludes multiplicative comparison problems (problems involving notions of times as much ; see Glossary, Table 2). 10

Geometry 3.G Reason with shapes and their attributes. 1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. 11

Grade 3 Cluster Emphases for Instruction Cluster Emphases for Instruction on the 2013 Grade 3 Common Core Mathematics Test Cluster Emphasis Recommended Instructional Time Approximate Number of Test Points Major 65 75% 70 80% Supporting 15 25% 10 20% Additional 5 15% 5 10% CCLS Standard Content Emphasis Operations and Algebraic Thinking 3.OA.1 Interpret products of whole numbers Major 3.OA.2 Interpret whole-number quotients of whole numbers Major 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving Major equal groups, arrays, and measurement quantities 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating to Major three whole numbers 3.OA.5 Apply properties of operations as strategies to multiply and divide Major 3.OA.6 Understand division as an unknown-factor problem Major 3.OA.7 Fluently multiply and divide within 100 Major 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding Major 3.OA.9 Identify arithmetic patterns and explain them using properties of operations Major Number and Operations in Base Ten 3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100 Additional 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms Additional 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies Additional based on place value and properties of operations 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole part is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b Major 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram 3.NF.3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their size Measurement and Data 3.MD.1 Tell and write time to the nearest minute and measure the time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes 3.MD.2 3.MD.3 3.MD.4 3.MD.5 Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. Generate measurement data by measuring using rulers marked with halves and fourths of an inch. Show the data by making a line plot Recognize area as an attribute of plane figures and understand concepts of area Major Major Major Major Supporting Supporting Post Major measurement 3.MD.6 Measure areas by counting unit squares Major 3.MD.7 Relate area to the operations of multiplication and division Major 12

3.MD.8 Solve real world and mathematical problems involving perimeters of polygons Additional Post Geometry 3.G.1 Understand that shapes in different categories may share attributes and that the shared Supporting 3.G.2 attributes can define a larger category. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. = Standards recommended for greater emphasis Post = Standards recommended for instruction in May-June Post Supporting 13

MVCSD GRADE 3 MATHEMATICS PACING GUIDE This guide using NYS Grade 3 Mathematics CCLS Modules was created to provide teachers with a time frame to complete the Grade 3 New York State Mathematics Curriculum. Module Title Standards Days Month i-ready Lessons 1 2 3 Properties of Multiplication and Division and Solving Problems with Units of 2 5 and 10 Place Value and Problem Solving with Units of Measure Multiplication and Division with Units of 0, 1, 6 9, and Multiples of 10 4 Multiplication and Area 5 Fractions as Numbers on the Number Line 3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8 25 Sept. 8 Oct. 16 3.NBT.1, 3.NBT.2, 3.MD.1, 3.MD.2 25 Oct. 19 Nov. 23 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9, 3.NBT.3 3.MD.5a, 3.MD.5b, 3.MD.6, 3.MD.7a, 3.MD.7b, 3.MD.7c, 3.MD.7d 3.NF.1, 3.NF.2a, 3.NF.2b, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.NF.3d, 3.G.2 25 Nov. 24 Jan. 8 20 Jan. 11 Feb. 8 27 Feb. 9 Mar. 31 Topic A 1; Topic B 4; Topic C 2; Topic D 3; Topic E 5; Topic F 11 Topic A 20, 21; Topic B 22, 23; Topic C 8; Topic D 9; Topic E 9 Topic A 6; Topic B 3; Topic C 2; Topic D 3, 12; Topic E 13; Topic F 2, 7, 10 Topic A 27; Topic B 28; Topic C 28; Topic D 29 Topic A 33; Topic B 14; Topic C 18; Topic D 15; Topic E 16, 17; Topic F 19 6 Collecting and Displaying Data 3.MD.3 7 Apr. 1 Apr. 12 Topic A 24, 25; Topic B 26 NYSED GRADE 3 MATHEMATICS TEST: WEDNESDAY, APRIL 13 FRIDAY, APRIL 15, 2016 6 Collecting and Displaying Data 3.MD.4 10 Apr. 18 May 2 Topic A 24, 25; Topic B 26 7 Geometry and Measurement Word Problems 3.MD.4, 3.MD.8, 3.G.1 36 May 3 Jun. 22 Red End of Module Assessment Period Green Priority Standards account for approximately 70-80% of number of test points. Topic A 12, 13; Topic B 31, 32; Topic C 30; Topic D 26; Topic E 30 Note that the curriculum assumes that each school day includes 70-75 minutes of math: one hour on the day s Session, and 10-15 minutes on Fluency activities. Designed to fit within the calendar of a typical school year, grade 3 includes a total of 137 lessons. This provides some leeway for going further with particular ideas and/or accommodating local circumstances. Although pacing will vary somewhat in response to variations in school calendars, needs of students, your school's years of experience with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from the way mathematical ideas are introduced, developed, and revisited across the year. Required Fluency: 3.OA.7 Multiply and divide within 100. & 3.NBT.2 Add and subtract within 1000. 14

Module Title Standards Days Month 1 Properties of Multiplication and Division and Solving Problems with Units of 2 5 and 10 3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8 25 Sept. 8 Oct. 16 i-ready Lessons Topic A 1; Topic B 4; Topic C 2; Topic D 3; Topic E 5; Topic F 11 This 25-day module begins the year by building on students fluency with addition and knowledge of arrays. Topic A initially uses repeated addition to find the total from a number of equal groups (2.OA.4). As students notice patterns, they let go of longer addition sentences in favor of more efficient multiplication facts (3.OA.1, 3.OA.9). Lessons in Topic A move students toward understanding familiar repeated addition from Grade 2 in the form of array models, which become a cornerstone of the module. Students use the language of multiplication as they understand what factors are and differentiate between the size of groups and the number of groups within a given context. In this module the factors 2, 3, 4, 5, and 10 provide an entry point for moving into more difficult factors in later modules. 15

Standards Topics and Objectives Days 3.OA.1 3.OA.3 3.OA.2 3.OA.6 3.OA.3 3.OA.4 3.OA.1 3.OA.5 3.OA.3 3.OA.4 3.OA.2 3.OA.4 3.OA.6 3.OA.7 3.OA.3 3.OA.8 3.OA.5 3.OA.7 3.OA.1 3.OA.2 3.OA.3 3.OA.4 A B Multiplication and the Meaning of the Factors Lesson 1: Understand equal groups of as multiplication. Lesson 2: Relate multiplication to the array model. Lesson 3: Interpret the meaning of factors the size of the group or the number of groups. Division as an Unknown Factor Problem Lesson 4: Understand the meaning of the unknown as the size of the group in division. Lesson 5: Understand the meaning of the unknown as the number of groups in division. Lesson 6: Interpret the unknown in division using the array model. C Analyze Arrays to Multiply Using Units of 2 and 3 Lessons 7 8: Demonstrate the commutativity of multiplication and practice related facts by skipcounting objects in array models. Lesson 9: Find related multiplication facts by adding and subtracting equal groups in array models. Lesson 10: Model the distributive property with arrays to decompose units as a strategy to multiply. Mid-Module Assessment: applications 1 day) Topics A C (assessment ½ day, return ½ day, remediation or further D Division Using Units of 2 and 3 Lesson 11: Model division as the unknown factor in multiplication using arrays and tape diagrams. Lesson 12: Interpret the quotient as the number of groups or the number of objects in each group using units of 2. Lesson 13: Interpret the quotient as the number of groups or the number of objects in each group using units of 3. E Multiplication and Division Using Units of 4 Lesson 14: Skip-count objects in models to build fluency with multiplication facts using units of 4. Lesson 15: Relate arrays to tape diagrams to model the commutative property of multiplication. Lesson 16: Use the distributive property as a strategy to find related multiplication facts. Lesson 17: Model the relationship between multiplication and division. 3 3 4 2 3 4 16

3.OA.6 3.OA.3 3.OA.5 3.OA.7 3.OA.8 3.OA.1 3.OA.2 3.OA.4 3.OA.6 F Distributive Property and Problem Solving Using Units of 2 5 and 10 Lessons 18 19: Apply the distributive property to decompose units. Lesson 20: Solve two-step word problems involving multiplication and division and assess the reasonableness of answers. Lesson 21: Solve two-step word problems involving all four operations and assess the reasonableness of answers. 4 End-of-Module Assessment: Topics A F (assessment ½ day, return ½ day, remediation or further 2 application 1 day) Total Number of Instructional Days 25 17

Module Title Standards Days Month 2 Place Value and Problem Solving with Units of Measure 3.NBT.1, 3.NBT.2, 3.MD.1, 3.MD.2 25 Sept. 8 Oct. 16 i-ready Lessons Topic A 1; Topic B 4; Topic C 2; Topic D 3; Topic E 5; Topic F 11 In this 25-day module, students explore measurement using kilograms, grams, liters, milliliters, and intervals of time in minutes. Students begin by learning to tell and write time to the nearest minute using analog and digital clocks in Topic A (3.MD.1). They understand time as a continuous measurement through exploration with stopwatches and use the number line, a continuous measurement model, as a tool for counting intervals of minutes within 1 hour (3.MD.1). Students see that an analog clock is a portion of the number line shaped into a circle. They use both the number line and clock to represent addition and subtraction problems involving intervals of minutes within 1 hour (3.MD.1). 18

Standards Topics and Objectives Days 3.NBT.2 3.MD.1 A Time Measurement and Problem Solving Lesson 1: Explore time as a continuous measurement using a stopwatch. Lesson 2: Relate skip-counting by 5 on the clock and telling time to a continuous measurement model, the number line. Lesson 3: Count by fives and ones on the number line as a strategy to tell time to the nearest minute on the clock. Lesson 4: Solve word problems involving time intervals within 1 hour by counting backward and forward using the number line and clock. Lesson 5: Solve word problems involving time intervals within 1 hour by adding and subtracting on the number line. 5 3.NBT.2 3.MD.2 3.NBT.8 B Measuring Weight and Liquid Volume in Metric Units Lesson 6: Build and decompose a kilogram to reason about the size and weight of 1 kilogram, 100 grams, 10 grams, and 1 gram. Lesson 7: Develop estimation strategies by reasoning about the weight in kilograms of a series of familiar objects to establish mental benchmark measures. Lesson 8: Solve one-step word problems involving metric weights within 100 and estimate to reason about solutions. Lesson 9: Decompose a liter to reason about the size of 1 liter, 100 milliliters, 10 milliliters, and 1 milliliter. Lesson 10: Estimate and measure liquid volume in liters and milliliters using the vertical number line. Lesson 11: Solve mixed word problems involving all four operations with grams, kilograms, liters, and milliliters given in the same units. 6 Mid-Module Assessment: Topics A B (assessment ½ day, return ½ day, remediation or further applications 1 day) 2 3.NBT.1 3.MD.1 3.MD.2 C Rounding to the Nearest Ten and Hundred Lesson 12: Round two-digit measurements to the nearest ten on the vertical number line. Lesson 13: Round two- and three-digit numbers to the nearest ten on the vertical number line. Lesson 14: Round to the nearest hundred on the vertical number line. 3.NBT.2 D Two- and Three-Digit Measurement Addition Using the Standard Algorithm 3 3 19

3.NBT.1 3.MD.1 3.MD.2 3.NBT.2 3.NBT.1 3.MD.1 3.MD.2 E Lesson 15: Add measurements using the standard algorithm to compose larger units once. Lesson 16: Add measurements using the standard algorithm to compose larger units twice. Lesson 17: Estimate sums by rounding and apply to solve measurement word problems. Two- and Three-Digit Measurement Subtraction Using the Standard Algorithm Lesson 18: Decompose once to subtract measurements including three-digit minuends with zeros in the tens or ones place. Lesson 19: Decompose twice to subtract measurements including three-digit minuends with zeros in the tens and ones places. Lesson 20: Estimate differences by rounding and apply to solve measurement word problems. Lesson 21: Estimate sums and differences of measurements by rounding, and then solve mixed word problems. End-of-Module Assessment: Topics A E (assessment ½ day, return ½ day, remediation or further applications 1 day) Total Number of Instructional Days 25 4 2 20

Module Title Standards Days Month i-ready Lessons 3 Multiplication and Division with Units of 0, 1, 6 9, and Multiples of 10 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9, 3.NBT.3 25 Nov. 24 Jan. 8 Topic A 6; Topic B 3; Topic C 2; Topic D 3, 12; Topic E 13; Topic F 2, 7, 10 This 25-day module builds directly on students work with multiplication and division in Module 1. By this point, Module 1 instruction coupled with fluency practice in Module 2 has students well on their way to meeting the Grade 3 fluency expectation for multiplying and dividing within 100 (3.OA.7). Module 3 extends the study of factors from 2, 3, 4, 5, and 10 to include all units from 0 to 10, as well as multiples of 10 within 100. Similar to the organization of Module 1, the introduction of new factors in Module 3 spreads across topics. This allows students to build fluency with facts involving a particular unit before moving on. The factors are sequenced to facilitate systematic instruction with increasingly sophisticated strategies and patterns. 21

Standards Topics and Objectives Days 3.OA.4 3.OA.5 3.OA.7 3.OA.9 3.OA.1 3.OA.2 3.OA.3 3.OA.6 A The Properties of Multiplication and Division Lesson 1: Study commutativity to find known facts of 6, 7, 8, and 9. Lesson 2: Apply the distributive and commutative properties to relate multiplication facts 5 n + n to 6 n and n 6 where n is the size of the unit. Lesson 3: Multiply and divide with familiar facts using a letter to represent the unknown. 3 3.OA.3 3.OA.4 3.OA.5 3.OA.7 3.OA.9 3.OA.1 3.OA.2 3.OA.6 3.OA.3 3.OA.4 3.OA.5 3.OA.7 3.OA.1 3.OA.2 3.OA.6 3.OA.8 B Multiplication and Division Using Units of 6 and 7 Lesson 4: Count by units of 6 to multiply and divide using number bonds to decompose. Lesson 5: Count by units of 7 to multiply and divide using number bonds to decompose. Lesson 6: Use the distributive property as a strategy to multiply and divide using units of 6 and 7. Lesson 7: Interpret the unknown in multiplication and division to model and solve problems using units of 6 and 7. C Multiplication and Division Using Units up to 8 Lesson 8: Understand the function of parentheses and apply to solving problems. Lesson 9: Model the associative property as a strategy to multiply. Lesson 10: Use the distributive property as a strategy to multiply and divide. Lesson 11: Interpret the unknown in multiplication and division to model and solve problems. Mid-Module Assessment: Topics A C (assessment ½ day, return ½ day, remediation or further applications 1 day) 4 4 2 22

Standards Topics and Objectives Days 3.OA.3 3.OA.4 3.OA.5 3.OA.7 3.OA.9 3.OA.1 3.OA.2 3.OA.6 3.OA.3 3.OA.7 3.OA.8 3.OA.9 3.OA.1 3.OA.2 3.OA.4 3.OA.6 3.OA.5 3.OA.8 3.OA.9 3.NBT.3 3.OA.1 D Multiplication and Division Using Units of 9 Lesson 12: Apply the distributive property and the fact 9 = 10 1 as a strategy to multiply. Lessons 13 14: Identify and use arithmetic patterns to multiply. Lesson 15: Interpret the unknown in multiplication and division to model and solve problems. E Analysis of Patterns and Problem Solving Including Units of 0 and 1 Lesson 16: Reason about and explain arithmetic patterns using units of 0 and 1 as they relate to multiplication and division. Lesson 17: Identify patterns in multiplication and division facts using the multiplication table. Lesson 18: Solve two-step word problems involving all four operations and assess the reasonableness of solutions. F Multiplication of Single-Digit Factors and Multiples of 10 Lesson 19: Multiply by multiples of 10 using the place value chart. Lesson 20: Use place value strategies and the associative property n (m 10) = (n m) 10 (where n and m are less than 10) to multiply by multiples of 10. Lesson 21: Solve two-step word problems involving multiplying single-digit factors and multiples of 10. 4 3 3 End-of-Module Assessment: application 1 day) Topics A F (assessment ½ day, return ½ day, remediation or further 2 Total Number of Instructional Days 25 23

Module Title Standards Days Month i-ready Lessons 4 Multiplication and Area 3.MD.5a, 3.MD.5b, 3.MD.6, 3.MD.7a, 3.MD.7b, 3.MD.7c, 3.MD.7d 20 Jan. 11 Feb. 8 Topic A 27; Topic B 28; Topic C 28; Topic D 29 In this 20-day module students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. In Grade 2, students partitioned a rectangle into rows and columns of same-sized squares and found the total number by both counting and adding equal addends represented by the rows or columns (2.G.2, 2.OA.4). 24

Standards Topics and Objectives Days 3.MD.5 3.MD.6 3.MD.7 A Foundations for Understanding Area Lesson 1: Understand area as an attribute of plane figures. Lesson 2: Decompose and recompose shapes to compare areas. Lesson 3: Model tiling with centimeter and inch unit squares as a strategy to measure area. Lesson 4: Relate side lengths with the number of tiles on a side. 4 3.MD.5 3.MD.6 3.MD.7a 3.MD.7b 3.MD.7d B Concepts of Area Measurement Lesson 5: Form rectangles by tiling with unit squares to make arrays. Lesson 6: Draw rows and columns to determine the area of a rectangle, given an incomplete array. Lesson 7: Interpret area models to form rectangular arrays. Lesson 8: Find the area of a rectangle through multiplication of the side lengths. 4 Mid-Module Assessment: Topics A B (assessment 1 day, return ½ day, remediation or further applications ½ day) 2 3.MD.5 3.MD.6 3.MD.7a 3.MD.7b 3.MD.7c 3.MD.7d 3.MD.6 3.MD.7a 3.MD.7b 3.MD.7c 3.MD.7d 3.MD.5 C D Arithmetic Properties Using Area Models Lesson 9: Analyze different rectangles and reason about their area. Lesson 10: Apply the distributive property as a strategy to find the total area of a large rectangle by adding two products. Lesson 11: Demonstrate the possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property. Applications of Area Using Side Lengths of Figures Lesson 12: Solve word problems involving area. Lessons 13 14: Find areas by decomposing into rectangles or completing composite figures to form rectangles. Lessons 15 16: Apply knowledge of area to determine areas of rooms in a given floor plan. End-of-Module Assessment: Topics A D (assessment 1 day, return ½ day, remediation or further applications ½ day) Total Number of Instructional Days 20 3 5 2 25

Module Title Standards Days Month i-ready Lessons 5 Fractions as Numbers on the Number Line 3.NF.1, 3.NF.2a, 3.NF.2b, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.NF.3d, 3.G.2 35 Feb. 9 Mar. 31 Topic A 33; Topic B 14; Topic C 18; Topic D 15; Topic E 16, 17; Topic F 19 In this 35-day Grade 3 module, students extend and deepen Grade 2 practice with equal shares to understanding fractions as equal partitions of a whole (2.G.3). Their knowledge becomes more formal as they work with area models and the number line. 26

Standards Topics and Objectives Days 3.G.2 3.NF.1 A Partitioning a Whole into Equal Parts Lesson 1: Specify and partition a whole into equal parts, identifying and counting unit fractions using concrete models. Lesson 2: Specify and partition a whole into equal parts, identifying and counting unit fractions by folding fraction strips. Lesson 3: Specify and partition a whole into equal parts, identifying and counting unit fractions by drawing pictorial area models. Lesson 4: Represent and identify fractional parts of different wholes. 4 3.NF.1 3.NF.3c 3.G.2 B Unit Fractions and their Relation to the Whole Lesson 5: Partition a whole into equal parts and define the equal parts to identify the unit fraction numerically. Lesson 6: Build non-unit fractions less than one whole from unit fractions. Lesson 7: Identify and represent shaded and non-shaded parts of one whole as fractions. Lesson 8: Represent parts of one whole as fractions with number bonds. Lesson 9: Build and write fractions greater than one whole using unit fractions. 5 3.NF.3d 3.NF.1 3.NF.3a 3.NF.3b 3.NF.3c 3.G.2 C Comparing Unit Fractions and Specifying the Whole Lesson 10: Compare unit fractions by reasoning about their size using fraction strips. Lesson 11: Compare unit fractions with different sized models representing the whole. Lesson 12: Specify the corresponding whole when presented with one equal part. Lesson 13: Identify a shaded fractional part in different ways depending on the designation of the whole. 4 Mid-Module Assessment: Topics A C (assessment 1 day, return 1 day, remediation or further applications 1 day) 3 3.NF.2a 3.NF.2b 3.NF.3c 3.NF.3d 3.MD.4 D Fractions on the Number Line Lesson 14: Place unit fractions on a number line with endpoints 0 and 1. Lesson 15: Place any fraction on a number line with endpoints 0 and 1. Lesson 16: Place whole number fractions and unit fractions between whole numbers on the number line. Lesson 17: Practice placing various fractions on the number line. 6 27

Standards Topics and Objectives Days Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0. Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional.) 3.NF.3a 3.NF.3b 3.NF.3c E Equivalent Fractions Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape. Lesson 21: Recognize and show that equivalent fractions refer to the same point on the number line. Lessons 22 23: Generate simple equivalent fractions by using visual fraction models and the number line. Lesson 24: Express whole numbers as fractions and recognize equivalence with different units. Lesson 25: Express whole number fractions on the number line when the unit interval is 1. Lesson 26: Decompose whole number fractions greater than 1 using whole number equivalence with various models. Lesson 27: Explain equivalence by manipulating units and reasoning about their size. 8 3.NF.3d F Comparison, Order, and Size of Fractions Lesson 28: Compare fractions with the same numerator pictorially. Lesson 29: Compare fractions with the same numerator using <, >, or = and use a model to reason about their size. Lesson 30: Partition various wholes precisely into equal parts using a number line method. End-of-Module Assessment: Topics A F (assessment 1 day, return 1 day, remediation or further applications 1 day) 3 3 Total Number of Instructional Days 35 28

Module Title Standards Days Month i-ready Lessons 6 Collecting and Displaying Data 3.MD.3 10 Apr. 1 Apr. 12 Topic A 24, 25; Topic B 26 NYSED GRADE 3 MATHEMATICS TEST: WEDNESDAY, APRIL 13 FRIDAY, APRIL 15, 2016 6 Collecting and Displaying Data 3.MD.4 10 Apr. 18 May 2 Topic A 24, 25; Topic B 26 In Module 6, students leave the world of exact measurements behind. By applying their knowledge of fractions from Module 5, they estimate lengths to the nearest halves and fourths of an inch and record that information in bar graphs and line plots. This module also prepares students for the multiplicative comparison problems of Grade 4 by asking students how many more and how many less questions about scaled bar graphs. 29

Standards Topics and Objectives Days 3.MD.3 A Generate and Analyze Categorical Data Lesson 1: Generate and organize data. Lesson 2: Rotate tape diagrams vertically. Lesson 3: Create scaled bar graphs. Lesson 4: Solve one- and two-step problems involving graphs. 3.MD.4 B Generate and Analyze Measurement Data Lesson 5: Create ruler with 1-inch, 1/2-inch, and 1/4-inch intervals and generate measurement data. Lesson 6: Interpret measurement data from various line plots. Lessons 7 8: Represent measurement data with line plots. Lesson 9: Analyze data to problem solve. End-of-Module Assessment: Topics A B (assessment ½ day, return ¼ day, remediation or further applications ¼ day) 4 5 1 Total Number of Instructional Days 10 30

Module Title Standards Days Month i-ready Lessons 7 Geometry and Measurement Word Problems 3.MD.4, 3.MD.8, 3.G.1 36 May 3 Jun. 22 Topic A 12, 13; Topic B 31, 32; Topic C 30; Topic D 26; Topic E 30 The final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter. The year rounds out with plenty of time to solve two-step word problems involving the four operations, and to improve fluency for concepts and skills initiated earlier in the year. In Module 7, students also describe, analyze, and compare properties of two-dimensional shapes. By now, students have done enough work with both linear and area measurement models to understand that there is no relationship in general between the area of a figure and perimeter, which is one of the concepts taught in the last module. 31

Standards Topics and Objectives Days 3.OA.8 A Solving Word Problems Lessons 1 2: Solve word problems in varied contexts using a letter to represent the unknown. Lesson 3: Share and critique peer solution strategies to varied word problems. 3.G.1 B Attributes of Two-Dimensional Figures Lesson 4: Compare and classify quadrilaterals. Lesson 5: Compare and classify other polygons. Lesson 6: Draw polygons with specified attributes to solve problems. Lesson 7: Reason about composing and decomposing polygons using tetrominoes. Lesson 8: Create a tangram puzzle and observe relationships among the shapes. Lesson 9: Reason about composing and decomposing polygons using tangrams. 3.MD.8 3.G.1 C Problem Solving with Perimeter Lesson 10: Decompose quadrilaterals to understand perimeter as the boundary of a shape. Lesson 11: Tessellate to understand perimeter as the boundary of a shape. (Optional.) Lesson 12: Measure side lengths in whole number units to determine the perimeter of polygons. Lesson 13: Explore perimeter as an attribute of plane figures and solve problems. Lesson 14: Determine the perimeter of regular polygons and rectangles when whole number measurements are missing. Lesson 15: Solve word problems to determine perimeter with given side lengths. Lesson 16: Use string to measure the perimeter of various circles to the nearest quarter inch. Lesson 17: Use all four operations to solve problems involving perimeter and missing measurements. Mid-Module Assessment: Topics A C (assessment 1 day) 1 3 6 8 3.MD.4 3.MD.8 3.G.1 D Recording Perimeter and Area Data on Line Plots Lesson 18: Construct rectangles from a given number of unit squares and determine the perimeters. Lesson 19: Use a line plot to record the number of rectangles constructed from a given number of unit squares. Lessons 20 21: Construct rectangles with a given perimeter using unit squares and determine their areas. Lesson 22: Use a line plot to record the number of rectangles constructed in Lessons 20 and 21. 5 32

Standards Topics and Objectives Days 3.MD.8 3.G.1 E Problem Solving with Perimeter and Area Lesson 23: Solve a variety of word problems with perimeter. Lessons 24 27: Use rectangles to draw a robot with specified perimeter measurements, and reason about the different areas that may be produced. Lessons 28 29: Solve a variety of word problems involving area and perimeter using all four operations. Lesson 30: Share and critique peer strategies for problem solving. 8 End-of-Module Assessment: Topics A E (assessment 1 day) 1 F Year in Review Lessons 31 32: Explore and create unconventional representations of one-half. Lesson 33: Solidify fluency with Grade 3 skills. Lesson 34: Create resource booklets to support fluency with Grade 3 skills. Total Number of Instructional Days 36 4 33

WORD WALLS ARE DESIGNED to promote group learning support the teaching of important general principles about words and how they work Foster reading and writing in content area Provide reference support for children during their reading and writing Promote independence on the part of young students as they work with words Provide a visual map to help children remember connections between words and the characteristics that will help them form categories Develop a growing core of words that become part of their vocabulary Important Notice A Mathematics Word Wall must be present in every mathematics classroom. Math Word Wall Create a math word wall Place math words on your current word wall but highlight them in some way.

SETUP OF THE MATHEMATICS CLASSROOM I. Prerequisites for a Mathematics Classroom Teacher Schedule Class List Seating Chart Code of Conduct / Discipline Grade Level Common Core Learning Standards (CCLS) Updated Mathematics Student Work Mathematics Grading Policy Mathematics Diagrams, Charts, Posters, etc. Grade Level Number Line Grade Level Mathematics Word Wall Mathematics Portfolios Mathematics Center with Manipulatives (Grades K - 12) II. III. Updated Student Work A section of the classroom must display recent student work. This can be of any type of assessment, graphic organizer, and writing activity. Teacher feedback must be included on student s work. Board Set-Up Every day, teachers must display the Lesson # and Title, Objective(s), Common Core Learning Standard(s), Opening Exercise and Homework. At the start of the class, students are to copy this information and immediately begin on the Fluency Activity or Opening Exercise. Student s Name: Teacher s Name: School: Date: Lesson # and Title: Objective(s) CCLS: Opening Exercise: IV. Spiraling Homework Homework is used to reinforce daily learning objectives. The secondary purpose of homework is to reinforce objectives learned earlier in the year. The assessments are cumulative, spiraling homework requires students to review coursework throughout the year. 35