Third Grade Common Core State Standards

Wayne County Public Schools Revised July, 2015 Curriculum Guide for Grade 3 Mathematics 2010 NC Standard Course of Study for Mathematics Grade 3 Overview  Operations and Algebraic Thinking (Weight on NC READY EOG: 30 – 35%) o Represent and solve problems involving multiplication and division. o Understand properties of multiplication and the relationship between multiplication and division. o Multiply and divide within 100. o Solve problems involving the four operations, and identify & explain patterns in arithmetic – use order of operations.  Number and Operations in Base Ten (Weight on NC READY EOG: 5 – 10%) o Use place value understanding and properties of operations to perform multi-digit arithmetic – round whole numbers to the nearest 10 or 100; add/subtract within 1000; multiply 1-digit whole numbers by multiples of 10 in the range 10 – 90.  Number and Operation – Fractions (with denominators: 2, 3, 4, 6, 8) (Weight on NC READY EOG: 20 – 25%) o Develop understanding of fractions as numbers --- partitioning a whole into equal parts; representing a fraction as a number on the number line; equivalence of fractions.  Measurement and Data (Weight on NC READY EOG: 22 – 27%) o Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects -- time to the nearest minute and time intervals in minutes; liquid volumes and masses of objects using standard units of g, kg, ml and l. o Represent and interpret data – with several categories. Use scaled picture graphs & scaled bar graphs; use line plots with markings in appropriate units – whole numbers, halves, or quarters. o Geometric measurement: understand concepts of area and relate area to multiplication and to addition. o Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.  Geometry (Weight on NC READY EOG: 10 – 15%) o Reason with shapes and their attributes. Identify shared attributes of shapes in different categories. Partition shapes into parts with equal areas; express the area of each part as a unit fraction of the whole. Resources: NC SCoS K – 12 Mathematics Standards: http://www.ncpublicschools.org/docs/acre/standards/common-core/standards-k-12.pdf NC DPI NC COMMON CORE INSTRUCTIONAL SUPPORT TOOLS Home page: http://www.ncpublicschools.org/acre/standards/common-core-tools/

*** NC DPI Grade 3 Unpacking Document: http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/3rd.pdf *** NC Math Wiki: Elementary Resources http://maccss.ncdpi.wikispaces.net/Elementary NC DPI Grade 3 Quick Reference Guide: http://aplus.ncdpi.wikispaces.net/file/view/ReferenceGuide_3rd_grade.pdf Building Conceptual Understanding and Fluency through Games: Grade 3 Games: http://maccss.ncdpi.wikispaces.net/file/view/3rdgrade_GAMES_8.22.14.pdf/519547204/3rdgrade_GAMES_8.22.14.pdf

Textbook Series: enVision Math, © 2009, Scott Foresman-Addison Wesley Investigations in Number, Data and Space, Pearson Publishing Investigations and the Common Core State Standards in Math: http://investigations.terc.edu/components/CCSS/CommonCore.cfm Math Common Core State Standards Grade 2 Correlations: http://investigations.terc.edu/library/common_core/G3_InvCCSS_Corr.pdf

CCSS : Standards for Mathematical Practice

Note: These 8 Standards for Mathematical Practice play a critical role in student understanding of the content standards set forth in the NC Standard Course of Study for Mathematics, grades K – 12. 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.

Third Grade – 2010 NC Standard Course of Study – MATH Based on the Common Core Standards for Mathematics Critical Areas 1. Developing understanding of multiplication and division and strategies for multiplication and division within 100 – Students develop an understanding 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in of the meanings of multiplication and division of whole numbers through 5 groups of 7 objects each. For example, describe a context in which a total number of activities and problems involving equal-sized groups, arrays, and area models; objects can be expressed as 5 × 7. multiplication is finding an unknown product, and division is finding an 3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of Students use properties of operations to calculate products of whole numbers, shares when 56 objects are partitioned into equal shares of 8 objects each. For example describe using increasingly sophisticated strategies based on these properties to solve a context in which a number of shares or a number of groups can be expressed a 56 ÷ 8. multiplication and division problems involving single-digit factors. By 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal comparing a variety of solution strategies, students learn the relationship groups, arrays, and measurement quantities, e.g., by using drawings and equations with a between multiplication and division. symbol 2. Developing understanding of fractions, especially unit fractions (fractions for the unknown number to represent the problem. (Note: See CCSS Glossary & Table 2.) with numerator 1) – Students develop an understanding of fractions, 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three beginning with unit fractions. Students view fractions in general as being built whole numbers. For example,determine the unknown number that makes the equation true in 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 each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?. is relative to the size of the whole. For example, 1/2 of the paint in a small Understand properties of multiplication and the relationship between multiplication and division. bucket could be less paint than 1/3 of the paint in a larger bucket; but 1/3 of a 3.OA.5 Apply properties of operations as strategies to multiply and divide. (Note: Students need not use ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is 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, also known --commutative property of multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, less than, and greater than one. They solve problems that involve comparing then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 --associative property of multiplication. fractions by using visual fraction models and strategies based on noticing Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = equal numerators or denominators. 40 + 16 = 56 --distributive property. 3. Developing understanding of the structure of rectangular arrays and of 3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the area – Students recognize area as an attribute of two-dimensional regions. number that makes 32 when multiplied by 8. 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 Multiply and divide within 100. with sides of unit length being the standard unit for measuring area. Students 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between understand that rectangular arrays can be decomposed into identical rows or multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties into identical columns. By decomposing rectangles into rectangular arrays of of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. Solve problems involving the four operations, and identify and explain patterns in arithmetic. 4. Describing and analyzing two-dimensional shapes – Students describe, 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using analyze, and compare properties of two-dimensional shapes. They compare and equations with a letter standing for the unknown quantity. Assess the reasonableness of answers classify shapes by their sides and angles, and connect these with definitions of using mental computation and estimation strategies including rounding. (Note: This standard is shapes. Students also relate their fraction work to geometry by expressing the limited to problems posed with whole numbers and having whole-number answers; students area of part of a shape as a unit fraction of the whole. should know how to perform operations in the conventional order when there are no parentheses Mathematical Practices to specify a particular order – Order of Operations.) 1. Make sense of problems and persevere in solving them. 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), 2. Reason abstractly and quantitatively. and explain them using properties of operations. For example, observe that 4 times a number is 3. Construct viable arguments and critique the reasoning of others. always even, and explain why 4 times a number can be decomposed into two equal addends. 4. Model with mathematics. 5. Use appropriate tools strategically. Number and Operations in Base Ten (Weight of Standard: 5 – 10%) 3.NBT 6. Attend to precision. Use place value understanding and properties of operations to perform multi-digit arithmetic. 7. Look for and make use of structure. (Note: A range of algorithms may be used.) 8. Look for and express regularity in repeated reasoning. 3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Operations and Algebraic Thinking (Weight of 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, Standard: 30 – 35%) 3.OA properties of operations, and/or the relationship between addition and subtraction. Represent and solve problems involving multiplication and division. 3.NBT.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. Number and Operations – Fractions (Weight of Std: 20 – 25%) 3.NF 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is Note: Grade 3 expectations are limited to fractions with denominators 2, 3, 4, 6, and 8. partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Develop understanding of fractions as numbers. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a scale is marked off in appropriate units – whole numbers, halves, or quarters. number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval Geometric measurement: understand concepts of area and relate area to multiplication from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that and to addition. each part has size 1/b and that the endpoint of the part based at 0 locates the 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area number 1/b on the number line. measurement. b. Represent a fraction a/b on a number line diagram by marking off a lengths a. A square with side length 1 unit, called “a unit square,” is said to have “one 1/b from 0. Recognize that the resulting interval has size a/b and that its square unit” of area, and can be used to measure area. endpoint locates the number a/b on the number line. b. A plane figure which can be covered without gaps or overlaps by n unit 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by squares is said to have an area of n square units. reasoning about their size. 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square a. Understand two fractions as equivalent (equal) if they are the same size, or ft, and improvised units). the same point on a number line. 3.MD.7 Relate area to the operations of multiplication and addition. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). a. Find the area of a rectangle with whole-number side lengths by tiling it, and Explain why the fractions are equivalent, e.g., by using a visual fraction show that the area is the same as would be found by multiplying the side lengths. model. b. Multiply side lengths to find areas of rectangles with whole-number side lengths c. Express whole numbers as fractions, and recognize fractions that are in the context of solving real world and mathematical problems, and represent equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; whole-number products as rectangular areas in mathematical reasoning. recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line c. Use tiling to show in a concrete case that the area of a rectangle with whole- diagram. number side lengths a and b + c is the sum of a × b and a × c. Use area models d. Compare two fractions with the same numerator or the same denominator by to represent the distributive property in mathematical reasoning. reasoning about their size. Recognize that comparisons are valid only when d. Recognize area as additive. Find areas of rectilinear figures by decomposing the two fractions refer to the same whole. Record the results of comparisons them into non-overlapping rectangles and adding the areas of the non- with the symbols >, =, or <, and justify the conclusions, e.g., by using a overlapping parts, applying this technique to solve real world problems. visual fraction model. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Measurement and Data (Weight of Standard: 22 – 27%) 3.MD 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, Solve problems involving measurement and estimation of intervals of time, liquid including finding the perimeter given the side lengths, finding an unknown side volumes, and masses of objects. length, and exhibiting rectangles with the same perimeter and different areas or 3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. with the same area and different perimeters. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Geometry (Weight of Standard: 10 – 15%) 3.G 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard Reason with shapes and their attributes. units of grams (g), kilograms (kg), and liters (l). (Note: Excludes compound 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and 3 units such as cm and finding the geometric volume of a container.) Add, others) may share attributes (e.g., having four sides), and that the shared attributes subtract, multiply, or divide to solve one-step word problems involving masses can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, or volumes that are given in the same units, e.g., by using drawings (such as a and squares as examples of quadrilaterals, and draw examples of quadrilaterals that beaker with a measurement scale) to represent the problem. (Note: Excludes do not belong to any of these subcategories. multiplicative comparison problems – problems involving notions of “times as 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit much”; see CCSS Glossary & Table 2.) 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.

Represent and interpret data. 3.MD.3 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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.MD.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 Major Work of the Grade Third Grade Major Clusters Supporting/Additional Clusters Operations and Algebraic Thinking Number and Operations in Base Ten  Represent and solve problems involving  Use place value understanding and multiplication and division. properties of operations to perform multi- digit arithmetic.  Understand properties of multiplication and the relationship between multiplication and division. Measurement and Data  Represent and interpret data.  Multiply and divide within 100.  Geometric measurement: recognize  Solve problems involving the four perimeter as an attribute of plane figures operations, and identify and explain and distinguish between linear and area patterns in arithmetic. measures.

Number and Operations—Fractions Geometry  Develop understanding of fractions as  Reason with shapes and their attributes. numbers.

Measurement and Data  Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Wayne County Public Schools 2010 NC Standard Course of Study: Mathematics Grade 3 Mathematics At-A-Glance Note: All teachers should have Investigations Teacher Resources; they were part of the enVision Math Textbook Adoption in 2009. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Operations and 3.OA.8 3.OA.4 3.OA.2 3.OA.4 Continuously Review Algebraic Thinking 3.OA.9 3.OA.5 3.OA.3 3.OA.5 3.OA.8 3.OA.6 3.OA.3 (30% – 35%) 3.OA.7 3.OA.1 3.OA.8 3.OA.7 3.OA.4

3.OA.3 3.OA.5 3.OA.8 3.OA.8 3.OA.9 Multiplication Symbols: x or * Multiplication Symbols: x or * Multiplication Symbols: x or * Multiplication Symbols: x or * Division Symbols: ÷ or / Division Symbols: ÷ or / Division Symbols: ÷ or / Division Symbols: ÷ or / Number and 3.NBT.1 3.NBT.3 Operations in Base 3.NBT.2 Ten (5% - 10%) Number and 3.NF.1 3.NF.2 Operations – 3.NF.3 Fractions (20% – 25%) Measurement and 3.MD.3 3.MD.1 3.MD.4 3.MD.2 Data 3.MD.5 3.MD.8 (22% – 27%) 3.MD.6 3.MD.7 3.MD.8 Geometry 3.G.1 3.G.2 (10% – 15%) Textbook: Use NC DPI’s Grade 3 Math Use NC DPI’s Grade 3 Math Unpacking Use NC DPI’s Grade 3 Math Unpacking Use NC DPI’s Grade 3 Math Unpacking enVision Math, © Unpacking Document Document Document Document Supplement with Textbook as Appropriate. Supplement with Textbook as Appropriate. Supplement with Textbook as Appropriate. Supplement with Textbook as Appropriate. 2009, Student 3 .OA.1; 3.OA.3 3OA.4; 3.OA.5; 3 .OA.7; 3.OA.8; 3.OA.9 3.OA.2; 3.OA.3; 3.OA.8 3.MD.2 Textbook and Topic 5: Lessons: 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, Topic 5: Lessons: 5-1, 5-2, 5-3, 5-4, 5-5, Topic 7: Lessons: 7-1, 7-3, 7-4, 7-5 Topic 15: Lessons: 15-3, 15-4 Investigations, 5-7, 5-8, 5-9, 5-10 5-6, 5-7, 5-8, 5-9, 5-10 Topic 8: Lessons: 8-1, 8-2, 8-3, 8-4, 8-5, 3.MD.8 Teacher Resources Topic 6: Lessons: 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7 Topic 6: Lessons: 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 8-6 Topic 16: Lessons: 16-1, 16-2, 16-3, Topic 12: Lesson: 12-10 6-7 3.NF.2; 3.NF.3 16-5, 16-6, 16-8 3.NBT.1 Topic 9: Lessons: 9-1, 9-2, 9-3, 9-6 Topic 12: Lessons: 12-2, 12-3, 12-4, 12-5, 3.OA.3; 3.OA.4; 3.OA.5; 3.OA.6; 3.OA.7; Primary/Best Topic 1: Lessons: 1-1, 1-5, 1-6 Topic 12: Lesson: 12-10 12-6, 12-7 3.OA.8 Resource: Topic 2: Lessons: 2-4, 2-8 Topic 18: Lesson: 18-1, 18-4 Topic 7: Lessons: 7-1, 7-3, 7-4, 7-5 3.NBT.2:3.OA.8; 3.OA.9 3.NF.1 3.MD.4 Topic 8: Lessons: 8-1, 8-2, 8-3, 8-4, 8-5, NC DPI’s Grade Topic 2: Lessons: 2-1, 2-2, 2-5, 2-6, 2-7, Topic 12: Lessons: 12-2, 12-3 Topic 14: Lessons: 14-1,14-2 8-6 3 Math 2-8, 2-9, 2-10 3.MD.1 Topic 20: Lesson: 20-8 Topic 3: Lessons: 3-1, 3-4, 3-5 Topic 17: Lessons: 17-1, 17-2, 17-3, 17-4 Unpacking Topic 4: Lessons: 4-1, 4-2, 4-3, 4-4, 4-5, 4-6 3.G.2 3.MD.5; 3.MD.6; 3.MD.7; 3.MD.8 Document Topic 16: Lesson: 16-4 Topic 12: Lesson: 12-1 Topic 16: Lessons: 16-1, 16-2, 16-3, 16-5, 3.MD.3 16-6, 16-8 Topic 20: Lessons: 20-1, 20-2, 20-3, 20-4, 20-9 3.G.1

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Topic 10: Lessons: 10-5, 10-6, 10-7, 10-8

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Wayne County Public Schools 2010 NC Standard Course of Study: Mathematics Grade 3 Mathematics At-A-Glance Pacing Guide w/Abbreviated Standards Note: All teachers should have Investigations Teacher Resources; they were part of the enVision Math Textbook Adoption in 2009. Domain First Quarter Second Quarter Third Quarter Fourth Quarter Operations and 3.OA.8- Focus on Addition & Subtraction Word 3.OA.4 – Focus on Multiplication Equation 3.OA.2 – Interpret whole number 3.OA.4 - Focus on Division equation Algebraic Thinking Problems(2-step problems) relating 3 Whole Numbers quotations; model division with relating 3 whole numbers (30% – 35%) 3.OA.9- Focus on Addition Pattern; explain 3.OA.5 – Focus on Multiplication partitioning equally 3.OA.5 - Focus on Division patterns using properties of operations 3.OA.7 – Focus on Multiplication - fluently x 3.OA.3 - Focus on Division within 100 3.OA.6 - Focus on Division 3.OA.7 - Focus on Division 3.OA.1 – Interpret products on whole numbers within 100 3.OA.8 - Focus on Division (2-step word 3.OA.3 – Focus on Multiplication within 100 3.OA.8 - Focus on Division (2-step 3.OA.8 – Focus on Multiplication Word problems) Problems- (2-step word problems) word problems) 3.OA.9 – Focus on Addition & Multiplication Use all 4 operations to solve 2-step Pattern; explain patterns using properties of word problems. operations Multiplication Symbols: x or * Multiplication Symbols: x or * Multiplication Symbols: x or * Multiplication Symbols: x or * Division Symbols: ÷ or / Division Symbols: ÷ or / Division Symbols: ÷ or / Division Symbols: ÷ or / Number and 3.NBT.1 - Place value; round to nearest 10 or 100 3.NBT.3 - Multiply 1–digit numbers by Operations in Base 3.NBT.2 - Problem solve with + & - within 1,000 multiples of 10 in the range 10 - 90 Ten (5% - 10%) Number and 3.NF.1 - Fractions: parts of whole; parts of 3.NF.2 - Fractions: represent on a number Operations – a set; partitioning into equal parts line diagram Fractions 3.NF.3 - Explain equivalence of fractions; compare by reasoning about their size (20% – 25%) Measurement and 3.MD.3 - Draw a scaled picture graph and a scaled 3.MD.1 – Time to the nearest minute; 3.MD.4 - Measure lengths to nearest whole, 3.MD.2 - Measure/estimate liquid Data bar-graph to represent data elapsed time on a number line diagram half, or one-fourth of an inch; record on a volumes and masses of objects line plot (22% – 27%) Note: In 3rd grade, students are expected 3.MD.8 – Perimeter of polygons to tell time within the hour; in 4th grade, 3.MD.5 – Relate concept of area to x & + students are expected to tell time over the 3.MD.6– Relate concept of area to x & + hour. 3.MD.7– Relate concept of area to x & + 3.MD.8 – Perimeter of polygons Geometry 3.G.1 - Investigate/classify 2D shapes and their 3.G.2 -Partition shapes into parts with (10% – 15%) attributes equal areas Textbook: Use NC DPI’s Grade 3 Math Unpacking Document Use NC DPI’s Grade 3 Math Unpacking Document Use NC DPI’s Grade 3 Math Unpacking Document Use NC DPI’s Grade 3 Math Unpacking Supplement with Textbook as Appropriate. Supplement with Textbook as Appropriate. Supplement with Textbook as Appropriate. Document enVision Math, © 3.OA.1; 3.OA.3 3OA.4; 3.OA.5; 3.OA.7; 3.OA.8; 3.OA.9 3.OA.2; 3.OA.3; 3.OA.8 Supplement with Textbook as Appropriate. 2009, Student Topic 5: Lessons: 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, Topic 5: Lessons: 5-1, 5-2, 5-3, 5-4, 5-5, Topic 7: Lessons: 7-1, 7-3, 7-4, 7-5 3.MD.2 Textbook and 5-7, 5-8, 5-9, 5-10 5-6, 5-7, 5-8, 5-9, 5-10 Topic 8: Lessons: 8-1, 8-2, 8-3, 8-4, Topic 15: Lessons: 15-3, 15-4 Investigations, Topic 6: Lessons: 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7 Topic 6: Lessons: 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 8-5, 8-6 3.MD.8 Topic 12: Lesson: 12-10 6-7 3.NF.2; 3.NF.3 Topic 16: Lessons: 16-1, 16-2, 16-3, Teacher Resources 3.NBT.1 Topic 9: Lessons: 9-1, 9-2, 9-3, 9-6 Topic 12: Lessons: 12-2, 12-3, 12-4, 16-5, 16-6, 16-8 Topic 1: Lessons: 1-1, 1-5, 1-6 Topic 12: Lesson: 12-10 12-5, 12-6, 12-7 3.OA.3; 3.OA.4; 3.OA.5; 3.OA.6; 3.OA.7; Primary/Best Topic 2: Lessons: 2-4, 2-8 Topic 18: Lesson: 18-1, 18-4 3.MD.4 3.OA.8 3.NBT.2:3.OA.8; 3.OA.9 3.NF.1 Topic 14: Lessons: 14-1,14-2 Topic 7: Lessons: 7-1, 7-3, 7-4, 7-5 Resource: Topic 2: Lessons: 2-1, 2-2, 2-5, 2-6, 2-7, 2-8, 2-9, 2-10 Topic 12: Lessons: 12-2, 12-3 Topic 20: Lesson: 20-8 Topic 8: Lessons: 8-1, 8-2, 8-3, 8-4, Topic 3: Lessons: 3-1, 3-4, 3-5 3.MD.1 3.MD.5; 3.MD.6; 3.MD.7; 3.MD.8 8-5, 8-6 NC DPI’s Grade Topic 4: Lessons: 4-1, 4-2, 4-3, 4-4, 4-5, 4-6 Topic 17: Lessons: 17-1, 17-2, 17-3, 17-4 Topic 16: Lessons: 16-1, 16-2, 16-3, 3 Math Topic 16: Lesson: 16-4 3.G.2 16-5, 16-6, 16-8 3.MD.3 Topic 12: Lesson: 12-1 Unpacking Topic 20: Lessons: 20-1, 20-2, 20-3, 20-4, 20-9 Document 3.G.1 Topic 10: Lessons: 10-5, 10-6, 10-7, 10-8

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Wayne County Public Schools Revisions (07/2015) to Pacing Guide are denoted in RED. 2010 NC Standard Course of Study: Mathematics Grade 3 Mathematics Pacing Guide w/Complete Standards Note: All teachers should have Investigations Teacher Resources; they were part of the enVision Math Textbook Adoption in 2009. Gr. 3 Domains First Quarter Second Quarter Third Quarter Fourth Quarter Operations and 3.OA.8 Solve 2-step word problems; Focus on 3.OA.4 Determine the unknown whole 3.OA.2 – Interpret whole-number 3.OA.4 Determine the unknown whole number in Addition & Subtraction Word Problems number in a multiplication equation relating quotients of whole numbers; model a division equation relating 3 whole numbers - Algebraic 3 whole numbers; Focus on Multiplication division with partitioning equally Focus on Division equations relating 3 whole Thinking 3.OA.9 Identify arithmetic patterns (including Equations relating 3 Whole Numbers. numbers. (30% – 35%) patterns in the addition table); Focus on 3.OA.3 Use division within 100 to Addition Patterns; explain patterns using 3.OA.5 Apply properties of operations as solve word problems in situations 3.OA.5 Apply properties of operations as strategies to divide; – Focus on Division 3.OA.1 – 3.OA.4 properties of operations; identify arithmetic strategies to multiply; – Focus on involving equal groups, arrays, and patterns using input and output tables Multiplication measurement quantities – by using (Note: Students do not need to use formal terms Represent and solve (Note: Students do not need to use formal drawings and equations with a symbol for these properties -- commutative, associative, problems involving terms for these properties -- commutative, for the unknown number to represent distributive…) multiplication and associative, distributive…) the problem - Focus on Division 3.OA.6 Understand division as an unknown-factor division. within 100. problem. 3.OA.7 – Fluently multiply within 100; - 3.OA.7 – Fluently multiply & divide within 100, 3.OA.5 - 3.OA6 3.OA.1 Interpret products of whole numbers. Focus on Multiplication within 100. using strategies such as the relationship between x Understand properties Note: By the end of grade 3, know and ÷; - Focus on Division within 100. of multiplication and the 3.OA.3 Use multiplication within 100 to from memory all product of 2 one-digit relationship between solve word problems in situations involving numbers. 3.OA.8 Solve 2-step word problems; Focus on multiplication and equal groups, arrays, and measurement Division division. quantities – by using drawings and equations Continuously Review: with a symbol for the unknown number to 3.OA.8 3.OA.8 3.OA.7 represent the problem.– Focus on 3.OA.8 Solve 2-step word problems using the Multiply and divide Solve 2-step word problems; Focus on Solve 2-step word problems using the 4 Multiplication within 100. 4 operations: +, -, X, ÷ operations: +, -, X, ÷ within 100. Addition, Subtraction, and Multiplication Word Problems. 3.OA.3 Use multiplication and division within Note: By the end of 100 to solve word problems in situations involving grade 3, know from equal groups, arrays, and measurement quantities memory all products of – by using drawings and equations with a symbol 2 one-digit numbers. 3.OA.9 for the unknown number to represent the problem Identify arithmetic patterns (including 3.OA.4 Determine the unknown whole number in 3.OA.8 – 3.OA.9 patterns in the addition table or a multiplication or division equation relating 3 Solve 2-step word multiplication table) – Focus on Addition & whole numbers. problems using the 4 Multiplication Patterns; explain patterns 3.OA.5 Apply properties of operations as operations, and identify using properties of operations; identify strategies to multiply ÷. & explain patterns in arithmetic patterns using input and output (Note: Students do not need to use formal terms arithmetic. tables. for these properties -- commutative, associative, distributive…) Multiplication Symbols: x or * Multiplication Symbols: x or * Multiplication Symbols: x or * Multiplication Symbols: x or * Division Symbols: ÷ or / Division Symbols: ÷ or / Division Symbols: ÷ or / Division Symbols: ÷ or / Number and 3.NBT.1 Use place value understanding to 3.NBT.3 - Multiply 1–digit whole numbers round whole numbers to nearest 10 or 100. by multiples of 10 in the range 10 – 90 Operations in using strategies based on place value and Base Ten 3.NBT.2 - Fluently add & subtract within properties of operations. (5% - 10%) 1000 using computation strategies and Focus on the special role of 10 in the base- computation algorithms based on place value, ten system. 3.NBT.1 – 3.NBT3 properties of operations, and/or the Use place value relationship between addition and subtraction; understanding and Problem solve with + & - within 1,000 properties of operations to perform multi-digit Note: A range of algorithms may be used. Note: A range of algorithms may be used. arithmetic. Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Gr. 3 Domains First Quarter Second Quarter Third Quarter Fourth Quarter Number and 3.NF.1 Understand a fraction of the form 3.NF.2 Understand a fraction as a 1/b (unit fraction -- has a numerator of 1) number on a number line; represent Operations – as the quantity formed by 1 part when a fractions on a number line diagram –-- Fractions whole is partitioned into b equal parts; represent a fraction 1/b on a number (20% – 25%) understand a fraction of the form a/b as a line diagram by defining the interval 0 quantity formed by a parts of size 1/b. to 1 as the whole and partitioning it Note: Grade 3 Fractions: parts of a whole; parts of a set; into b equal parts; represent the expectations are limited to partitioning into equal parts. fraction a/b on a number line diagram fractions with Students express fractions as fair sharing, by marking off a lengths of size 1/b denominators 2, 3, 4, 6, parts of a whole. from 0. and 8. 3.NF.3 - Explain equivalence of Note: Students will build fractions from fractions; compare fractions (with the 3.NF.1 – 3.NF.3 unit fractions. There is no need to same denominator) by reasoning about Develop understanding introduce “improper fractions” initially. their size. Understand equality and of fractions as numbers. inequality. Note: Teach this standard with 3.G.2. Note: Recognize that comparisons are valid only when the 2 fractions refer to the same whole. Record the results of comparisons with the symbols; >, =. <; justify the conclusions using a visual fraction model. Measurement and 3.MD.3 - Draw a scaled picture graph and a 3.MD.1 – Tell and write time to the nearest 3.MD.4 – Generate measurement data 3.MD.8 – Solve real world problems involving scaled bar-graph to represent a data set with minute and measure time intervals in by measuring lengths using rulers Perimeter of polygons - may include irregular Data several categories. minutes; marked with halves, and fourths of an shapes. Extend the problem solving to include (22% – 27%) Solve one- & two-step word problems asking Solve word problems involving additions & inch. Show the data by making a line finding an unknown side length and to exhibiting 3.MD.1 – 3.MD.2 How many more? and How many less? using subtraction of time intervals in minutes plot, where the horizontal scale is rectangles with the same perimeter and different Solve problems information presented in scaled bar graphs. using a number line diagram --- represent marked off in appropriate units --- areas or with the same area and different elapsed time on a number line diagram. whole numbers, halves, or quarters. perimeters. involving measurement & estimation of intervals Note: In 3rd grade, students are expected of time, liquid volumes, to tell time within the hour; in 4th grade, and masses of objects. students are expected to tell time over the 3.MD.5 – Recognize area as an rd Note: In 3 grade, hour. attribute of plane figures and students are expected to understand concepts of area 3.MD.2 - Measure/estimate liquid volumes and tell time within the hour; measurement. masses of objects using standard units of g, kg, ml, th in 4 grade, students are 3.MD.6– Measure areas by counting and l. expected to tell time over unit squares (square cm, square m, +, -, x, ÷ to solve 1-step word problems involving the hour. square in, square ft, and improvised masses or volumes that are given in the same units units). by using drawings. 3.MD.3 – 3.MD.4 3.MD.7– Relate concept of area to the Note; Students are not expected to do conversions Represent & interpret operations of x & +. between units, but reason as they estimate, using data. (use tiling; recognize area as additive benchmarks to measure weight and capacity. 3.MD.5 – 3.MD.7 by decomposing rectilinear figures Note: Standards do not differentiate between Geometric measurement: into non-overlapping rectangles, etc) weight and mass. understand concept of area and relate area to multiplication and to addition. 3.MD. 8 Geometric measurement: 3.MD.8 – Solve real world and recognize perimeter as an mathematical problems involving attribute of plane figures perimeters of polygons -- finding the & distinguish between perimeter given the side lengths. linear and area measures.

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Gr. 3 Domains First Quarter Second Quarter Third Quarter Fourth Quarter Geometry 3.G.1 Understand that shapes in different 3.G.2 -Partition shapes into parts with equal (10% – 15%) categories (rhombuses, rectangles, areas. Express the area of each part as a parallelogram, etc) may share attributes unit fraction of the whole. 3.G.1. – 3.G.2 (having 4 sides, vertices, corners, etc), and that the shared attributes can define a Note: Teach this standard with 3.NF.1. Reason with shapes and larger category (quadrilaterals). Recognize their attributes. rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories (examples, non-examples). Investigate/ classify 2D shapes and their attributes; recognize examples and non-examples. Textbook: Use NC DPI’s Grade 3 Math Use NC DPI’s Grade 3 Math Unpacking Use NC DPI’s Grade 3 Math Use NC DPI’s Grade 3 Math Unpacking enVision Math, © Unpacking Document Document Unpacking Document Document Supplement with Textbook as Appropriate. Supplement with Textbook as Appropriate. Supplement with Textbook as Supplement with Textbook as Appropriate. 2009, Student 3 .OA.1; 3.OA.3 3OA.4; 3.OA.5; 3 .OA.7; 3.OA.8; 3.OA.9 Appropriate. 3.MD.2 Textbook and Topic 5: Lessons: 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, Topic 5: Lessons: 5-1, 5-2, 5-3, 5-4, 5-5, 3.OA.2; 3.OA.3; 3.OA.8 Topic 15: Lessons: 15-3, 15-4 Investigations, 5-7, 5-8, 5-9, 5-10 5-6, 5-7, 5-8, 5-9, 5-10 Topic 7: Lessons: 7-1, 7-3, 7-4, 7-5 3.MD.8 Teacher Resources Topic 6: Lessons: 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, Topic 6: Lessons: 6-1, 6-2, 6-3, 6-4, 6-5, Topic 8: Lessons: 8-1, 8-2, 8-3, 8-4, Topic 16: Lessons: 16-1, 16-2, 16-3, 6-7 6-6, 6-7 8-5, 8-6 16-5, 16-6, 16-8 Topic 12: Lesson: 12-10 Topic 9: Lessons: 9-1, 9-2, 9-3, 9-6 3.NF.2; 3.NF.3 3.OA.3; 3.OA.4; 3.OA.5; 3.OA.6; 3.OA.7; 3.OA.8 Primary/Best 3.NBT.1 Topic 12: Lesson: 12-10 Topic 12: Lessons: 12-2, 12-3, 12-4, Topic 7: Lessons: 7-1, 7-3, 7-4, 7-5 Resource: Topic 1: Lessons: 1-1, 1-5, 1-6 Topic 18: Lesson: 18-1, 18-4 12-5, 12-6, 12-7 Topic 8: Lessons: 8-1, 8-2, 8-3, 8-4, 8-5, Topic 2: Lessons: 2-4, 2-8 3.NF.1 8-6 NC DPI’s Grade 3 3.NBT.2:3.OA.8; 3.OA.9 Topic 12: Lessons: 12-2, 12-3 3.MD.4 Math Unpacking Topic 2: Lessons: 2-1, 2-2, 2-5, 2-6, 2-7, 3.MD.1 Topic 14: Lessons: 14-1,14-2 2-8, 2-9, 2-10 Topic 17: Lessons: 17-1, 17-2, 17-3, 17-4 Topic 20: Lesson: 20-8 Document Topic 3: Lessons: 3-1, 3-4, 3-5 3.G.2 Topic 4: Lessons: 4-1, 4-2, 4-3, 4-4, 4-5, 4-6 Topic 12: Lesson: 12-1 3.MD.5; 3.MD.6; 3.MD.7; 3.MD.8 Topic 16: Lesson: 16-4 Topic 16: Lessons: 16-1, 16-2, 16-3, 3.MD.3 16-5, 16-6, 16-8 Topic 20: Lessons: 20-1, 20-2, 20-3, 20-4, 20-9 3.G.1 Topic 10: Lessons: 10-5, 10-6, 10-7, 10-8

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015

Wayne County Public Schools Grade 3 Math Scope and Sequence: Units, Standards, and “I Can” Statements

Quarter 1 Units (Suggested # of Days) Math Standards “I Can” Statements Addition and Subtraction : (15 days) Apply Place Value Understanding to Rounding and to 3.NBT.1 Use place value understanding to round whole numbers to nearest 3.NBT.1 I can round a whole number to Addition & Subtraction 10 or 100. the nearest 10 and nearest 100. 3.NBT.2 Fluently + and – within 1000 using strategies and algorithms 3.NBT.2 I can use strategies for adding based on place value, properties of operations, and/or the relationship and subtracting within 1000. between addition and subtraction 3.OA.8 I can use + and – to solve 2-step word Problem Solve: + and - 3.OA.8 Solve 2-step word problems: + and – problems where a variable is used to represent an unknown quantity. I can use strategies to decide if my answer is reasonable. Identify Arithmetic Patterns – focus on addition patterns 3.OA.9 Identify arithmetic patterns --- focus on addition patterns, including 3.OA.9 I can identify and explain addition patterns in the addition table; explain patterns using properties of operations; patterns such as those in the addition table. I can identify addition patterns using input and output identify arithmetic patterns using input and output tables tables. Multiplication: (10 days) Interpret Products of Whole Numbers 3.OA.1 Interpret products of whole numbers. 3.OA.1 I can use multiplication to find the total number of objects in an array or equal groups. Explore Multiplication 3.OA.3 Use multiplication within 100 to solve word problems using equal 3.OA.3 I can multiply within 100 to Problem Solve using equal groups. arrays, and groups, arrays, and measurement quantities; use drawings and equations solve word problems. measurement quantities. with a symbol for the unknown number to represent the problem. Measurement & Data: Scaled Graphs: (7 days) - Represent/Interpret Data using Scaled Picture Graphs 3.MD.3 Draw a scaled picture graph and a scaled bar-graph to represent a 3.MD.3 I can create a scaled picture & Scaled Bar-Graphs; data set with several categories. graph and a scaled bar graph with - Problem Solve using Information Displayed in Scaled - Solve one- & two- step word problems asking How many more? and How multiple categories. Bar Graphs many less? using information presented in scaled bar graphs. - I can analyze graphs to solve problems. Geometry: (8 days) Reason with Shapes (Quadrilaterals) and Their 3.G.1 Understand that shapes in different categories (rhombuses, 3.G.1. I understand that all shapes Attributes rectangles, parallelograms, etc) may share attributes (having 4 sides) and within a category share similar that the shared attributes can define a larger category (quadrilaterals). attributes. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, - I can identify and describe shapes and draw examples of quadrilaterals that do not belong to any of these based on their attributes. subcategories. - I can draw examples that do not belong based on their attributes.

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Wayne County Public Schools Grade 3 Math Scope and Sequence: Units, Standards, and “I Can” Statements Quarter 2 Units (Suggested # of Days) Math Standards “I Can” Statements Multiplication : (15 days) Apply Place Value Understanding & Properties of 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 3.NBT.3 I can use strategies to multiply Operations to Multiply One-Digit Whole Numbers by 10-90, using strategies based on place value and properties of operations. 1-digit numbers by multiples of 10. Multiples of 10 Apply Strategies to Multiply 3.OA.4 Determine the unknown whole number in a multiplication equation 3.OA.4 I can find a missing number in a relating 3 whole numbers. multiplication problem. 3.OA. 5 Apply properties of operations as strategies to multiply. 3.OA. 5 I can use the properties of 3.OA.7 Fluently multiply within 100. multiplication to solve problems. 3.OA.7 I can multiply within 100.

Identify/Explain Multiplication Patterns 3.OA.9 Identify arithmetic patterns --- focus on multiplication patterns, 3.OA.9 I can identify and explain including patterns in the multiplication table; explain patterns using arithmetic patterns such as those in the properties of operations; identify arithmetic patterns using input and output multiplication table and the addition tables. table. - I can identify and explain arithmetic patterns using input and output tables. Problem Solve: +. -, x 3.OA.8 Solve 2-step word problems: + , - , x 3.OA.8 I can use + , -, and x to solve 2-step word problems where a variable is used to represent an unknown quantity. I can use strategies to decide if my answer is reasonable. Number & Operations: Fractions: (10 days) Note: Grade 3 expectations are limited to fractions with 3.NF.1 Understand a fraction of the form 1/b (unit fraction) and a/b. 3.NF.1 - I can recognize a unit fractions. denominators 2, 3, 4, 6, and 8 - I can recognize fractions as parts of a 1/b (unit fraction): the quantity formed by 1 part when a whole is whole. I understand the difference Develop Understanding of Fractions as Numbers partitioned into b equal parts. a/b: the quantity formed by a parts of size between numerators and denominators. 1/b. Students express fractions as fair sharing, parts of a whole. Note: Students will build fractions from unit fractions. There is no need to introduce improper fractions” initially. Geometry: (5 days) 3.G.2 I can divide shapes into equal parts, using unit fractions to describe Partition Shapes into Parts with Equal Areas 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. each part. Measurement & Data: Time – Number Line Diagrams : (10 days) 3.MD.1 Tell and write time to the nearest minute and measure time 3.MD.1 - I can tell and write time to the intervals in minutes. Solve word problems involving addition and nearest minute. Tell and Write Time to the Nearest Minute; subtraction of time intervals in minutes by representing the problem on a - I can solve time problems. Measure Time Intervals in Minutes; number line diagram. Solve Time Problems Using a Number Line Diagram Note: In 3rd grade, students are expected to tell time within the hour; in 4th grade, students are expected to tell time over the hour.

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Quarter 3 Wayne County Public Schools --- Grade 3 Math Scope and Sequence: Units, Standards, and “I Can” Statements Units (Suggested # of Days) Math Standards “I Can” Statements

Division: (12 days) 3.OA.2 Interpret whole-number quotients of whole numbers (partitioning into 3.OA.2 I can divide to show how to share a set of Interpret Whole-Number Quotients of Whole equal shares). objects equally. I can use division to partition a set of Numbers objects into equal groups. Explore Division 3.OA.3 Use division & multiplication within 100 to solve word problems using 3.OA.3 I can multiply and divide within 100 to solve Problem Solve using equal groups. arrays, and equal groups, arrays, and measurement quantities; use drawings and equations word problems. measurement quantities. with a symbol for the unknown number to represent the problem. 3.OA.8 I can use + , -, x, and ÷ to solve 2-step word problems where a variable is used to represent an Problem Solve: +. -, x, ÷ 3.OA.8 Solve 2-step word problems: + , - , x, and ÷ unknown quantity. I can use strategies to decide if my answer is reasonable. Number & Operations: Fractions: (16 days) 3.NF.2 Understand a fraction as a number on the number line; represent 3.NF.2 I understand that fractions can be - Develop Understanding of Fractions as Numbers; fractions on a number line diagram. represented on a number line. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and - Represent Fractions on a Number Line Diagram 3.NF.2a I can represent a fraction on a number line partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 from 0 to 1. 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 of size 1/b from 0. Recognize that 3.NF.2b I can divide a number line into equal parts the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. in order to represent a fraction on a number line. 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions 3.NF.3 I can compare fractions. - Develop an Understanding of Equivalent (Equal) by reasoning about their size. 3.NF.3a I understand what makes fractions equivalent (equal). Fractions; a. Understand 2 fractions as equivalent (equal) if they are the same size or the same point on a number line. 3.NF.3b I can recognize and form simple - Compare Fractions ( >, =, <) by Reasoning about b. Recognize and generate simple equivalent fractions, e.g., ½ = 2/4; 4/6 = 2/3. equivalent fractions. Their Size Explain why the fractions are equivalent by using a visual model. 3.NF.3c I can express whole numbers as fractions. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. 3.NF.3d I can compare fractions that have the d. Compare 2 fractions with the same numerator or the same denominator by reasoning about their size. same numerator or the same denominator. I can Recognize that comparisons are valid only when the 2 fractions refer to the same whole. Record the results justify the comparisons. of comparisons with symbols >, =, <; justify the conclusions by using a visual model. Measurement & Data : Line Plots – Wholes, 3.MD.4 Generate measurement data by measuring lengths using rulers marked 3.MD.4 I can gather data on lengths of inches, half inches, and quarter inches. I can show the data on a Halves, Quarters ; PERIMETER & AREA : (12 days) with halves and fourths of an inch. Show the data by making a line plot, where line plot. Use a Line Plot with the Horizontal Scale Marked the horizontal scale is marked off in appropriate units --- whole numbers, halves, or quarters. 3.MD.8 I can solve for the perimeters of polygons in Units of Whole Numbers, Halves, Quarters to when given the side lengths. Display Measurement Data that Includes 3.MD.8 Solve real world and mathematical problems involving perimeters of 3.MD.5 I understand area of a plane figure. Fractional Amounts 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 3.MD 5a I can use square units to measure area. Explore Perimeter; Recognize Perimeter as an different perimeters 5.MD.5b I can find area by using square units laid Attribute of Plane Figures 3.MD.5 Recognize area as an attribute of plane figures and understand side to side without gaps or overlaps. concepts of area measurement. 3.MD.6 I can find areas by counting square units - Recognize Area as an Attribute of Plane Figures a. A square with side length 1 units, called “a unit square,” is said to have “one square unit” of area and can be used to (customary and metric). measure area. - Develop an Understanding of Area Measurement 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. 3.MD.7 I can use multiplication and addition to solve - Relate Area to the Operations of x and + for area. 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, 3.MD.7a I can find the area by multiplying the side square ft, and improvised units). Measure Areas by Counting Unit Squares lengths. 3.MD.7 Relate area to the operations of x and +. 3.MD.7b I can solve problems involving areas of a. Find the area of a rectangle with whole-number side lengths by tiling it; show that the area is the same as would be rectangles. found by multiplying the side lengths. 3.MD.7c I can find the area of a rectangle by using b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and the distributive property of multiplication. 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 3.MD.7d I can find the area of a rectangular polygon Relate Area to Multiplication and Addition of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. by separating it into smaller rectangles and adding the Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and areas. adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Wayne County Public Schools Grade 3 Math Scope and Sequence: Units, Standards, and “I Can” Statements - Quarter 4 Units (Suggested # of Days) Math Standards “I Can” Statements Division : (20 days) 3.OA.4 I can find a missing number in a multiplication or division problem. - Apply Strategies to Divide 3.OA.4 Determine the unknown whole number in a division or 3.OA.5 I can use the properties of - Develop an Understanding of Division as an Unknown multiplication equation relating 3 whole numbers. multiplication & division to solve Factor Problem 3.OA.5 Apply properties of operations as strategies to divide and multiply. problems. - Develop and Understanding of the Relationship 3.OA.6 Understand division as an unknown-factor problem. 3.OA.6 I can use my understanding of between Multiplication & Division 3.OA.7 Fluently multiply and divide within 100, using strategies such as the multiplication to solve division problems. - Fluently Multiply & Divide within 100 relationship between multiplication and division. 3.OA.7 I can multiply and divide within 100.

Problem Solve: +. -, x, ÷ 3.OA.8 Solve 2-step word problems: + , - , x, and ÷ 3.OA.8 I can use + , -, x, and ÷ to solve 2-step word problems where a variable is used to represent an unknown quantity. I can use strategies to decide if my answer is reasonable. More Problem Solving: Ongoing 3.OA.3 Use multiplication & division within 100 to solve word problems 3.OA.3 I can multiply and divide within All 4 Operations: + - x ÷ using equal groups, arrays, and measurement quantities; use drawings and 100 to solve word problems. equations with a symbol for the unknown number to represent the problem. 3.OA.8 I can use + , -, x, and ÷ to solve 2-step 3.OA.8 Solve 2-step word problems: +, -, x, ÷ word problems where a variable is used to represent an unknown quantity. I can use strategies to decide if my answer is reasonable. Measurement & Data: (20 days) 3.MD.8 -I can distinguish between linear and 3.MD.8 Solve real world and mathematical problems involving perimeters area measures. PERIMETER; AREA; MASS/VOLUME - I can solve problems involving perimeters of of polygons, including finding the perimeter given the side lengths, finding polygons when given various pieces of Solve Perimeter & Area Problems; an unknown side length, and exhibiting rectangles with the same perimeter information. Distinguish Between Linear and Area Measures and different areas or with the same area and different perimeters. - I can show examples of rectangles with the same perimeter and different areas or with the 3.MD.2 Measure and estimate liquid volumes and masses of objects using same area and different perimeters. standard units of g, kg, ml, and l. 3.MD.2 I can measure volume and mass Measure/Estimate Liquid Volumes and Masses of Note: Students are not expected to do conversions between units, but using customary and metric units. Objects reason as they estimate, using benchmarks to measure weight and capacity. Note: Excludes compound units such as cm3 and finding the geometric volume of a container. 3.MD.2 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units; use drawings 3.MD.2 I can solve volume and mass Solve Mass or Volume Problems that Are Given in the such as a beaker with a measurement scale to represent the problem. problems that are given in the same Same Units Note: Excludes multiplicative comparison problems --- problems units.. involving notions of “times as much.” Review as Needed: 3.NF.1, 3.NF.2, 3.NF.3 See Quarters 2 & 3. 3.NF.1 -3 I can show you that I Number and Operations – Fractions Note: understand fractions as numbers. Grade 3 expectations are limited to fractions with denominators 2, 3, 4, 6, and 8.

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Note: By the end of grade 3, know from memory 3.OA.7 I can express fluently all products all products of 2 one-digit numbers. 3.OA.7 of 2 one-digit numbers. Wayne County Public Schools 2010 NC Standard Course of Study for Mathematics Grade 3 Mathematics

Textbook Resource: Grade 3 enVision Math, © 2009, Scott Foresman- Addison Wesley, Pearson Education, Inc. Alignment of Textbook Topic Content to the 2010 NC Math Standard Course of Study : NOTE: Not all sections of each Topic are aligned to the 2010 NC Math SCoS – be sure to use ONLY the sections that are aligned to the 2010 NC Math SCoS . Table of Topics Topic 1: Numeration Topic 2: Adding Whole Numbers Topic 3: Subtraction Number Sense Topic 4: Subtracting Whole Numbers to Solve Problems Topic 5: Multiplication Meanings and Facts Topic 6: Multiplication Fact Strategies: Use Known Facts Topic 7: Division Meanings Topic 8: Division Facts Topic 9: Patterns and Relationships Topic 10: Solids and Shapes Topic 11: Congruence and Symmetry Omit Topic 12: Understanding Fractions Omit Circle Graphs Topic 13: Decimals and Money Omit Topic 14: Customary Measurement Topic 15: Metric Measurement Topic 16: Perimeter, Area, and Volume Topic 17: Time and Temperature Topic 18: Multiplying Greater Numbers

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 Topic 19: Dividing with 1-Digit Numbers Omit Topic 20: Data, Graphs, and Probability Omit Section 5- Rectangular Coordinate System 2010 NC SCoS: Mathematics K – 8 Continuum of Math Domains Domains K 1 2 3 4 5 6 7 8

Major Counting and Cardinality CC Major Major Major 30-35% 12-17% 5-10% Operations and Algebraic Thinking OA Major Major Major 5-10% 22-27% 22-27% Number and Operations in Base Ten NBT Support Major & Major & 22-27% 12-17% 10-15% Measurement and Data MD Support Support Support Support Support 10-15% 12-17% 2-7% 12-17% 22-27% 20-25% Geometry G

20-25% 27-32% 47-52% Number and Operations -- Fractions NF

Ratios and Proportional 12-17% 22-27% Relationships RP

27-32% 7-12% 2-7% The Number System NS

27-32% 22-27% 27-32% Expressions and Equations EE

7-12% 12-17% 15-20% Statistics and Probability SP

22-27% Functions F

For K – 2, the Major Work of the Grade is composed of Major Clusters and Supporting/Additional Clusters as denoted in chart.

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015 For grades 3 – 8, the % ranges are weight distributions determined by NC DPI – Division of Accountability Services, 3-10-15. NC EOG Information: http://www.ncpublicschools.org/accountability/testing/eog/math

Note regarding Fluency: By the end of Grade 3, students should know from memory all products of two 1-digit numbers. Rev. 07/2015