Oregon Mathematics Crosswalk to the Common Core State Standards (CCSS) Grade 3

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1 Oregon Mathematics Crosswalk to the Common Core State Standards (CCSS) Grade 3

2 It is the policy of the State Board of Education and a priority of the Oregon Department of Education that there will be no discrimination or harassment on the grounds of race, color, sex, marital status, religion, national origin, age or handicap in any educational programs, activities, or employment. Persons having questions about equal opportunity and nondiscrimination should contact the State Superintendent of Public Instruction at the Oregon Department of Education. Developed by the Office of Educational Improvement and Innovation Oregon Department of Education 255 Capitol Street NE Salem, Oregon (503) Susan Castillo State Superintendent of Public Instruction Colleen Mileham Assistant Superintendent C. Michelle Hooper Director, Teaching & Learning Mark Freed Mathematics Education Specialist All or any part of this document may be photocopied for educational purposes without permission from the Oregon Department of Education and distributed for the cost of reproduction.

3 Oregon Mathematics Crosswalk: Quick Reference Guide Indexed by Common Core State Standards and Oregon Standards

4 OREGON MATHEMATICS CROSSWALK Indexed by Oregon Mathematics Standards (OR) CCSS GRADE 3 CCSS Grade CCSS Index OR 1 Grade Δ Operations and Algebraic Thinking (3.OA) Partial OR 2 Grade Δ Partial 3 3OA1 32(NAD)1 0 2 Both 32(NAD) (NA)2-1 2 OR>CCSS 3 3OA2 32(NAD)2 0 2 Both 3 3OA3 32(NAD)1 0 2 CCSS>OR 32(NAD) (NA)2-1 2 Both 52(NA)1-2 2 OR>CCSS 3 3OA4 32(NAD) OA5 32(NAD) (NA)2-1 2 Both 3 3OA6 32(NAD) OA7 32(NAD)4 0 2 Both 42(NA)1-1 2 CCSS>OR 3 3OA8 42(NA)3-1 2 Both 3 3OA9 32(NAD)6 0 2 Both Number and Operations in Base Ten (3.NBT) 3 3NBT1 0 0.OR(-) 3 3NBT2 0 0.OR(+) 3 3NBT3 0 0.OR(-) Number and Operations - Fractions (3.NF) 3 3NF1 31(N)1 0 3 OR>CCSS 31(N)2 0 2 Both 3 3NF2 2 Both 3 3NF2a 31(N)1 0 2.SS Both 3 3NF2b 31(N)1 0 2.SS Both 3 3NF3 41(N)2-1 2 Both 3 3NF3a 31(N)3 0 2.SS Both 31(N)5 0 2.SS OR>CCSS 3 3NF3b 31(N)3 0 2.SS Both 31(N)5 0 2.SS Both 3 3NF3c 31(N)3 0 2.SS Both 31(N)5 0 2.SS OR>CCSS OR 3 3 3NF3d 31(N)2 0 3.SS 31(N)3 0 2.SS OR>CCSS 31(N)4 0 2.SS OR>CCSS 31(N)5 0 2.SS CCSS>OR 41(N)4-1 2.SS Both Measurement and Data (3.MD) Grade Δ 3 3MD1 0 0.OR(+) 3 3MD2 0 0.NC 3 3MD3 32(NAD)7 0 2 OR>CCSS 3 3MD4 31(N)1 0 1 Both 3 3MD5 43(M) (M)2-1 2 CCSS>OR 43(M)3-1 2 CCSS>OR 3 3MD6 43(M)2-1 2 OR>CCSS 43(M) MD7 2 Both 3 3MD7a 43(M)2-1 2.SS CCSS>OR 43(M)5-1 2.SS OR>CCSS 3 3MD7b 42(NA)2-1 2.SS OR>CCSS 43(M)5-1 1.SS 3 3MD7c 43(M)5-1 2.SS Both 3 3MD7d 33(GM)5 0 1.SS Both 43(M)6-1 3.SS 3 3MD8 33(GM)7 0 2 Both 43(M)7-1 2 CCSS>OR 43(M)8-1 2 CCSS>OR Geometry (3.G) 3 3G1 33(GM) (GM) G2 31(N)1 0 1 Both 31(N)2 0 1 Both Partial OR 4 Grade Δ Partial OR 5 Grade Δ Alignment Alignment Alignment Alignment Alignment Partial Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade

5 OREGON MATHEMATICS CROSSWALK Indexed by Oregon Mathematics Standards (OR) OREGON GRADE 3 Partial CCSS 2 Grade Δ Partial 31(N) - Number and Operations: Develop an understanding of fractions and fraction equivalence. CCSS (N)1 3NF1 0 3 OR>CCSS 3NF2a 0 2 Both 3NF2b 0 2 Both 3G2 0 1 Both 3MD4 0 1 Both 3 31(N)2 3NF1 0 2 Both 3NF3d 0 3 3G2 0 1 Both 3 31(N)3 3NF3a 0 2 Both 3NF3b 0 2 Both 3NF3c 0 2 Both 3NF3d 0 2 OR>CCSS 3 31(N)4 3NF3d 0 2 OR>CCSS 3 31(N)5 3NF3a 0 2 OR>CCSS 3NF3b 0 2 Both 3NF3d 0 2 CCSS>OR 3NF3c 0 2 OR>CCSS 3 31(N)6 4NF3d 1 2 CCSS>OR 4NF3a 1 2 CCSS>OR 32(NAD) - Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts. Grade Δ 3 32(NAD)1 2OA4-1 2 OR>CCSS 3OA1 0 2 Both 3OA3 0 2 CCSS>OR 3 32(NAD)2 3OA2 0 2 Both 3 32(NAD)3 3OA OA (NAD)4 3OA OA7 0 2 Both 3 32(NAD)5 3OA OA (NAD)6 3OA9 0 2 Both 3 32(NAD)7 3MD3 0 2 OR>CCSS 33(GM) - Geometry and Measurement: Describe and analyze properties of two-dimensional shapes, including perimeters. 3 33(GM)1 4MD5 1 1 CCSS>OR 4G1 1 2 CCSS>OR 4G (GM)2 3G G2 1 2 Both 4G1 1 2 CCSS>OR 3 33(GM)3 3G G1-1 2 Both 3 33(GM)4 2G1-1 2 OR>CCSS KG4-3 2 Both 3 33(GM)5 3MD7d 0 1 Both KG (GM)6 4G1 1 2 Both 4G2 1 2 Both 5G3 2 2 OR>CCSS 3 33(GM)7 3MD8 0 2 Both 3 33(GM)8 4G1 1 2 Both 4G2 1 2 Both 4G3 1 2 Both Partial CCSS 4 Grade Δ Partial CCSS 5 Grade Δ OR Grade OR Index CCSS 1 Grade Δ Alignment Alignment Alignment Alignment Alignment Partial

6 Oregon Mathematics Crosswalk: 3rd Grade Indexed by Common Core State Standards 46

7 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Operations and Algebraic Thinking (3.OA) Represent and solve problems involving multiplication and division. (CC.3.OA.1, CC.3.OA.2, CC.3.OA.3, CC.3.OA.4) CC.3.OA.1 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. OR Represent and apply the concept of multiplication as repeated addition. OR Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems. Comment 0 2 Both CCSS assumes prior knowledge /use of repeated addition (seen in CC.2.OA.4) This CCSS uses equal groups, and does not explicitly refer to repeated addition. 0 1 OR standard is applying representations/models and meanings of multiplication and division broadly. CCSS standard is about viewing multiplication as groups of objects. There is no mention of division except in what would be the "bold" statement. CC.3.OA.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. OR Apply understanding of models for multiplication (e.g., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive). OR Represent and apply the concept of division as repeated subtraction and forming equal groups OR>CCSS Oregon had more models and properties are listed. 0 2 Both The OR standard indentifies both repeated subtraction (measurement) and partitioning division models. The CCSS only identifies partitioning, and does not identify either repeated subtraction or measurement models. The OR standard may have greater latitude for factors, CCSS limited to whole number division problems with whole number quotients. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 47

8 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.OA.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. OR Represent and apply the concept of multiplication as repeated addition. 0 2 CCSS>OR Repeated addition (OR) could be used as one way to meet this CC standard. CCSS doesn't address repeated addition specifically in grade 3, and lists other methods for representing & solving problems. CC.3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. OR Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems. OR Apply understanding of models for multiplication (e.g., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive). OR Apply understanding of models for division (e.g., equal-sized groups, arrays, area models, equal intervals on the number line) and the relationship of division to multiplication to solve problems. OR Apply the inverse relationship between multiplication and division (e.g., 5 x 6 = 30, 30 6 = 5) and the relationship between multiples and factors. 0 3 Appears fairly interchangeable -1 2 Both CCSS relates division to multiplication. OR standard utilizes properties and doesn't limit to 100. The intent of the 4th grade OR standard is to apply with understanding multiplication of numbers larger than a single digit. CCSS also emphasizes using equations with a symbol for the unknown number to represent the problem OR>CCSS OR includes the relationship between multiplication & division 0 3 The inverse relationship between multiplication and division (OR) is a key strategy to finding the unknown whole value relating three numbers (CCSS). Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 48

9 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Operations and Algebraic Thinking Understand properties of multiplication and the relationship between multiplication and division. (CC.3.OA.5, CC.3.OA.6) CC.3.OA.5 Apply properties of operations as strategies to multiply and divide. OR Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts. Comment 0 3 CCSS focuses only on properties of operations and does not specify number properties (place value, identity, and zero). CC.3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 8 by finding the number that makes 32 when multiplied by 8. Operations and Algebraic Thinking (3.OA) Multiply and divide within 100. (CC.3.OA.7) CC.3.OA.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 one-digit numbers. OR Apply understanding of models for multiplication (e.g., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive). OR Apply the inverse relationship between multiplication and division (e.g., 5 x 6 = 30, 30 6 = 5) and the relationship between multiples and factors. OR Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts. OR Apply with fluency multiplication facts to 10 times 10 and related division facts Both Oregon standard has models and CCSS includes division. Both include properties of operations. 0 3 CCSS has same content (relationship mult/div) in 3.OA.4; 3.OA.6; 3.OA Both CCSS specifies fluency; OR standards require fluency at 4th grade CCSS>OR CCSS includes using properties and relationship between multiplication and division. CCSS identifies fluency with basic multiplication facts by the end of 3rd grade. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 49

10 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Operations and Algebraic Thinking (3.OA) Solve problems involving the four operations, and identify and explain patterns in arithmetic. (CC.3.OA.8, CC.3.OA.9) CC.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. OR Select and use appropriate estimation strategies for multiplication (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers. Comment -1 2 Both The OR standard uses estimation to calculate mentally, and CCSS uses estimation to verify answers. The OR standard is about multiplication, and CCSS includes all four operations. CCSS also emphasizes using equations with a letter standing for the unknown quantity. CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. OR Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12,...}, {1, 2, 4, 8,...} ). 0 2 Both The OR standard has greater level of complexity, but only includes multiplication and addition. CCSS only includes "identify", but also includes all arithmetic patterns. Number and Operations in Base Ten (3.NBT) Use place value understanding and properties of operations to perform multi-digit arithmetic. (CC.3.NBT.1, CC.3.NBT.2, CC.3.NBT.3) CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or OR(-) No exact match, however rounding is identified in OR (multiplication), OR (division). Could be implied as part of OR (add/sub) as well. CC.3.NBT.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. CC.3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. 0 0.OR(+) No exact match, however content is generally addressed in OR (boundaries aren't identified in Oregon 2nd grade standard). 0 0.OR(-) No exact match, however content would generally be addressed in OR 3.2.4, OR 4.2.3, and OR Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 50

11 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Number and Operations - Fractions (3.NF) Develop understanding of fractions as numbers. (CC.3.NF.1, CC.3.NF.2, CC.3.NF.3) CC.3.NF.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. OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. Comment 0 3 OR>CCSS OR standard identifies common fractions, and CCSS limits denominators to 2, 3, 4, 6, 8. The OR standard has the possibility of including more fractions then. Note: In the CCSS introduction to grade 3 - fifths are used as an example, however, fifths are not listed in domain of denominators in this standard. CC.3.NF.2Understand a fraction as a number on the number line; represent fractions on a number line diagram. OR Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole. 0 2 Both OR standard is not covered in its entirety by the CCSS because the concept of the "whole" is not addressed in this CCSS standard. 2 Both Content in CC.NF.2 matches to OR CC.3.NF.2a 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. OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. 0 2.SS Both CCSS focus is on a number line model of fractions; parts of a whole and parts of a set models are not specified. CC.3.NF.2b 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. OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. 0 2.SS Both CCSS focus is on a number line model of fractions; parts of a whole and parts of a set models are not specified. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 51

12 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. OR Use models to connect and compare equivalent fractions and decimals Both Content in CC.3.NF.3 matches to OR 4.1.2, OR 3.1.3, and OR CCSS does not include decimals. OR standard does not include reasoning based on size of fraction. CCSS standards from 3.NF.3a, 3b, 3c each use models to find/compare fractions. CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. CC.3.NF.3b 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. CC.3.NF.3c 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. OR Use fractions to represent numbers that are equal to, less than, or greater than one. OR Identify equivalent fractions using models, including the number line. OR Use fractions to represent numbers that are equal to, less than, or greater than one. OR Identify equivalent fractions using models, including the number line. OR Use fractions to represent numbers that are equal to, less than, or greater than one. OR Identify equivalent fractions using models, including the number line. 0 2.SS Both OR standard talks more generally about understanding fractions. CCSS focuses on fractions as numbers. CCSS does not explicitly have comparisons of fractions to the number SS OR>CCSS The OR standard does not limit models to number line. 0 2.SS Both The OR standard talks more generally about understanding fractions CCSS focuses on fractions as numbers. Missing specifics about mixed numbers. 0 2.SS Both CCSS asks students to generate equivalent fractions using models and explain whereas the OR standard asks student to only identify equivalent fractions. The OR standard highlights multiple modes; CCSS does not. 0 2.SS Both The OR standard talks more generally about understanding fractions. CCSS focuses on expressing whole numbers as fractions in this standard. Missing specifics about mixed numbers. 0 2.SS OR>CCSS Match on identifying whole numbers as fractions and recognizing these points on a number line. The OR standard does not limit to equivalent fractions to whole numbers. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 52

13 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring 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. OR Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole. 0 3.SS CCSS addresses this OR standard in the context of comparing fractions. CCSS specifies recording the comparison using symbols. CC.3.MD.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. OR Use fractions to represent numbers that are equal to, less than, or greater than one. OR Solve problems that involve comparing and ordering fractions by using models, benchmarks (0, ½, 1), or common numerators or denominators. OR Identify equivalent fractions using models, including the number line. OR Compare and order fractions and decimals. Measurement and Data (3.MD) Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. (CC.3.MD.1, CC.3.MD.2) 0 2.SS OR>CCSS Lacking specific focus on mixed numbers. 0 1.SS OR>CCSS The OR standard asks to solve problems by comparing and ordering multiple fractions. CCSS compares only 2 numbers with the same numerator or denominator. CCSS does not refer to comparisons to benchmark values. 0 2.SS CCSS>OR Match on comparing equivalent fractions. CCSS specifies the size and comparison to the same whole. Oregon does not limit the types of denominators used; CCSS does limit to denominators of 2, 3, 4, 6, & SS Both CCSS includes using symbols to compare, and justifying conclusions. OR includes fractions and fraction and decimal comparisons. 0 0.OR(+) No exact match. Telling time is evident in the Oregon Standards but writing time is not explicit and solving problems involving time is not evident. OR identifies and understanding of time, and OR identifies telling time on digital and analog clocks. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 53

14 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) 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. 0 0.NC New Content - Possible match to OR & OR 5.3.7, however the Oregon standards are not as complex or specific. Measurement and Data (3.MD) Represent and interpret data. (CC.3.MD.3, CC.3.MD.4) CC.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. CC.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 scale is marked off in appropriate units whole numbers, halves, or quarters. OR Analyze frequency tables, bar graphs, picture graphs, and line plots; and use them to solve problems involving addition, subtraction, multiplication, and division. OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. 0 2 OR>CCSS CCSS only identifies addition/subtraction problems and bar graphs. The OR standard indentifies all four operations and also includes line plots, picture graphs, and frequency tables. 0 1 Both Weak connection in the discussion of partitioning a number line into equal lengths. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 54

15 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment Measurement and Data (3.MD) Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (CC.3.MD.5, CC.3.MD.6, CC.3.MD.7) CC.3.MD.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. OR Recognize area as an attribute of two-dimensional regions CC 3.MD.5 is a match to (recognize area attributes) CC 3.MD.5b is a match to (cover shape without overlaps) CC 3.MD.5a is a match to (unit square) OR Determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps CCSS>OR CC 3.MD.5b is a match to (cover shape without overlaps) CC 3.MD.5a is a match to (unit square area) OR Recognize a square that is one unit on a side as the standard unit for measuring area CCSS>OR CC 3.MD.5 is a match to (recognize area attributes) CC 3.MD.5a is a match to (unit square area) CC 3.MD.5 is a match to (recognize area attributes) CC 3.MD.5b is a match to (cover shape without overlaps) Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 55

16 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). OR Determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps OR>CCSS Oregon includes knowing that area covers a shape without gaps. CC.3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). OR Determine the appropriate units, strategies, and tools to solving problems that involve estimating or measuring area CC standard may imply using appropriate units and tools. CC standard does NOT include estimation strategies CC.3.MD.7 Relate area to the operations of multiplication and addition. CC.3.MD.7a 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. CC.3.MD.7b 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. OR Determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps. OR Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle. OR Apply understanding of models for multiplication (e.g., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive). OR Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle. 2 Both Content within CC.3.MD.7 matches to OR.4.3.5, OR.4.3.2, OR.4.2.2, OR.3.3.5, and OR SS CCSS>OR CCSS makes the connection between concept and multiplication SS OR>CCSS Connection of area model to multiplication. OR standard also asks for justification SS OR>CCSS CCSS Standard speaks specifically to using the area model as a representation for multiplication. OR standard lists this representation among others SS Weak match on connecting area model and multiplication Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 56

17 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.MD.7c 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. OR Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle SS Both The CC standard is about multiplication and proving with an area model but it is specific to proving the distributive property. The OR standard is more general in connecting area to the representation/model of multiplication. CC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. OR Investigate and describe the results of decomposing, combining, and transforming polygons to make other polygons. 0 1.SS Both The OR standard and CCSS are different in that the CCSS focuses on multiplication and division and the OR standard is focused on geometric reasoning. OR Find the areas of complex shapes that can be subdivided into rectangles SS Good match of skills needed to solve real world problems Measurement and Data (3.MD) Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. (CC.3.MD.8) CC.3.MD.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 area or with the same area and different perimeter. OR Determine an appropriate unit, tool, or strategy to find the perimeter of polygons. 0 2 Both CCSS does not talk about tools or strategies, but also asks students to apply higher level reasoning skills than the OR standard. Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 57

18 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.MD.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 area or with the same area and different perimeter. OR Solve problems involving perimeters and areas of rectangles and squares CCSS>OR The CCSS standard is about understanding area and linear measurement of plane figures. In both cases students are asked to solve problems involving perimeter. OR also asks for area. CCSS wants students to consider rectangles of different sizes with same perimeter or rectangles of the same size with different perimeters. Geometry (3.G) Reason with shapes and their attributes. (CC.3.G.1, CC.3.G.2) CC.3.G.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. OR Recognize that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas. OR Identify, describe, compare, analyze, and informally classify triangles by their sides and angles. OR Identify, describe, compare, analyze, and classify quadrilaterals (square, rectangle, parallelogram, rhombus, and trapezoid) by their sides and angles CCSS>OR CCSS is more inclusive by looking at polygons rather than only rectangles. 0 1 Weak connection in comparing triangles. CCSS also indentifies more 2D shapes and generally seems focused on quadrilaterals. 0 3 CCSS focus is on identifying quadrilaterals and non examples. Higher cognitive demand tasks missing in the CCSS (compare, analyze and classify) that get at a deeper understanding Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 58

19 Indexed by Common Core State Standards (CCSS) CCSS GRADE 3 CC standard OR standard Grade Δ Alignment Partial Comment CC.3.G.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 is 1/4 of the area of the shape. OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. 0 1 Both Weak connection in discussing of partitioning into equal areas. OR Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole. 0 1 Both Weak connection in discussion of parts of whole Unmatched CCSS Key 0.NC - New Content (NC) 0.OR(+) - Generally the same OR grade 0.SS - CCSS Sub-standard 0.OR(-) - Generally a later OR grade 59

20 Oregon Mathematics Crosswalk: 3 rd Grade Indexed by Oregon Standards 235

21 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. CC.3.NF.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. CC.3.NF.2a 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. CC.3.NF.2b 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. CC.3.G.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 is 1/4 of the area of the shape. 0 3 OR>CCSS OR standard identifies common fractions, and CCSS limits denominators to 2, 3, 4, 6, 8. The OR standard has the possibility of including more fractions then. Note: In the CCSS introduction to grade 3 - fifths are used as an example, however, fifths are not listed in domain of denominators in this standard. 0 2 Both CCSS focus is on a number line model of fractions; parts of a whole and parts of a set models are not specified. 0 2 Both CCSS focus is on a number line model of fractions; parts of a whole and parts of a set models are not specified. 0 1 Both Weak connection in discussing of partitioning into equal areas. 236

22 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Represent common fractions (e.g., halves, thirds, fourths, tenths) as equal parts of a whole, parts of a set, or points or distances on a number line. CC.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 scale is marked off in appropriate units whole numbers, halves, or quarters. 0 1 Both Weak connection in the discussion of partitioning a number line into equal lengths. OR Recognize and demonstrate that sizes of fractional parts are relative to the size of the whole. CC.3.NF.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. CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring 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. CC.3.G.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 is 1/4 of the area of the shape. 0 2 Both OR standard is not covered in its entirety by the CCSS because the concept of the "whole" is not addressed in this CCSS standard. 0 3 CCSS addresses this OR standard in the context of comparing fractions. CCSS specifies recording the comparison using symbols. 0 1 Both Weak connection in discussion of parts of whole OR Use fractions to represent numbers that are equal to, less than, or greater than one. CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 0 2 Both OR standard talks more generally about understanding fractions. CCSS focuses on fractions as numbers. CCSS does not explicitly have comparisons of fractions to the number

23 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Use fractions to represent numbers that are equal to, less than, or greater than one. OR Solve problems that involve comparing and ordering fractions by using models, benchmarks (0, ½, 1), or common numerators or denominators. OR Identify equivalent fractions using models, including the number line. CC.3.NF.3b 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. CC.3.NF.3c 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. CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring 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. CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring 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. CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 0 2 Both The OR standard talks more generally about understanding fractions CCSS focuses on fractions as numbers. Missing specifics about mixed numbers. 0 2 Both The OR standard talks more generally about understanding fractions. CCSS focuses on expressing whole numbers as fractions in this standard. Missing specifics about mixed numbers. 0 2 OR>CCSS Lacking specific focus on mixed numbers. 0 2 OR>CCSS The OR standard asks to solve problems by comparing and ordering multiple fractions. CCSS compares only 2 numbers with the same numerator or denominator. CCSS does not refer to comparisons to benchmark values. 0 2 OR>CCSS The OR standard does not limit models to number line. 238

24 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Identify equivalent fractions using models, including the number line. OR Add common fractions with like denominators. CC.3.NF.3b 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. CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring 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. CC.3.NF.3c 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. CC.4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. CC.4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 0 2 Both CCSS asks students to generate equivalent fractions using models and explain whereas the OR standard asks student to only identify equivalent fractions. The OR standard highlights multiple modes; CCSS does not. 0 2 CCSS>OR Match on comparing equivalent fractions. CCSS specifies the size and comparison to the same whole. Oregon does not limit the types of denominators used; CCSS does limit to denominators of 2, 3, 4, 6, & OR>CCSS Match on identifying whole numbers as fractions and recognizing these points on a number line. The OR standard does not limit to equivalent fractions to whole numbers. 1 2 CCSS>OR CCSS does not include addition of fractions at grade CCSS>OR OR has students add common fractions. CCSS has students understand both addition and subtraction of fractions. 239

25 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Represent and apply the concept of multiplication as repeated addition. OR Represent and apply the concept of division as repeated subtraction and forming equal groups. CC.2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. CC.3.OA.1 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. CC.3.OA.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. CC.3.OA.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 OR>CCSS CCSS limits 5 x 5 array but identifies expressing multiplication as the sum of equal addends (repeated addition). 0 2 Both CCSS assumes prior knowledge /use of repeated addition (seen in CC.2.OA.4) This CCSS uses equal groups, and does not explicitly refer to repeated addition. 0 2 CCSS>OR Repeated addition (OR) could be used as one way to meet this CC standard. CCSS doesn't address repeated addition specifically in grade 3, and lists other methods for representing & solving problems. 0 2 Both The OR standard indentifies both repeated subtraction (measurement) and partitioning division models. The CCSS only identifies partitioning, and does not identify either repeated subtraction or measurement models. The OR standard may have greater latitude for factors, CCSS limited to whole number division problems with whole number quotients. 240

26 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems. CC.3.OA.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. CC.3.OA.1 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. 0 3 Appears fairly interchangeable 0 1 OR standard is applying representations/models and meanings of multiplication and division broadly. CCSS standard is about viewing multiplication as groups of objects. There is no mention of division except in what would be the "bold" statement. OR Apply increasingly sophisticated CC.3.OA.5 Apply properties of operations as strategies based on the number properties strategies to multiply and divide. (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts. OR Apply the inverse relationship between multiplication and division (e.g., 5 x 6 = 30, 30 6 = 5) and the relationship between multiples and factors. CC.3.OA.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 one-digit numbers. CC.3.OA.6 Understand division as an unknown-factor problem. For example, divide 32 8 by finding the number that makes 32 when multiplied by CCSS focuses only on properties of operations and does not specify number properties (place value, identity, and zero). 0 2 Both CCSS specifies fluency; OR standards require fluency at 4th grade. 0 3 CCSS has same content (relationship mult/div) in 3.OA.4; 3.OA.6; 3.OA.7 241

27 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Apply the inverse relationship between multiplication and division (e.g., 5 x 6 = 30, 30 6 = 5) and the relationship between multiples and factors. CC.3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. OR Represent, analyze and extend CC.3.OA.9 Identify arithmetic patterns number patterns using rules that involve (including patterns in the addition table or multiplication and/or addition (e.g., {3, 6, 9, multiplication table), and explain them 12,...}, {1, 2, 4, 8,...} ). using properties of operations. 0 3 The inverse relationship between multiplication and division (OR) is a key strategy to finding the unknown whole value relating three numbers (CCSS). 0 2 Both The OR standard has greater level of complexity, but only includes multiplication and addition. CCSS only includes "identify", but also includes all arithmetic patterns. OR Analyze frequency tables, bar graphs, picture graphs, and line plots; and use them to solve problems involving addition, subtraction, multiplication, and division. CC.3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and twostep how many more and how many less problems using information presented in scaled bar graphs. 0 2 OR>CCSS CCSS only identifies addition/subtraction problems and bar graphs. The OR standard indentifies all four operations and also includes line plots, picture graphs, and frequency tables. OR Identify right angles in twodimensional shapes and determine if angles shapes that are formed wherever two rays CC.4.MD.5Recognize angles as geometric are greater than or less than a right angle share a common endpoint, and understand (obtuse and acute). concepts of angle measurement: -- a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. -- b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees. 1 1 CCSS>OR The OR standard asks students to only identify right, obtuse, and acute angles. CCSS is more specific around the concept of an angle, and understanding the meaning of all degree angles in a full rotation. 242

28 Indexed by Oregon Standards (OR) Oregon Grade 3 OR standard CC standard Grade Δ Alignment Partial Comment OR Identify right angles in twodimensional shapes and determine if angles rays, angles (right, acute, obtuse), and CC.4.G.1 Draw points, lines, line segments, are greater than or less than a right angle perpendicular and parallel lines. Identify (obtuse and acute). these in two-dimensional figures. OR Identify, describe, compare, analyze, and informally classify triangles by their sides and angles. CC.4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. CC.3.G.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. CC.4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 1 2 CCSS>OR The OR standard identifies and compares right, obtuse, or acute. CCSS has a much broader scope of this measurement 1 1 Both standards connect to classifying twodimensional shapes, but one is about classifying angles as obtuse and acute (OR) and the other is about classifying figures based on attributes such as lines and angles (CCSS). 0 1 Weak connection in comparing triangles. CCSS also indentifies more 2D shapes and generally seems focused on quadrilaterals. 1 2 Both OR standard focused on classifying to triangles. CCSS identifies a greater variety of identifying shapes beyond triangles. The OR standard also asks more cognitive demands than CCSS (e.g. describe, compare, and analyze) 243

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