Oregon Mathematics Crosswalk to the Common Core State Standards (CCSS) Grade 4

Transcription

1 Oregon Mathematics Crosswalk to the Common Core State Standards (CCSS) Grade 4

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 4 CCSS Grade CCSS Index OR 1 Grade Δ Operations and Algebraic Thinking (4.OA) Partial OR 2 Grade Δ Partial 4 4OA1 0 0.NC 4 4OA2 0 0.NC 4 4OA3 52(NA)3-1 2 CCSS>OR 52(NA)6-1 2 Both 4 4OA4 0 0.NC 4 4OA5 0 0.NC Number and Operations in Base Ten (4.NBT) 4 4NBT1 0 0.NC 4 4NBT2 0 0.OR(+) 4 4NBT3 0 0.OR(+) 4 4NBT4 0 0.OR(+) 4 4NBT5 42(NA) (NA)5 0 2 OR>CCSS 4 4NBT6 52(NA)1-1 2 Both 52(NA)2-1 2 Both 52(NA)4-1 2 Both 52(NA)5-1 2 Both Number and Operations - Fractions (4.NF) 4 4NF1 41(N)2 0 2 Both 4 4NF2 41(N)4 0 2 Both 4 4NF3 2 CCSS>OR 4 4NF3a 31(N)6 1 2.SS CCSS>OR 4 4NF3b 2.SS SS 4 4NF3c 2.SS SS 4 4NF3d 31(N)6 1 2.SS CCSS>OR 4 4NF4 61(N)2-2 2 OR>CCSS 4 4NF4a 2.SS SS 4 4NF4b 2.SS SS 4 4NF4c 2.SS SS 4 4NF5 0 0.OR(-) 4 4NF6 41(N)1 0 2 OR>CCSS 41(N) (N) (N) NF7 41(N)4 0 2 OR>CCSS Measurement and Data (4.MD) 4 4MD1 61(N)7-2 2 OR>CCSS 4 4MD2 41(N)6 0 2 CCSS>OR 4 4MD3 43(M)7 0 2 OR>CCSS 4 4MD4 0 0.OR(-) 4 4MD5 33(GM)1 1 1 CCSS>OR 4 4MD6 0 0.NC 4 4MD7 0 0.NC Geometry (4.G) OR 3 4 4G1 33(GM)1 1 2 CCSS>OR 33(GM)2 1 2 CCSS>OR 33(GM)6 1 2 Both 33(GM)8 1 2 Both 53(GMA)1-1 2 Both 4 4G2 33(GM) (GM)2 1 2 Both 33(GM)6 1 2 Both 33(GM)8 1 2 Both 53(GMA)1-1 2 Both Grade Δ 4 4G3 13(G) (GM)8 1 2 Both 93G1-5 2 OR>CCSS 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 4 Partial CCSS 2 Grade Δ Partial CCSS 3 Grade Δ 41(N) - Number and Operations: Develop an understanding of decimals, including the connections between fractions and decimals. 4 41(N)1 5NBT3a 1 2 Both 4NF6 0 2 OR>CCSS 5NBT (N)2 4NF NF1 0 2 Both 3NF3-1 2 Both 4 41(N)3 7NS2d 3 1 4NF (N)4 3NF3d -1 2 Both 4NF7 0 2 OR>CCSS 4NF2 0 2 Both 5NBT3b 1 2 Both 4 41(N)5 5NF (N)6 2MD8-2 2 Both 4MD2 0 2 CCSS>OR 42(NA) - Number and Operations and Algebra: Develop fluency with multiplication facts and related division facts, and with multi-digit whole number multiplication. 4 42(NA)1 3OA7-1 2 CCSS>OR 4 42(NA)2 3OA1-1 2 OR>CCSS 3OA3-1 2 Both 3OA5-1 2 Both 4NBT MD7b -1 2 OR>CCSS 4 42(NA)3 3OA8-1 2 Both 7EE (NA)4 5NBT5 1 2 OR>CCSS 4 42(NA)5 4NBT5 0 2 OR>CCSS 5NBT5 1 2 OR>CCSS 43(M) - Measurement: Develop an understanding of area and determine the areas of two-dimensional shapes. 4 43(M)1 3MD (M)2 3MD6-1 2 OR>CCSS 3MD7a -1 2 CCSS>OR 3MD5-1 2 CCSS>OR 4 43(M)3 3MD5-1 2 CCSS>OR 4 43(M)4 3MD (M)5 3MD7a -1 2 OR>CCSS 3MD7b MD7c -1 2 Both 4 43(M)6 3MD7d (M)7 4MD3 0 2 OR>CCSS 3MD8-1 2 CCSS>OR 4 43(M)8 3MD8-1 2 CCSS>OR 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: 4th Grade Indexed by Common Core State Standards 60

7 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Operations and Algebraic Thinking (4.OA) Use the four operations with whole numbers to solve problems. (CC.4.OA.1, CC.4.OA.2, CC.4.OA.3) CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Comment 0 0.NC New CCSS content - Appears loosely related to OR.3.2.4, but not enough to be considered a match. CC.4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. OR Select and use appropriate estimation strategies for division (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers. 0 0.NC New content found within the CCSS CCSS>OR OR standard focused on estimation strategies for division; CCSS references all 4 operations, use of variable, inclusive to rounding. The estimation component of the CC standard seems to imply that estimation should be used after solving a problem rather than as a part of sense-making in solving the problem. OR Determine the most appropriate form of the quotient and interpret the remainder in a problem situation Both CCSS has more: equations with variable, mental computation, estimation strategies. Oregon asks for most appropriate form of the quotient 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 61

8 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Operations and Algebraic Thinking (4.OA) Gain familiarity with factors and multiples. (CC.4.OA.4) CC.4.OA.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. Comment 0 0.NC New CCSS contentpossibly related to the justification element of OR or operations with fractions in OR strand 5.1, but not enough to be considered a match. Operations and Algebraic Thinking Generate and analyze patterns. (CC.4.OA.5) CC.4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Number and Operations in Base Ten (4.NBT) Generalize place value understanding for multi-digit whole numbers. (CC.4.NBT.1, CC.4.NBT.2, CC.4.NBT.3) CC.4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. CC.4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 0 0.NC New CCSS content - possibly related to OR and OR.6.3.5, but not enough to be considered a match. 0 0.NC New CCSS content - possibly related to OR and OR through OR.2.1.4, but not enough to be considered a match. 0 0.OR(+) No exact match. Content is related to OR.2.1.1, OR.2.1.3, and OR.4.1.1, but not enough to be considered a match. In Oregon's standard, students are expected to decompose numbers in these ways. There is no explicit mention of comparing whole numbers and determining inequalities. 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 62

9 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Comment CC.4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. 0 0.OR(+) No exact match. Content is related to OR.2.2.4, OR.4.2.3, but not enough to be considered a match. Oregon's standard at the second grade level asks that students develop procedures for adding and subtracting. As these are applied in mental math contexts it is reasonable to expect that students would round. The grade 4 standards explicates rounding for estimating products and quotients but there isn't an explicit standard that does this for sums and differences. Rounding as an isolated skill is not present in Oregon's standards. Number and Operations in Base Ten (4.NBT) Use place value understanding and properties of operations to perform multi-digit arithmetic. (CC.4.NBT.4, CC.4.NBT.5, CC.4.NBT.6) CC.4.NBT.4 Fluently add and subtract multidigit whole numbers using the standard algorithm. 0 0.OR(+) No exact match, but content is related to OR and OR If OR standard "efficient procedure" means the standard algorithm (e.g. the US standard algorithm), then it would be a match. However, there are other efficient procedures. CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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). 0 3 CCSS specifies whole numbers up to four digits by one digit and two digit numbers. OR Develop fluency with efficient procedures for multiplying multi-digit whole numbers and justify why the procedures work on the basis of place value and number properties. 0 2 OR>CCSS Oregon does not limit the number of digits. 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 63

10 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Comment CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 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 Both The only difference between 5.NBT.6 and 4.NBT.6 is two-digit vs. one-digit divisors. OR standards do not specify the size of dividends or divisors beyond multi-digit. The OR standard also includes models. CC standard includes strategies based on place value and properties of operations. OR Apply concepts of place value and the properties of operations to solve problems involving division. OR Develop and use accurate, efficient, and generalizable methods to find quotients for multi-digit division problems Both The only difference between 5.NBT.6 and 4.NBT.6 is two-digit vs. one-digit divisors. OR standards do not specify the size of dividends or divisors beyond multi-digit. The division computation strategies included in both the OR and CC standard is applying concepts of place value and properties of operations Both The only difference between 5.NBT.6 and 4.NBT.6 is two-digit vs. one-digit divisors. OR standards do not specify the size of dividends or divisors beyond multi-digit. In this case, Both recognize multiple methods for finding quotients. OR focuses on finding accurate and efficient strategies the CCSS standards does not communicate such an analysis is taking place. CCSS names specific strategies to be used. 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 64

11 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial CC.4.NBT.6 Find whole-number quotients OR Develop fluency with efficient and remainders with up to four-digit procedures for dividing whole numbers dividends and one-digit divisors, using and justify why the procedures work on strategies based on place value, the the basis of place value and number properties of operations, and/or the properties. relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Comment -1 2 Both The only difference between 5.NBT.6 and 4.NBT.6 is two-digit vs. one-digit divisors. OR standards do not specify the size of dividends or divisors beyond multi-digit. In this case, OR asks for fluency with the procedure; CCSS makes reference to place value and number properties but also asks for models. Number and Operations - Fractions (4.NF) Extend understanding of fraction equivalence and ordering. (CC.4.NF.1, CC.4.NF.2) CC.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. CC.4.NF.2Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. OR Use models to connect and compare equivalent fractions and decimals. OR Compare and order fractions and decimals. 0 2 Both Good match for using models to connect and compare equivalent fractions. CCSS is missing decimals and OR is missing explaining why. 0 2 OR>CCSS CC standard does not include decimals. CC standards also does not specify ordering. OR standard does not include recording results with symbols and justifying the conclusion. 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 65

12 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Comment Number and Operations - Fractions (4.NF) Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (CC.4.NF.3, CC.4.NF.4) CC.4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 2 CCSS>OR CC.4.NF.3 matches to and 3.1 in general. Subtraction of fractions is not specifically identified at the third grade, but is identified at the fifth grade level in Oregon (OR & OR.5.1.5) CC.4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CC.4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. CC.4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 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.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. CC.4.NF.4a Understand a fraction a/b as a multiple of 1/b. OR Add common fractions with like denominators. OR Add common fractions with like denominators. OR Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of fractions. 1 2.SS CCSS>OR OR has students add common fractions. CCSS has students understand both addition and subtraction of fractions. 2.SS SS No specific match, but CC.4.NF.3 matches in general to OR SS SS No specific match, but CC.4.NF.3 matches in general to OR SS CCSS>OR CCSS does not include addition of fractions at grade OR>CCSS CC standard only identifies multiplication of fractions by a whole number. OR also includes division, and does not specify the types of fractions used. 2.SS SS No specific match, but CC.4.NF.4 matches in general to 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 66

13 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Comment CC.4.NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. 2.SS SS No specific match, but CC.4.NF.4 matches in general to OR CC.4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. Number and Operations - Fractions (4.NF) Understand decimal notation for fractions, and compare decimal fractions. (CC.4.NF.5, CC.4.NF.6, CC.4.NF.7) CC.4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and SS SS No specific match, but CC.4.NF.4 matches in general to OR OR(-) No exact match, but content appears to be related to OR.4.1.1, OR.4.1.2, OR.5.1.1, and OR CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. OR Extend the base-ten system to read, write, and represent decimal numbers (to the hundredths) between 0 and 1, between 1 and 2, etc. OR Use models to connect and compare equivalent fractions and decimals. OR Determine decimal equivalents or approximations of common fractions. 0 2 OR>CCSS CCSS fulfills the "represent" part of this OR standard. Representations beyond numerals is not clear in this CC standard. 0 1 Weak match because there is no reference to using models in CCSS. Could be a stronger match if the mathematical processes were included in the standards (Math Practice #4). No comparison or equivalency identified in this standard. 0 1 CCSS focuses only on decimal equivalencies for fractions with a denominator of 10 or 100. CC standard would exclude finding decimal equivalents of fractions such as 1/2 or 3/4. Does not specify making the conceptual connection between fractions and decimals. 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 67

14 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. CC.4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. CC.4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. OR Use the relationship between common decimals and fractions to solve problems including problems involving measurement. OR Compare and order fractions and decimals. OR Use the relationship between common decimals and fractions to solve problems including problems involving measurement. Comment Measurement and Data (4.MD) Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. (CC.4.MD.1, CC.4.MD.2, CC.4.MD.3) -2 1 CCSS specifies fractions with denominators 10 or 100. Does not include solving problems, only specifies using decimal notation. 0 2 OR>CCSS CC standard does not include fractions. CC standard also does not specify ordering. CCSS includes using symbols to compare and justifying using a visual model OR>CCSS CCSS identifies relationships between measurement units in this 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 68

15 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Comment CC.4.MD.2 Use the four operations to solve OR Represent money amounts to 0 2 CCSS>OR OR standard only includes money. CCSS also word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. $10.00 in dollars and cents, and apply to situations involving purchasing ability and making change. includes other word problems, such as those involving distance, time, volume, and mass. CCSS is not explicit about making change. CC.4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Measurement and Data (4.MD) Represent and interpret data. (CC.4.MD.4) CC.4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. OR Solve problems involving perimeters and areas of rectangles and squares. 0 2 OR>CCSS CCSS is more specific with the use of formula. 0 0.OR(-) No exact match. Content appears to be related to OR.3.1.1, OR.3.2.7, and OR.5.1.7, but not enough to be considered a match. Content within CC.4.MD.4 is very similar to CC.5.MD.2. 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 69

16 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Measurement and Data (4.MD) Geometric measurement: understand concepts of angle and measure angles. (CC.4.MD.5, CC.4.MD.6, CC.4.MD.7) CC.4.MD.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand 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. OR Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute). Comment 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. CC.4.MD.6 Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. CC.4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. 0 0.NC New CCSS contentthe use of protractors is not specified in the Oregon standards, although they could be used in the construction of circle graphs (OR.5.1.7) or measurement of polygon angles (OR & OR.8.3.3) 0 0.NC New CCSS contentclosest content related to this standard would be in the analysis of two dimensional figures (OR.8.3.1, OR.8.3.2, & OR.8.3.3) 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 70

17 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Geometry (4.G) Draw and identify lines and angles, and classify shapes by properties of their lines and angles. (CC.4.G.1, CC.4.G.2, CC.4.G.3) CC.4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. OR Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute). Comment 1 2 CCSS>OR The OR standard identifies and compares right, obtuse, or acute. CCSS has a much broader scope of this measurement OR Identify, describe, compare, analyze, and informally classify triangles by their sides and angles. OR Build, draw, and analyze twodimensional shapes to understand attributes and properties of twodimensional space. OR Use attributes and properties of two-dimensional shapes to solve problems including applications involving parallel and perpendicular lines, congruence, symmetry, and perimeter. OR Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral). 1 2 CCSS>OR Both standards involve identifying based on sides and angles but OR is specific to triangle classification. CCSS is not specific to a particular shape and also asks that students draw points, lines, etc. and is about drawing and identifying. OR standards include identifying, describing, comparing, etc. triangles based on sides and angles. 1 2 Both CCSS is more specific with geometric attributes. The Oregon focus is more on building 2D shapes. 4.G.1 and 4.G.2 together are a close match to OR Both CC.4.G.1, 4.G.2, and 4.G.3 work together to cover drawing and identifying aspect of the OR standard. Oregon also asks for use and application involving 2D shapes Both Classification of triangles by angle isn't specified by this CCSS, but could be inferred based upon the CC header and standard. Classification of triangles by side isn't included. CCSS includes more than triangles by expanding classification to all 2D figures. 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 71

18 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial Comment 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. OR Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse and acute). 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). CC.4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. OR Identify, describe, compare, analyze, and informally classify triangles by their sides and angles. OR Build, draw, and analyze twodimensional shapes to understand attributes and properties of twodimensional space. OR Use attributes and properties of two-dimensional shapes to solve problems including applications involving parallel and perpendicular lines, congruence, symmetry, and perimeter. OR Identify and classify triangles by their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral). OR Recognize and create shapes that are congruent or have symmetry. 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) 1 2 Both Match on classifying or analyzing 2D shapes. 4.G.1 and 4.G.2 together are a close match to OR Both CC.4.G.1, 4.G.2, and 4.G.3 work together to cover drawing and identifying aspect of the OR standard. Oregon also asks for use and application involving 2D shapes Both OR standard is specific to classifying triangles. CCSS specifies using lines and angles to classify 2D figures. CCSS only specifically identifies right triangles as a category. 3 1 First reference to symmetry in CCSS, so it appears to be the best match to the OR standards. The CCSS is more detailed but does not include congruence. 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 72

19 Indexed by Common Core State Standards (CCSS) CCSS GRADE 4 CC standard OR standard Grade Δ Alignment Partial CC.4.G.3 Recognize a line of symmetry for OR Use attributes and properties of a two-dimensional figure as a line across two-dimensional shapes to solve problems the figure such that the figure can be including applications involving parallel folded along the line into matching parts. and perpendicular lines, congruence, Identify line-symmetric figures and draw symmetry, and perimeter. lines of symmetry. Comment 1 2 Both CC standard makes no mention of solving problems with the content. CC.4.G.3 is the only CCSS standard in K-8 that identifies symmetry. OR G.1 Recognize and identify line and rotational symmetry of twodimensional figures OR>CCSS CCSS specific to reflection symmetry and does not address rotation symmetry. CC.4.G.3 is the only CCSS standard in K-8 that identifies symmetry. 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 73

20 Oregon Mathematics Crosswalk: 4 th Grade Indexed by Oregon Standards 247

21 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Extend the base-ten system to read, write, and represent decimal numbers (to the hundredths) between 0 and 1, between 1 and 2, etc. CC.5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. CC.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 1 2 Both OR standard sees as extension of the base 10 system. CCSS goes thru thousandths and uses expanded notation 0 2 OR>CCSS CCSS fulfills the "represent" part of this OR standard. Representations beyond numerals is not clear in this CC standard. 1 1 Connection on the representation of decimal numbers, but CCSS also includes a general understanding of all base ten values. OR Use models to connect and compare equivalent fractions and decimals. CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. CC.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. CC.3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 0 1 Weak match because there is no reference to using models in CCSS. Could be a stronger match if the mathematical processes were included in the standards (Math Practice #4). No comparison or equivalency identified in this standard. 0 2 Both Good match for using models to connect and compare equivalent fractions. CCSS is missing decimals and OR is missing explaining why Both 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. 248

22 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Determine decimal equivalents or approximations of common fractions. OR Compare and order fractions and decimals. CC.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. 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.4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 3 1 CCSS does not address the intent of the OR standard - making sure students understand the connection between fractions and decimals. CCSS focuses on the skill of dividing to determine equivalencies. 0 1 CCSS focuses only on decimal equivalencies for fractions with a denominator of 10 or 100. CC standard would exclude finding decimal equivalents of fractions such as 1/2 or 3/4. Does not specify making the conceptual connection between fractions and decimals Both CCSS includes using symbols to compare, and justifying conclusions. OR includes fractions and fraction and decimal comparisons. 0 2 OR>CCSS CC standard does not include fractions. CC standard also does not specify ordering. CCSS includes using symbols to compare and justifying using a visual model. 249

23 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Compare and order fractions and decimals. OR Estimate decimal or fractional amounts in problem solving. CC.4.NF.2Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CC.5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 0 2 Both CC standard does not include decimals. CC standards also does not specify ordering. OR standard does not include recording results with symbols and justifying the conclusion. 1 2 Both CCSS includes using symbols to compare, OR standard includes fractions, and fractions/ decimals together. 1 1 OR standard specifies problem solving and CC specifies word problems, which are not the same thing. CC includes only addition and subtraction of fractions. The OR standard includes decimals and does not specify an operation. The OR standard is also more focused on estimation skills in problem solving. CC standard is more focused on computing skills to solve problems. OR Represent money amounts to $10.00 in dollars and cents, and apply to situations involving purchasing ability and making change. CC.2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and (cents) symbols appropriately Both OR standard includes representing money amounts and CCSS has a broader application. 250

24 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Represent money amounts to $10.00 in dollars and cents, and apply to situations involving purchasing ability and making change. CC.4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 0 2 CCSS>OR OR standard only includes money. CCSS also includes other word problems, such as those involving distance, time, volume, and mass. CCSS is not explicit about making change. OR Apply with fluency multiplication facts to 10 times 10 and related division facts. 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 CC.3.OA.1 Interpret products of whole multiplication (e.g., equal-sized groups, numbers, e.g., interpret 5 7 as the total arrays, area models, equal intervals on the number of objects in 5 groups of 7 objects number line), place value, and properties of each. operations (commutative, associative, and distributive). 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 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 OR>CCSS Oregon had more models and properties are listed 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. 251

25 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Apply understanding of models for CC.3.OA.5 Apply properties of operations as multiplication (e.g., equal-sized groups, strategies to multiply and divide. arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive). CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models Both Oregon standard has models and CCSS includes division. Both include properties of operations. 0 3 CCSS specifies whole numbers up to four digits by one digit and two digit numbers. 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>CCSS CCSS Standard speaks specifically to using the area model as a representation for multiplication. OR standard lists this representation among others. 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. 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 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. 252

26 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment 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. CC.7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 3 1 Connection on estimation strategies, but CCSS includes rational numbers in any form. OR Develop and use accurate, efficient, and generalizable methods to multiply multi-digit whole numbers. CC.5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. OR Develop fluency with efficient CC.4.NBT.5 Multiply a whole number of up procedures for multiplying multi-digit to four digits by a one-digit whole number, whole numbers and justify why the and multiply two two-digit numbers, using procedures work on the basis of place value strategies based on place value and the and number properties. properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 1 2 OR>CCSS The OR standard identifies efficient and generalizable methods and not just a single algorithm. The OR standard also has higher cognitive levels of thinking. 0 2 OR>CCSS Oregon does not limit the number of digits. CC.5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. 1 2 OR>CCSS Oregon requires justification. 253

27 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Recognize area as an attribute of two-dimensional regions. 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 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. CC.3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 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.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>CCSS Oregon includes knowing that area covers a shape without gaps CCSS>OR CCSS makes the connection between concept and multiplication 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) CC 3.MD.5 is a match to (recognize area attributes) 254

28 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Recognize a square that is one unit on a side as the standard unit for measuring area. 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 CCSS>OR 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) OR Determine the appropriate units, strategies, and tools to solving problems that involve estimating or measuring area. CC.3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units) CC standard may imply using appropriate units and tools. CC standard does NOT include estimation strategies OR Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle. 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>CCSS Connection of area model to multiplication. OR standard also asks for justification Weak match on connecting area model and multiplication 255

29 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle. 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 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. OR Find the areas of complex shapes that can be subdivided into rectangles. 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 Solve problems involving perimeters and areas of rectangles and squares. CC.4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 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. 0 2 OR>CCSS CCSS is more specific with the use of formula 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. 256

30 Indexed by Oregon Standards (OR) Oregon Grade 4 OR standard CC standard Grade Δ Alignment Partial Comment OR Recognize that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas. 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 CCSS>OR CCSS is more inclusive by looking at polygons rather than only rectangles. 257