DoDEA CCRSM Gap Analysis Second Grade College and Career Ready Standards for Mathematics (CCRSM) DoDEA Standards Alignment Notes CLUSTER: Represent and solve problems involving addition and subtraction. Explain and demonstrate addition and subtraction for two-digit numbers without regrouping, e.g., doubling, making jumps of ten, partial sums or differences, counting up or back. DoDEA standards do not specify all the meanings for addition and subtraction listed in CCRSM. 2.M.1e Explain and demonstrate addition and subtraction for two-digit numbers with regrouping, e.g., doubling, making jumps of ten, partial sums or differences, counting up or back. For 2.OA.A.1:This standard specifically names 5 different problem situations and “unknowns in all positions” refers to 3 additional types of problems. There are 15 problem types in all, all of which 2nd grade students have to master. These problem types, and their cognitive load/difficulty, are described in Table 1 in the Glossary, which the standard refers to in a footnote. They don’t address the differences between “add to” and “put together” problems, and they don’t mention “compare” problems at all. 2.M.1g Solve multi-step problems involving addition and subtraction. 2.M.2c Use symbols to represent unknown quantities and identify values for symbols. 2.M.2f Model and describe a problem situation using symbols and operations. OPERATIONS AND ALGEBRAIC THINKING 2.M.1d 2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Alignment of DoDEA CCRSM with the DoDEA Academic Standards Page 37 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) DoDEA Standards Alignment Notes CLUSTER: Add and subtract within 20. 2.OA.B.2 2.OA.C.3 NUMBER AND OPERATIONS IN BASE TEN 2.OA.C.4 2.NBT.A.1 2.NBT.A.1.A Note that the expectation for fact memory is two years earlier for addition and subtraction in Fluently add and subtract within 20 using CCRSM. DoDEA standard includes four mental strategies. By end of Grade 2, know from 4.M.1m operations. CCRSM also explicitly includes use of memory all sums of two one-digit numbers. mental strategies. Using mental strategies is not mentioned in DODEA standard. CLUSTER: Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to Identify numbers as even or odd 20) has an odd or even number of members, numbers and determine DoDEA standard does not include the writing of 2.M.1b whether a set of objects has an e.g., by pairing objects or counting them by 2s; an equation. write an equation to express an even number as odd or even number of a sum of two equal addends. elements. Use addition to find the total number of objects DoDEA standard goes further in terms of size and Model and demonstrate arranged in rectangular arrays with up to 5 rows variety of representation but does not include 2.M.1i multiplication and division and up to 5 columns; write an equation to writing the equation as repeated addends and problems. express the total as a sum of equal addends. the emphasis on arrays. CLUSTER: Understand place value. Demonstrate mastery in sums to 20 and related subtraction facts and multiplication through 12X12 and related division facts. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens — called a "hundred." 2.M.1a Use place value to represent whole numbers through 1000 using numerals, words, and physical models. 2.M.1a Use place value to represent whole numbers through 1000 using numerals, words, and physical models. Alignment of DoDEA CCRSM with the DoDEA Academic Standards DoDEA standards do not specify all the key ideas in CCRSM, but general wording should contain all these parts. The DoDEA standard includes multiple representations. Page 38 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) 2.NBT.A.1.B 2.NBT.A.2 2.NBT.A.3 2.NBT.A.4 2.NBT.B.5 DoDEA Standards Alignment Notes The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Count within 1000; skip-count by 5s, 10s, and 100s. Use place value to represent whole numbers through 1000 2.M.1a using numerals, words, and physical models. Count by twos, fives, and tens to DoDEA standard only goes to 100 and does not 2.M.1h 100. include counting by hundreds. Use place value to represent Reading is considered a part of representation. whole numbers through 1000 2.M.1a DODEA standards do not require nor specify using numerals, words, and “expanded form.” physical models. Read and write numbers to 1000 using base-ten Identify and generate numerals, number names, and expanded form. equivalent representations for the same number by DODEA standard does not specify “based on the 4.M.1b decomposing and composing meanings of hundreds, tens, ones”. the whole number up to 1,000,000. Compare whole numbers, up to 10,000, using mathematical Compare two three-digit numbers based on The DoDEA standard is a year later, but goes to symbols (>, <, =) and words meanings of the hundreds, tens, and ones digits, 3.M.1e 10,000. (greater than, less than, equal using >, =, and < symbols to record the results of to) and arrange them in comparisons. numerical order. CLUSTER: Use place value understanding and properties of operations to add and subtract. Explain and demonstrate addition and subtraction for Separate DoDEA standards combine to give the Fluently add and subtract within 100 using two-digit numbers without full range of cases. CCRSM aims at students strategies based on place value, properties of mastering their understanding of addition and 2.M.1d regrouping, e.g., doubling, operations, and/or the relationship between making jumps of ten, partial subtraction using strategies, properties, and addition and subtraction. sums or differences, counting relationships within the number system. up or back. Alignment of DoDEA CCRSM with the DoDEA Academic Standards Page 39 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations. 2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.B.8 Mentally add 10 or 100 to a given number 100900, and mentally subtract 10 or 100 from a given number 100-900. 2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. DoDEA Standards Alignment Notes Explain and demonstrate addition and subtraction for two-digit numbers with regrouping, e.g., doubling, making jumps of ten, partial sums or differences, counting up or back. CCRSM not just asking for a procedure but for the use of varying strategies based on understanding place value and properties. DODEA standard can be interpreted as procedure only without the specificity of CCRSM. 2.M.1g Solve multi-step problems involving addition and subtraction. DoDEA standards do not specify four addends, but the CCSSM would be included in the set of multistep problems. This CCRSM is aimed at generalization of the properties, the number system and their relationship to abstract symbols. 3.M.1g Explain and solve problems involving the sum or difference of two whole numbers up to 10,000. DoDEA standard, although a year later, does go to 10,000. Mental strategies require use of the number system to construct meaning. 2.M.1e 3.M.1g 3.M.1g Alignment of DoDEA CCRSM with the DoDEA Academic Standards Explain and solve problems involving the sum or difference of two whole numbers up to 10,000. Explain and solve problems involving the sum or difference of two whole numbers up to 10,000. Mental strategies are not included in DoDEA standards. Although "explain" is included in DoDEA standard, the "why" is not. Justification present in CCRSM is not clearly present in DoDEA standard. Page 40 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) MEASUREMENT AND DATA 2.MD.A.1 2.MD.A.2 2.MD.A.3 2.MD.A.4 2.MD.B.5 DoDEA Standards CLUSTER: Measure and estimate lengths in standard units. Identify common instruments 1.M.4a used for measurement, i.e., rulers, scales, measuring cups. Measure the length of an object by selecting Measure and differentiate and using appropriate tools such as rulers, objects using both comparative yardsticks, meter sticks, and measuring tapes. 1.M.4b terms and standard units of measure, e.g., inches, centimeters. Decide which unit of measure is 2.M.4c appropriate in a given situation. Measure the length of an object twice, using length units of different lengths for the two not aligned measurements; describe how the two measurements relate to the size of the unit chosen. Estimate and measure a variety Estimate lengths using units of inches, feet, 1.M..4c of attributes of objects using centimeters, and meters. standard and nonstandard units. Measure and differentiate Measure to determine how much longer one objects using both comparative object is than another, expressing the length 1.M.4b terms and standard units of difference in terms of a standard length unit. measure, e.g., inches, centimeters. CLUSTER: Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given Solve multi-step problems in the same units, e.g., by using drawings (such 2.M.1g involving addition and as drawings of rulers) and equations with a subtraction. symbol for the unknown number to represent the problem. Alignment of DoDEA CCRSM with the DoDEA Academic Standards Alignment Notes Combined, these seem to give tools and units. Appropriate unit helps with choice of tool. DoDEA standards in K-4 are silent on how unit size and number of units reported are related. Metric and customary units are included in DoDEA Grade 1 standards. DoDEA standard also includes comparative terms. The length context is not mentioned in the DoDEA standards specifically. This aspect of length is not represented in DODEA standards in terms of addition and subtraction. Page 41 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) 2.MD.B.5 2.MD.B.6 DoDEA Standards Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.M.2c Use symbols to represent unknown quantities and identify values for symbols. 2.M.2f Model and describe a problem situation using symbols and operations. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. not aligned Alignment Notes Positioning fractions and decimals on a number line is found in DoDEA 4.M.1l. CLUSTER: Work with time and money. 2.MD.C.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.M.4a Tell time in five-minute intervals. DoDEA standard does not include a.m. and p.m. or writing time. DODEA standard indicates a procedure to be followed. 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 4.M.4j Know the process for counting coins and bills using standard money notations. Example with the DoDEA standard confirmed the idea that money context would involve practical application. Alignment of DoDEA CCRSM with the DoDEA Academic Standards Page 42 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) DoDEA Standards Alignment Notes CLUSTER: Represent and interpret data. 2.MD.D.9 2.MD.D.10 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. 1.M.4c Estimate and measure a variety of attributes of objects using standard and nonstandard units. 3.M.5b Translate information from one data representation to a graph or table, e.g., frequency table, bar graph, picture graph, line plot. 2.M.5b Collect, organize, represent, and interpret data using pictographs, bar graphs, and tables. 2.M.5d Read and interpret graphs and tables to identify main ideas, draw conclusions, and make predictions. CCRSM problem types specified are not included in DoDEA standards. GEOMETRY CLUSTER: Reason with shapes and their attributes. 2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. K.M.3a Name, describe, sort, compare, and draw two-dimensional shapes. K.M.3b Identify and compare threedimensional objects. Alignment of DoDEA CCRSM with the DoDEA Academic Standards Shape identification and comparison seems to span the grades. Explicit focus on attributes begins in DoDEA Grade 3. Creating or drawing a figure from attributes does not seem to be included in DoDEA standard statements. Page 43 DoDEA CCRSM Gap Analysis College and Career Ready Standards for Mathematics (CCRSM) DoDEA Standards 1.M.3a 2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 1.M.3d 3.M.3a 2.G.A.2 2.G.A.3 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Identify triangles, rectangles, squares, and circles as the faces of three-dimensional objects. Identify and determine whether two-dimensional shapes are congruent, i.e., same shape and size; or similar, i.e., same shape and proportional size. Identify and compare twodimensional shapes and threedimensional objects using attributes and properties, e.g., sides and angles in twodimensional shapes, faces and edges in three-dimensional objects. not aligned 2.M.1j Alignment of DoDEA CCRSM with the DoDEA Academic Standards Alignment Notes Use words, numerals, and physical models to represent fractions and their relationship to the whole. Seems like a pre-area readiness activity, but was not found in DoDEA standards. DoDEA standard does not include the reference to equal shares not necessarily being the same shape. Page 44 DoDEA CCRSM Gap Analysis Second Grade Alignment Sorted by DoDEA Standards X = grade level with similar alignment to current DoDEA standards Gray shading = no alignment with CCRSM at specified grade levels DoDEA Standards Second Grade 2.M.1a: use place value to represent whole numbers through 1000 using numerals, words, and physical models 2.M.1b: identify numbers as even or odd numbers and determine whether a set of objects has an odd or even number of elements 2.M.1c: show equivalent representations for whole numbers by using addition and subtraction facts 2.M.1d: explain and demonstrate addition and subtraction for two-digit numbers without regrouping 2.M.1e: explain and demonstrate addition and subtraction for two-digit numbers with regrouping 2.M.1f: estimate and verify answers in addition and subtraction problems with two-digit numbers CCRSM Kdg Gr 2 Gr 3 Gr 4 X X X 2.M.1g: solve multi-step problems involving addition and subtraction 2.M.1h: count by twos, fives, and tens to 100 Gr 1 X X X X X X X X X 2.M.1i: model and demonstrate multiplication and division problems X 2.M.1j: use words, numerals, and physical models to represent fractions and their relationship to the whole X X 2.M.2a; create and describe patterns with multiple attributes 2.M.2b: identify and extend a linear pattern by its rules Alignment of DoDEA CCRSM with the DoDEA Academic Standards Page 45 DoDEA CCRSM Gap Analysis DoDEA Standards Second Grade CCRSM Kdg Gr 1 Gr 2 2.M.2c; use symbols to represent unknown quantities and identify values for symbols X X 2.M.2d: represent equivalence and extend the concept to situations involving symbols X 2.M.2e: solve open sentences by representing an expression in more than one way using the associative property of addition X 2.M.2f: model and describe a problem situation using symbols and operations Gr 3 Gr 4 X 2.M.2g: describe qualitative changes 2.M.2h: describe quantitative changes, especially those involving addition and subtraction 2.M.3a: predict the results of putting together and taking apart two-dimensional shapes X X 2.M.3b: find and name locations using simple relationships and in coordinate systems 2.M.3c: identify shapes that have been rotated (turned), reflected (flipped), and translated (slide). Describe direction of translation 2.M.3d: identify and create shapes with symmetry 2.M.4a: tell time in five-minute intervals X X 2.M.4b: describe and compare relationships of time 2.M.4c: decide which unit of measure is appropriate in a given situation Alignment of DoDEA CCRSM with the DoDEA Academic Standards X X Page 46 DoDEA CCRSM Gap Analysis DoDEA Standards Second Grade CCRSM Kdg Gr 1 Gr 2 Gr 3 2.M.4d: make and use estimates of measurement, including time volume, weight, and area. Verify result X 2.M.4e: use repetition of a single unit to measure something larger than the unit X 2.M.5a: develop categories for sorting a collection of materials 2.M.5b: collect, organize, represent, and interpret data using pictographs, bar graphs, and tables 2.M.5c: generate questions, collect and organize data to address the questions, and draw conclusions 2.M.5d: read and interpret graphs and tables to identify main ideas, draw conclusions, and make prediction Gr 4 X X X 2.M.5e: describe events that are more likely, least likely, or equally likely to happen 2.M.5f: use physical models and pictures to represent possible arrangements of two or three objects 2.M.5g: identify events that can have more than one outcome Alignment of DoDEA CCRSM with the DoDEA Academic Standards Page 47

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