Kindergarten 5 th Grade Alignment/Comparison of Standards

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1 Kindergarten 5 th Grade Alignment/Comparison of Standards This document was developed based on the 2007 SC Academic Standards for Mathematics (2207) which are shown below in the left-hand column. The content of the related Common Core State Standards for Mathematics (CCSS-M) and the South Carolina College- and Career-Ready Standards for Mathematics (SCCCR-M) was then aligned/compared to each 2007 standard and, when appropriate, set forth in that same row. In some cases there is not an exact match between/among all mathematical aspects of listed standards. As a result, professional judgment should be used when reviewing and utilizing this alignment/comparison document. In addition, as with all support materials, the value comes from educator participation in development; not from a pre-developed tool. Since this document is merely guidance, the actual South Carolina State Board of Education adopted South Carolina College- and Career-Ready Standards for Mathematics should be referenced when developing curriculum and other instructional materials SC Academic Standards for Mathematics K-2.1 Recall numbers counting forward through 99 and backward from 10 For questions/comments please contact Mary Ruzga at mruzga@ed.sc.gov Kindergarten Alignment/Comparison Common Core Standards for Mathematics K.CC.1: Count to 100 by ones and by tens. South Carolina College- and Career- Ready Standards for Mathematics K NS.1 Count forward by ones and tens to 100. K-2.2 Translate between numeral and quantity through K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.4: Understand the relationship between numbers and K.NS.2 Count forward by ones beginning from any number less than 100. K.NS.3 Read numbers from 0-20 and represent a number of objects 0-20 with a written numeral. K.NS.4 Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that:

2 quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. c. Understand that each successive number name refers to a quantity that is one larger. K.CC.5 Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. a. the last number said tells the number of objects in the set (cardinality); b. the number of objects is the same regardless of their arrangement or the order in which they are counted (conservation of number); c. each successive number name refers to a quantity that is one more and each previous number name refers to a quantity that is one less. K.NS.5 Count a given number of objects from 1-20 and connect this sequence in a one-to-one manner. K.NS.6 Recognize a quantity of up to ten objects in an organized arrangement (subitizing). 2

3 K 2.3 Compare sets of no more than 31 objects by using the terms more than, less than, and the same as. K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Note: Include groups with up to ten objects.) K.CC.7: Compare two numbers between 1 and 10 presented as written numerals. K.NS.7 Determine whether the number of up to ten objects in one group is more than, less than, or equal to the number of up to ten objects in another group using matching and counting strategies. K.NS.8 Compare two written numerals up to 10 using more than, less than or equal to. 3

4 K 2.4 Represent simple joining and separating situations through 10. K-2.5 Understand that addition results in increase and subtraction results in decrease. K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. K.ATO.1 Model situations that involve addition and subtraction within 10 using objects, fingers, mental images, drawings, acting out situations, verbal explanations, expressions, or equations. K.ATO.3 Compose and decompose numbers up to 10 using objects, drawings, and equations. K.ATO.4 Create a sum of 10 using objects and drawings when given one of two addends 1-9. K-2.6 Analyze the magnitude of digits through 99 on the basis of their place values. 4 K 2.7 Represent the place value of each digit in a 2-digit whole number. K.NBT.1. Compose and decompose numbers from 11 to 19 into 10 ones and some further ones and record each composition or decomposition by a drawing or equation; understand that these numbers are composed of 10 ones and one, two, three, four, five, six, seven, eight, or nine ones. Moved to 1 st Grade K.NSBT.1 Compose and decompose numbers from separating ten ones from the remaining ones using objects and drawings. Moved to 1 st Grade

5 K-2.8 Identify ordinal positions through 31 st. K.NS.9 Identify first through fifth and last positions in a line of objects. K-3.1 Identify simple growing patterns. K-3.2 Analyze simple repeating and growing relationships to extend patterns. K-3.3 Translate simple repeating and growing patterns into rules. K 3.4 Classify objects according to one or more attributes such as color, size, shape and thickness. K 4.1 Identify the 2-dimensional shapes square, circle, triangle, and rectangle and the 3-dimensional shapes cube, sphere, and cylinder. 5 Moved to 3 rd Grade K.MD.3: Classify objects or people into given categories; count the numbers in each category and sort the categories by count. (Note: Limit category counts to be less than or equal to 10.) K.G.2: Correctly name shapes regardless of their orientations or overall size. K.G.3: Identify shapes as twodimensional (lying in a plane, flat ) or three-dimensional ( solid ). K.G.4: Analyze and compare twoand three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other K.ATO.6 Describe simple repeating patterns using AB, AAB, ABB, and ABC type patterns. Moved to 3 rd Grade K.MDA.3 Sort and classify data into 2 or 3 categories with data not to exceed 20 items in each category. K.G.2 Identify and describe a given shape and shapes of objects in everyday situations to include two-dimensional shapes (i.e., triangle, square, rectangle, hexagon, and circle) and threedimensional shapes (i.e., cone, cube, cylinder, and sphere). K.G.3 Classify shapes as twodimensional/flat or threedimensional/solid and explain the reasoning used. K.G.4 Analyze and compare two- and three-dimensional shapes of different sizes and orientations using informal

6 attributes (e.g., having sides of equal length). language. K-4.2 Represent two-dimensional geometric shapes. K 4.3 Use the positional words near, far, below, above, decide, next to, across from, and between to describe the location of an object. K-4.4 Use the directional words left and right to describe movement. K.G.5: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.1: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. K.G.5 Draw two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, and circle) and create models of threedimensional shapes (i.e., cone, cube, cylinder, and sphere). K.G.1 Describe positions of objects by appropriately using terms including below, above, beside, between, inside, outside, in front of, or behind. K-5.1 Identify a penny, a nickel, a dime, a quarter, and a dollar and the value of each. K 5.2 Compare the lengths of two objects both directly and indirectly to order objects according to length. K 5.3 Use nonstandard units to explore measurement concepts (length and weight). K-5.4 Identify measuring devices used to measure length (rulers, yardsticks, tape measures), weight (scales, balances), time 6 K.MD.2: Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Moved to 1 st Grade K.MDA.2 Compare objects using terms such as shorter/longer, shorter/taller, and lighter/heavier. Moved to 1 st Grade Moved to 2 nd Grade

7 (calendar, clock digital and analog), and temperature (thermometer digital and standard). K-5.5 Understand which measure is appropriate for a given situation (length, weight, time, and temperature). K-5.6 Use clocks (analog and digital) to tell time to the hour. K-5.7 Use a calendar to identify dates, days of the week, and months of the year. K-5.8 Recall equivalencies associated with time (7 days = 1 week and 12 months = 1 year). K-6.1 Organize data in graphic displays in the form of drawings and pictures. K-6.2 Interpret data in graphic displays in the form of drawings and pictures. Moved down from 1 st Grade; similar to K- 2.4 but now students actually add and subtract. 7 K.MD.1: Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Moved to 1 st Grade K.G.6: Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle? K.OA.2: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to K.MDA.1 Identify measurable attributes (length, weight) of an object. Moved to 1 st Grade K.MDA.4 Represent data using object and picture graphs and draw conclusions from the graphs. Moved to 1 st Grade K.ATO.2 Solve real-world/story problems using objects and drawings to find sums up to 10 and differences within 10.

8 Moved down from 1 st Grade; similar to K-2.4 but now students actually add and subtract. represent the problem. K.OA.5: Fluently add and subtract within 5. K.ATO.5 Add and subtract fluently within 5. 8

9 2007 SC Academic Standards for Mathematics Translate between numeral and quantity through st Grade Alignment/Comparison Common Core Standards for Mathematics 1.NBT.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. South Carolina College- and Career- Ready Standards for Mathematics 1.NSBT.1 Extend the number sequence to: a. count forward by ones to 120 starting at any number; b. count by fives and tens to 100, starting at any number; c. read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form; d. read and write in word form numbers zero through nineteen, and multiples of ten through ninety Use estimation to determine the approximate number of objects in a set of 20 to 100 objects Represent quantities in word form through ten. 1.NBT.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. Moved to Kindergarten for a set of up to ten objects. 1.NSBT.1 Extend the number sequence to: a. count forward by ones to 120 starting at any number; b. count by fives and tens to 100, starting at any number; c. read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form; d. read and write in word form numbers zero through nineteen, and multiples of ten through ninety. 9

10 1-2.4 Recognize whole number words that correspond to numerals (through twenty) Compare whole-number quantities through 100 by using the terms is greater than, is less than, and is equal to Recall basic addition facts to 9+9 and corresponding subtraction facts Summarize the inverse relationship between addition and 10 1.NBT.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.3: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 1.OA.1: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (Note: See Glossary, Table 1.) 1.OA.4: Understand subtraction as an unknown-addend problem. For 1.NSBT.1 Extend the number sequence to: a. count forward by ones to 120 starting at any number; b. count by fives and tens to 100, starting at any number; c. read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form; d. read and write in word form numbers zero through nineteen, and multiples of ten through ninety. 1.NSBT.3 Compare two two-digit numbers based on the meanings of the tens and ones digits, using the words greater than, equal to, or less than. 1.ATO.6 Demonstrate a. addition and subtraction through 20 b. fluency with addition and related subtraction facts through 10 1.ATO.1 Solve real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 20 with unknowns in all positions. 1.ATO.5 Recognize how counting relates to addition and subtraction.

11 subtraction. example, subtract 10 8 by finding the number that makes 10 when added to 8. 1.NBT.4: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1.ATO.4 Understand subtraction as an unknown addend problem Generate strategies to add and subtract without regrouping through twodigit numbers NBT.4: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding 1.NSBT.4 Add through 99 using concrete models, drawings, and strategies based on place value to: a. add a two-digit number and a onedigit number, understanding that sometimes it is necessary to compose a ten (regroup); b. add a two-digit number and a multiple of ATO.6 Demonstrate a. addition and subtraction through 20

12 two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. b. fluency with addition and related subtraction facts through Analyze the magnitude of digits through 999 on the basis of their place values OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 4 = = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). 1.NBT.2: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones called a ten. b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 1.NSBT.2 Understand place value through 99 by demonstrating that: a. ten ones can be thought of as a bundle (group) called a ten ; b. the tens digit in a two-digit number represents the number of tens and the ones digit represents the number of ones; c. two-digit numbers can be decomposed in a variety of ways (e.g., 52 can be decomposed as 5 tens and 2 ones or 4 tens and 12 ones, etc.) and record the decomposition as an equation.

13 1 3.1 Analyze numeric patterns in addition and subtraction to develop strategies for acquiring basic facts. 1.OA.5: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.ATO.5 Recognize how counting relates to addition and subtraction Translate patterns into rules for some simple addition and subtraction. Moved to 3 rd Grade Moved to 3 rd Grade Illustrate the commutative property based on basic facts. 1.OA.3: Apply properties of operations as strategies to add and subtract. (Note: Students need not use formal terms for these properties.) Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) 1.ATO.3 Apply Commutative and Associative Properties of Addition to find the sum (through 20) of two or three addends Analyze numeric relationships to complete and extend simple patterns. 13 Moved to 3 rd Grade Classify a number as odd or even. Moved to 2 nd Grade Moved to 2 nd Grade Classify change over time as quantitative and qualitative. Moved to 6-8 Moved to ATO.9 Create, extend and explain using pictures and words for: a. repeating patterns (e.g., AB, AAB, ABB, and ABC type patterns); b. growing patterns (between 2 and 4 terms/figures) Identify the three-dimensional 1.G.2: Compose two-dimensional 1.G.2 Combine two-dimensional shapes

14 geometric shapes prism, pyramid, and cone Analyze the two-dimensional shapes circle, square, triangle, and rectangle. shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Note: Students do not need to learn formal names such as right rectangular prism. ) 1.G.1: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. (i.e., square, rectangle, triangle, hexagon, rhombus, and trapezoid) or threedimensional shapes (i.e., cube, rectangular prism, cone, and cylinder) in more than one way to form a composite shape. 1.G.1 Distinguish between a twodimensional shape s defining (e.g., number of sides) and non-defining attributes (e.g., color). 1.G.4 Identify and name twodimensional shapes (i.e., square, rectangle, triangle, hexagon, rhombus, trapezoid, and circle) Classify 2-dimensional shapes as polygons or non-polygons. While closed shapes are identified as an attribute in 1.G.1 above, the term polygon is not formally introduced until 3 rd grade Identify a line of symmetry. Moved to 4 th Grade Moved to 4 th Grade Use the positional and directional terms north, south, east, and west to describe location and movement. While closed shapes are identified as an attribute in 1.G.1 above, the term polygon is not formally introduced until 3 rd grade Use a counting procedure to determine the value (less than a dollar) of a collection of pennies, nickels, dimes, and 14 Moved to 2 nd Grade Moved to second Grade.

15 quarters Represent a nickel, a dime, a quarter, a half-dollar, and a dollar by combinations of coins Represent money by using the cent and dollar notations Use customary units (whole inches) to measure the length of an object Generate common referents for whole inches Use common referents to make estimates (whole inches) Use nonstandard units to measure the weight of objects Use clocks (digital and analog) to tell and record time to the half-hour Illustrate past and future dates on a calendar Represent dates in standard form (June 1, 2007) and numeric form ( ) Use thermometers (Celsius and Fahrenheit) to identify temperatures. Moved to 2 nd Grade Moved to 2 nd Grade Moved to 2 nd Grade Moved to 2 nd Grade Moved to Kindergarten 1.MD.3: Tell and write time in hours and half-hours using analog and digital clocks. Moved to 2 nd Grade 1.MDA.6 Identify a penny, nickel, dime and quarter and write the coin values using a ȼ symbol. Moved to 2 nd Grade Moved to 2 nd Grade Moved to 2 nd Grade Moved to Kindergarten 1.MDA.3 Use analog and digital clocks to tell and record time to the hour and half hour Use survey questions to collect data Organize data in picture graphs, 15 1.MD.4: Organize, represent, and interpret data with up to three categories; ask and answer 1.MDA.4 Collect, organize, and represent data with up to 3 categories using object graphs, picture graphs, t-

16 object graphs, bar graphs, and tables Interpret data in picture graphs, object graphs, bar graphs and tables by using the comparative terms more, less, greater, fewer, greater than, and less than. Came from 2 nd Grade questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.7: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, = 2 + 5, = OA.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8+? = 11, 5 =? 3, =?. charts and tallies. 1.MDA.5 Draw conclusions from given object graphs, picture graphs, t-charts, tallies, and bar graphs. 1.ATO.2 Solve real-world/story problems that include three whole number addends whose sum is less than or equal to ATO.7 Understand the meaning of the equal sign as a relationship between two quantities (sameness) and determine if equations involving addition and subtraction are true. 1.ATO.8 Determine the missing number in addition and subtraction equations within

17 1.NBT.5: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1.NBT.6: Subtract multiples of 10 in the range from multiples of 10 in the range (positive or zero differences), 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 and explain the reasoning used. 1.MD.1: Order three objects by length; compare the lengths of two objects indirectly by using a third object. 1.MD.2: Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or 1.NSBT.5 Determine the number that is 10 more or 10 less than a given number through 99 and explain the reasoning verbally and with multiple representations including concrete models. 1.NBST.6 Subtract a multiple of 10 from a larger multiple of 10, both in the range 10 to 90, using concrete models, drawings, and strategies based on place value. 1.MDA.1 Order three objects by length using indirect comparison. 1.MDA.2 Use nonstandard physical models to show the length of an object as the number of same size units of length with no gaps or overlaps. 17

18 overlaps. 1.G.3: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 1.G.3 Partition two-dimensional shapes (i.e., square, rectangle, circle) into two or four equal parts. 18

19 2007 SC Academic Standards for Mathematics Generate estimation strategies to determine the approximate number of objects in a set of at most 1,000 objects. 2 nd Grade Alignment/Comparison Common Core Standards for Mathematics South Carolina College- and Career- Ready Standards for Mathematics Represent quantities in word form (through twenty) Represent multiples of ten in word form (through ninety) Compare whole number quantities (through 999) with symbols (<, >, =) and words (is less than, is greater than, is equal to) Interpret models of equal grouping (multiplication as repeated addition and arrays.) Interpret models of sharing equally (division) as repeated subtraction and arrays. 2.NBT.3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 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. 2.NSBT.3 Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form. 2.NSBT.3 Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form. 2.NSBT.4 Compare two numbers with up to three digits using words and symbols (i.e., >, =, or <). 2.ATO.4 Use repeated addition to find the total number of objects arranged in a rectangular array with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends Generate strategies to add and 2.NBT.7: Add and subtract within 2.NSBT.7 Add and subtract through

20 subtract pairs of two-digit whole numbers with regrouping. 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.6: Add up to four two-digit numbers using strategies based on place value and properties of operations. using concrete models, drawings, and symbols which convey strategies connected to place value understanding. 2.NSBT.6 Add up to four two-digit numbers using strategies based on knowledge of place value and properties of operations Generate addition and subtraction strategies to find missing addends and subtrahends in number combinations through Generate strategies to round numbers through 90 to the nearest OA.1: Use addition and subtraction within 100 to solve oneand 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. (Note: See Glossary, Table 1.) Rounding moved to 3 rd Grade 2.ATO.1 Solve one- and two-step realworld/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 99 with unknowns in all positions. Rounding moved to 3 rd Grade 20

21 Analyze the magnitude of digits through 9999 on the basis of their place values Analyze numeric patterns in skip counting that use the numerals 1 through Translate patterns into rules for simple multiples Analyze relationships to complete and extend growing and repeating patterns involving numbers, symbols and objects. 2.NBT.1: 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: a. 100 can be thought of as a bundle of ten tens called a hundred. b. 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). 2.NBT.2: Count within 1000; skipcount by 5s, 10s, and 100s. Moved to 3 rd Grade Skip counting (extending a pattern) is addressed in 1 st Grade 2.NSBT.1 Understand place value through 999 by demonstrating that: a. 100 can be thought of as a bundle (group) of ten tens called a hundred ; b. the hundreds digit in a three-digit number represents the number of hundreds, the tens digit represents the number of tens, and the ones digit represents the number of ones; c. three-digit numbers can be decomposed in multiple ways (e.g., 524 can be decomposed as 5 hundreds, 2 tens and 4 ones or 4 hundreds, 12 tens, and 4 ones, etc.) 2.NSBT.2 Count by tens and hundreds to 1,000 starting with any number. Moved to 3 rd Grade Skip counting (extending a pattern) is addressed in 1 st Grade Identify quantitative and qualitative change over time Analyze quantitative and qualitative change over time. Moved to 6-8 Moved to 6-8 Moved to 6-8 Moved to Analyze the thee-dimensional shapes spheres, cubes, cylinders, prisms, pyramids, and cones according to the 21

22 number and shape of the faces, edges, corners, and bases of each Identify multiple lines of symmetry. Moved to 4 th Grade Moved to 4 th Grade Predict the results of combining and subdividing polygons and circles Use accounting procedure to determine the value of a collection of coins and bills Use coins to make change up to one dollar Use appropriate tools to measure objects to the nearest whole unit: measuring length in centimeters, feet, and yards; measuring liquid volume in cops, 22 2.G.3: 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. 2.MD.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? 2.MD.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? 2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and 2.G.3 Partition squares, rectangles and circles into two or four equal parts, and describe the parts using the words halves, fourths, a half of, and a fourth of. Understand that when partitioning a square, rectangle or circle into two or four equal parts, the parts become smaller as the number of parts increases. 2.MDA.7 Solve real-world/story problems involving dollar bills using the $ symbol or involving quarters, dimes, nickels, and pennies using the symbol. 2.MDA.7 Solve real-world/story problems involving dollar bills using the $ symbol or involving quarters, dimes, nickels, and pennies using the symbol. 2.MDA.1 Select and use appropriate tools (e.g., rulers, yardsticks, meter sticks, measuring tapes) to measure the length of an object.

23 courts, and gallons; measuring weight in ounces and pounds; and measuring temperature on Celsius and Fahrenheit thermometers. measuring tapes Generate common measurement referents for feet, yards, and centimeters Use common measurement referents to make estimates in feet, yards, and centimeters Predict whether the measurement will be greater or smaller when different units are used to measure the same object Use analog and digital clocks to tell and record time to the nearest quarter hour and to the nearest five-minute interval Match a.m. and p.m. to familiar situations Recall equivalencies associated with length (12 inches = 1 foot, 3 feet = 1 yard) and time (60 minutes = 1 hour, 24 hours = 1 day) MD.3: Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.3: Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.7: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MDA.3 Estimate and measure length/distance in customary units (inch, foot, yard) and metric units (centimeter, meter). 2.MDA.3 Estimate and measure length/distance in customary units (i.e., inch, foot, yard) and metric units (i.e., centimeter, meter). 2.MDA.2 Measure the same object or distance using a standard unit of one length and then a standard unit of a different length and explain verbally and in writing how and why the measurements differ. 2.MDA.6 Use analog and digital clocks to tell and record time to the nearest fiveminute interval using a.m. and p.m.

24 2-6.1 Create survey questions to collect data Organize data in charts, pictographs, and tables. 2.MD.9: 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 wholenumber units. 2.MD.10: 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. (Note: See Glossary, Table 1.) 2.MDA.9 Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a single-unit scale. 2.MDA.8 Generate data by measuring objects in whole-unit lengths and organize the data in a line plot using a horizontal scale marked in whole number units. 2.MDA.9 Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a single-unit scale Infer trends in a data set as increasing, decreasing, or random Predict on the basis of data whether events are more likely or less likely to occur. Moved to 6-8 Moved to 6-8 Moved to 6-8 Moved to 6-8 Was previously Generate Strategies now fluency is required OA.2: Fluently add and subtract within 20 using mental strategies. (Note: See standard 1.OA.6 for a list of mental strategies). By end of 2.ATO.2 Demonstrate fluency with addition and related subtraction facts through 20.

25 Moved up from 1 st Grade 25 Grade 2, know from memory all sums of two one-digit numbers. 2.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.NBT.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.8: Mentally add 10 or 100 to a given number , and mentally subtract from a given number NBT.9: Explain why addition and subtraction strategies work, using place value and the properties of operations. (Note: Explanations may be supported by drawings or objects.) 2.MD.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 2.MD.5: Use addition and 2.ATO.3 Determine whether a number through 20 is odd or even using pairings of objects, counting by twos, or finding two equal addends to represent the number (e.g., = 6). 2.NSBT.5 Add and subtract fluently through 99 using knowledge of place value and properties of operations. 2.NSBT.8 Determine the number that is 10 or 100 more or less than a given number through 1,000 and explain the reasoning verbally and in writing. 2.MDA.4 Measure to determine how much longer one object is than another, using standard length units.

26 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.MD.6 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. 2.MDA.5 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 through 99 on a number line diagram. 2.MDA.10 Draw conclusions from t- charts, object graphs, picture graphs, and bar graphs. 2.G.1: Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Note: Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2: Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 2.G.1 Identify triangles, quadrilaterals, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. 2.G.2 Partition a rectangle into rows and columns of same-size squares to form an array and count to find the total number of parts. 26

27 2007 SC Academic Standards for Mathematics Compare whole number quantities (through 999,999) with symbols (<, >, =) and words (is less than, is greater than, is equal to). 3rd Grade Alignment/Comparison Common Core Standards for Mathematics South Carolina College- and Career- Ready Standards for Mathematics 3.NSBT.5 Compare and order numbers through 999,999 and represent the comparison using the symbols >, =, or < Represent whole numbers in word form. (through 999,000) Apply an algorithm to add and subtract whole numbers fluently Apply procedures to round any whole number to the nearest 10, 100, or Understand fractions as parts of a whole 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. 3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 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. 3.NSBT.4 Read and write numbers through 999,999 in standard form and equations in expanded form. 3.NSBT.2 Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations. 3.NSBT.1 Use place value understanding to round whole numbers to the nearest 10 or NSF.1 Develop an understanding of fractions (i.e., denominators limited to 2, 3, 4, 6, 8, 10) as numbers. a. A fraction 1/b (called a unit fraction) is the quantity formed by one part when a whole is partitioned into b equal parts; b. A fraction a/b is the quantity formed by a parts of size 1/b; c. A fraction is a number that can be represented on a number line based on counts of a unit fraction;

28 3 2.6 Represent fractions that are greater than or equal to Recall basic multiplication facts through 12 x 12 and the corresponding division facts. 3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.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 two one-digit numbers. d. A fraction can be represented using set, area, and linear models. 3.NSF.2 Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: a. two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line; b. fraction equivalence can be represented using set, area, and linear models; c. Whole numbers can be written as fractions (e.g., and ); d. fractions with the same numerator or same denominator can be compared by reasoning about their size based on the same whole. 3.NSF.3 Develop an understanding of mixed numbers (i.e., denominators limited to 2, 3, 4, 6, 8, 10) as iterations of unit fractions on a number line. 3.ATO.7 Demonstrate fluency with basic multiplication and related division facts of products and dividends through

29 3 2.8 Compare the inverse relationship between multiplication and division Analyze the effect that adding, subtracting, or multiplying odd and/or even numbers has on the outcome Generate strategies to multiply and divide whole numbers by using one singledigit factor and one multi-digit factor OA.6: Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. 3:OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 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. For example, describe a context in which a number of shares or a number of groups can be expressed as OA.5: Apply properties of operations as strategies to multiply and divide. (Note: Students need not use formal terms for these properties.) Examples: If 6 4 = 24 is known, then 4 6 = 24 is also 3.ATO.6 Understand division as a missing factor problem. 3.ATO.9 Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table). 3.ATO.1 Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and explain the relationship between the factors (i.e., 0-10) and the product. 3.ATO.2 Use concrete objects, drawings and symbols to represent division without remainders and explain the relationship among the whole-number quotient (i.e., 0-10), divisor (i.e., 1-10), and dividend. 3.ATO.5 Apply properties of operations (i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and divide and explain the reasoning.

30 Use basic number combinations to compute related multiplication problems that involve multiples of Analyze the magnitude of digits through 999,999 on the basis of their place value Create numeric patterns that involve whole-number operations Apply procedures to find missing numbers in numeric patterns that involve whole-number operations. 30 known. (Commutative property of multiplication.) can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = 56. (Distributive property.) 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. 3:OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, 3.NSBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90, using knowledge of place value and properties of operations. 3.NSBT.5 Compare and order numbers through 999,999 and represent the comparison using the symbols >, =, or <. 3.ATO.9 Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table). 3.ATO.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor,

31 3 3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction, or multiplication equation. determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = 3, 6 6 =?. 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. (Note: This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order -- Order of Operations.) product, dividend, divisor, or quotient. 3.ATO.8 Solve two-step real-world problems using addition, subtraction, multiplication and division of whole numbers and having whole number answers. Represent these problems using equations with a letter for the unknown quantity Illustrate situations that show change over time as increasing. Moved to 6-8 Moved to Identify the specific attributes of circles: center, radius, circumference, and diameter Classify polygons as either triangles, quadrilaterals, pentagons, hexagons, or octagons according to the number of their sides. 31 Moved to 6-8 with a higher degree of expectation other than simply identify. 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 Moved to 6-8 with a higher degree of expectation other than simply identify. 3.G.1 Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share attributes (e.g., 4-sided figures) and the shared attributes can define a larger

32 3-4.3 Classify lines and line segments as either parallel, perpendicular, or intersecting Classify angles as either right, acute, or obtuse Classify triangles by lengths of side (scalene, isosceles, equilateral) and by sizes of angles. (acute, obtuse, right) Exemplify points, lines, line segments, rays, angles Analyze the results of combining and subdividing circles, triangles, quadrilateral s, pentagons, hexagons, and octagons. 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. Moved to 4 th Grade Moved to 4 th Grade 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 as 1/4 of the area of the shape. category (e.g., quadrilateral). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Moved to 4 th Grade 3.G.3 Use a right angle as a benchmark to identify and sketch acute and obtuse angles. Moved to 4 th Grade 3.G.2 Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction. Recognize that equal parts of identical wholes need not have the same shape Predict the results of one transformation (slide, flip, turn) of a geometric shape. Moved to 6-8 Moved to Use the fewest possible number of coins when making change. 32