# NCSD 2012-2013 K-5 Math Standards

```NCSD Math Common Core State Standards: Grade K 2012-&shy;‐2013 Mathematical Practices K.MP The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. K.MP.1 K.MP.2 K.MP.3 K.MP.4 K.MP.5 K.MP.6 K.MP.7 K.MP.8 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Counting and Cardinality A. Know number names and the count sequence. K.CC K.CC.1 Count to 100 by ones and by tens. 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-&shy;‐20 (with 0 representing a count of no objects). B. Count to tell the number of objects. K.CC.4 K.CC.5 C. Understand the relationship between numbers and 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. 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. Compare numbers. K.CC.6 K.CC.7 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 (include groups with up to ten objects). Compare two numbers between 1 and 10 presented as written numerals. Operations and Algebraic Thinking D. K.OA.2 K.OA.3 K.OA.4 K.OA.5 E. K.OA K.NBT Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Measurement and Data Describe and compare measurable attributes. K.MD.1 K.MD.2 K.MD Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 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. Classify objects and count the number of objects in each category. K.MD.3 Geometry Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) K.G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1 K.G.2 K.G.3 I. Work with numbers 11–19 to gain foundations for place value. K.NBT.1 H. Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem.(This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. 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 = 2 + 3 and 5 = 4 + 1). 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. Fluently add and subtract within 5. Number and Operations in Base Ten G. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.1 F. 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. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-&shy;‐dimensional (lying in a plane, “flat”) or three-&shy;‐dimensional (“solid”). Analyze, compare, create, and compose shapes. K.G.4 K.G.5 K.G.6 Analyze and compare two-&shy;‐ and three-&shy;‐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 attributes (e.g., having sides of equal length). Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” NCSD Math Content Standards: Grade 1 2012-&shy;‐2013 (ODE + CCSS) 2007 ODE: Number and Operations: Develop an understanding of whole number relationships, including grouping in tens and ones. 1.1.1 Compare and order whole numbers to 100. 1.1.2 Represent whole numbers on a number line, demonstrating an understanding of the sequential order of the counting numbers and their relative magnitudes. 1.1.3 Count and group objects in tens and ones. 1.1.4 Identify the number of tens and ones in whole numbers between 10 and 100, especially recognizing the numbers 10 to 19 as 1 group of ten and a particular number of ones. 1.1.5 Determine the value of collections of pennies, nickels, and dimes. CCSS-&shy;‐M: Operations and Algebraic Thinking 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. 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.OA.7 Using the equal sign to show equivalent expressions and determining whether equations are true or false. 2007 ODE: Number and Operations and Algebra: Develop understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts. 1.2.1 Model “part-&shy;‐whole,” “adding to,” “taking away from,” and “comparing” situations to develop an understanding of the meanings of addition and subtraction. 1.2.2 Develop and use efficient strategies for adding and subtracting whole numbers using a variety of models, including discrete objects, length-&shy;‐based models (e.g., lengths of connecting cubes) and number lines. 1.2.3 Apply with fluency sums to 10 and related subtraction facts. 1.2.4 Use the concept of commutative [4 + 2 = 2 + 4], associative [(4 + 3) + 7 = 4 + (3 + 7)], and identity [0 + 3 = 3] properties of addition to solve problems involving basic facts. 1.2.5 Relate addition and subtraction as inverse operations. 1.2.6 Identify, create, extend, and supply a missing element in number patterns involving addition or subtraction by a single-&shy;‐digit number. CCSS-&shy;‐M: Number and Operations in Base 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. 1.NBT.2. Understand that the two digits of a two-&shy;‐digit number represent amounts of tens and ones. 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). 2007 ODE: Geometry: Compose and decompose two-&shy;‐ and three-&shy;‐dimensional geometric shapes. 1.3.1 Describe geometric attributes of shapes (e.g., round, corners, sides) to determine how they are alike and different. 1.3.2 Recognize and create shapes that are congruent or have symmetry. 1.3.3 Compose and decompose shapes (e.g., cut a square into two right triangles and put two cubes together to make a rectangular prism), thus building an understanding of part-&shy;‐whole relationships as well as the properties of the original and composite shapes. 1.3.4 Recognize shapes when viewed from different perspectives and orientations. CCSS-&shy;‐M: Geometry 1.G.1. Distinguish between defining attributes (e.g, triangles are closed and three-&shy;‐sided) versus non-&shy;‐