# CCSS-M Non-Negotiable Skills in Elementary Grades

Primary Grades: Kindergarten through Second Grade During the first three years—from Kindergarten through second grade, the goal of CCSS-M is that children understand, master and apply additive reasoning. This means children acquire true understanding and mastery of counting numbers (number concept), addition and subtraction concepts, facts, procedures and see addition and subtraction as inverse relationships—given a subtraction problem, they can solve it by addition and vice-versa. They should also understand the concept of place value (as a pattern of representing numbers in the base-ten system. At the same time, children are able to name, recognize, and represent (draw) the commonly found objects in their environment and are able to perform simple operations such as finding their perimeters. CCSS-M recommends three years to achieve this fundamental goal, which is the foundation of all future mathematics. Moreover, mastery should reflect understanding, fluency, and applicability of this important concept of additive reasoning. Kindergarten The focus of mathematics teaching and learning for children in Kindergarten is to acquire the number concept and relationships between numbers. Number concept[1] means:
• Representing, comparing, and recognizing whole numbers in different forms and modes: discrete (sets of random objects—counting objects), continuous (visual/spatial—comparing visually the length and area of objects, such as Cuisenaire rods to determine larger, smaller, etc.), pictures (like marks on a paper, clusters, number line, etc.), abstract (forming and recognizing numbers);
• Fluency in number relationships up to ten—mastery with understanding (decomposition/recomposition of a number, e.g., the number 7 can be seen as made of 7 and 0 (0 and 7), 6 and 1 (1 and 6), 5 and 2 (2 and 5), 4 and 3 (3 and 4);
• Fluency of 45 sight facts[2] (can recognize the facts by sight just like children can recognize certain words by sight);
• Expressing numbers (two-digit) through place value representation (e.g., 56 = 50 + 6 = 40 + 16 = 30 + 26 = 20 + 36 = 10 + 46 = etc.);
• Fluently able to count numbers and understanding role of number words (difference between a quantitative and non-quantitative words, difference between cardinal and ordinal numbers); and
• Recognizing, identifying, and naming commonly found objects and shapes in their environment and spatial relationships and corresponding vocabulary.
In order to achieve the appropriate level of competence in these concepts, a great deal of teaching and learning time (almost 70% of allotted instructional time) in Kindergarten should be devoted to the development of number concept and its mastery. In addition, at the end of Kindergarten, children should be able to represent the first 30 numbers on the number line and fluently count forward and backward by 1, 2, and 10 from any number up to 100 and beyond. First Grade The focus of first grade work is to build on the number concept. Children learn number relationships and place value, specifically
• Understanding addition and subtraction concepts and learning   efficient strategies (using decomposition and recomposition of numbers and sight facts) for and fluency in (10 by10) addition facts and constructing and arriving at subtraction facts within 20 (without counting);
• Developing an understanding of whole number relationships and place value, including groupings in tens and ones to understand two and three digit numbers fluently (e.g., 346 = 300 + 40 + 6 = 300 + 46 = 340 + 6 = 306 + 40 = etc.);
• Developing an understanding of linear measurement and measuring lengths as iterating length units (moving from egocentric measurement to using “go between” units, e.g., the room is 35 foot lengths to it is 40 book lengths); and
• Reasoning about, attributes of, and composing and decomposing geometric shapes commonly found in the child’s environment.
• Mastery of (fluency with strategic understanding—using decomposition and recomposition of numbers and sight facts) addition and subtraction facts;
• Properties of numbers: even and odd;
• Fluency in executing standard and alternative procedures of addition and subtraction with understanding that these procedures are based on place-value;
• Mastering place value beyond hundreds; expressing the number as:
5,467 = 5,000 + 400 + 60 + 7 (expanded form–canonical decomposition) = 5400 + 67 = 5000 + 467 = etc. (expanded from–non-canonical form);
• Using standard units of measure (understanding that the smaller the unit of measurement the larger the iterated quantity and vice-versa); and
• Describing and analyzing shapes.