K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
K.CC.4.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. (one-to-one correspondence)
K.CC.4.b Understand that the last number name said tells the number of objects counted. (cardinality) The number of objects is the same regardless of their arrangement or the order in which they were counted.
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
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. (Drawings need not show details, but should show the mathematics in the problem.)
K.OA.2 Solve addition and subtraction word problems.
K.OA.2.a Solve addition and subtraction word problems (within 10), involving result unknown problems, put together/take apart total unknown, and put together/take apart addend unknown, e.g., using objects or drawings to represent the problem.
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 = 2 + 3 and 5 = 4 + 1).
Work with numbers 11-19 to gain foundations for place value.
K.NBT.1 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.
K.G.4 Analyze and compare two- and 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 attributes (e.g., having sides of equal length).