one-to-one correspondence, each object counted is matched accurately with a number word in correct sequence, conservation of set, the same number of objects are counted and then rearranged, the quantity of objects in that set does not change, cardinality, the last counting number identified represents the number of objects in the set, hierarchical inclusion, concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases, tagging with synchrony, when one object is touched it is matched with the correct word, cardinal number, a number that names the quantity of objects in a set, subitizing, the ability to name the number of objects in a set without counting but rather by identifying the arrangement of objects, number sense, an awareness and understanding about what numbers are, their relationships, their magnitude and the relative effect of operating on numbers (including mental math and estimation), number fluency, knowing how a number can be composed and decomposed then using that information flexibly and efficiently, Making Tens, the link to understanding place value and our system of tens.

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