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As a student, I always enjoyed mathematics. In high school I accepted all math classes provided, such as Calculus. The first math class I took in school was a cinch, and I believed that this one could be absolutely different. What would I find out about basic school math that I did not already know? The first day of course showed me exactly what a ridiculous question that has been and I moved on to find out things about mathematics that had never before been brought to my attention. This paper will discuss what I have learned about subtraction, concerning students, about the Common Core State Standards, and the way my theory map has changed since my first draft. Cardinality and Subitizing Cardinality and subitizing aren't subjects encountered in daily life, if you don't happen to be a math education specialist. Both were labels I had not heard previously for theories that hadn't previously happened to me. They had been the start of my math vocabulary--an important asset when expected to talk openly about math. Van de Walle, Karp, also Bay-Williams clarify that understanding the concept of cardinality means knowing that "the last count word indicates the quantity of the group" (p. 127). People who know this concept--that the previous number counted has value--"are stated to possess the cardinality principle" (Van de Walle, et. al, 2010, p. 127). The concept of cardinality originally puzzled me--that I took for granted that counting had meaning. However, placing a title to the idea helped to solidify my comprehension of numbers and provided me with a vital part of language when discussing mathematics. The same is true for subitizing. Clements describes subitizing as "the lead perceptual fear of the numberosity of a group" or "immediately seeing just how many" (1999, p. 400). I.