As a student, I always liked mathematics. In high school I took every math class offered, including Calculus. The first math class I took in college was a breeze and I thought this one would be no different. What could I learn about elementary school math that I didn't already know? The first day of class showed me how ridiculous that question was, and I continued to learn things about math that had never been brought to my attention before. This article will discuss what I have learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.Cardinality and SubitizationCardinality and subitization are not topics you encounter in everyday life, unless it happens to be a mathematics education specialist. Both were labels I had never heard before for concepts that had never occurred to me. They were the beginning of my mathematical vocabulary, an important resource when I was expected to talk freely about mathematics. Van de Walle, Karp, and Bay-Williams explain that understanding the concept of cardinality means knowing that “the last count word indicates the amount of the set” (p. 127). Those who understand this concept – that the last number counted has value – “are said to possess the principle of cardinality” (Van de Walle, et. al, 2010, p. 127). Initially the concept of cardinality left me perplexed: I took it for granted that counting had a meaning. However, naming the concept helped solidify my understanding of numbers and provided me with crucial vocabulary when discussing mathematics. The same goes for subitizing. Clements describes subitization as “the direct perceptual apprehension of the numerousness of a group” or “instantly seeing how many” (1999, p. 400). I......middle of the paper......nship between addition. The difference between kindergarten and fifth grade only affects the numbers within which these calculations should be performed. Works Cited Van De Walle, J.A., Karp, K.S., Bay-Williams, J.M., (2010). Mathematics for elementary and middle schools. Boston: Allyn & Bacon.Smith, S.S., & Stein, M.K., (1998). Selecting and creating mathematical tasks: From research to practice. Teaching mathematics in middle school, 3(4), 268-275.Battista, Michael T., (1999, February). The mathematics miseducation of American youth: Ignoring scientific research and study in education. Phi Delta Kappan.Clements, D.H., (1999, March). Subitization: what is it? Why teach it?. Teaching mathematics to children. Taylor, A. R., Breck, S. E., Aljets, C. M., (2004, October). What Nathan teaches us about transitional thinking Teaching math to children.