Week 5

The latest concept explored in Math 251 would be the "base" concept. So to explain, when we add, and the sum of two placeholders is greater than 10, we carry the one to the next placeholder to be added there. Its something drilled into our heads at a young age and becomes second nature later in life. The issue with these "second nature" equations is that when trying to explain why we do this to children, our only answer is "because thats how you do it." So to better understand why, and how, this concept occurs, we experimented with different bases.

For example, base of four

  231     Why is this? Because when two numbers of a placeholder reached 4, we had to carry one
+121     and add from there, just like we do with ten! So, in the 2nd placeholder, since 3+2=5, we had
_____   lower the one leftover, and carry what would be the base four to the next placeholder.
  1012

Changing the rules to better understand your own understanding of a concept, will heighten your ability to be a better teacher in that concept. Its like seeing things from many perspectives to understand it better as a whole! Which is a great way to teach.