My Calc BC kiddos took their AP test last Thursday and we still have classes through next Wednesday. So, I have some time to play with. This year is the first time through for me teaching a Discrete Math elective and one of the topics I ran through with that class was the notion of different number bases along with a little history about some counting systems and the symbols used. I decided that my Calc BC students deserved the opportunity to think about this as well and for the past two days we have had fun saying things like 5 + 4 = 13 (guess the base!) and things like 5 X 2 = A. My students have appreciated me joking that they should make sure to go home and tell their parents that I said 5 + 4 = 13. What I have appreciated is seeing the combination of discomfort and curiosity which turns into a bit of joy as my students wrap their heads around this topic. It is especially in testing to me to see that the BC kids, who are really the top math scholars here, are not inherently more comfortable with this topic than my Discrete students were. There is a pretty big gap in the comfort level with mathematical ideas between these two groups of students, but this notion of fundamentally reconstructing meaning for numbers is a great equalizer. In BC today I even threw out this question – convert the base 8 number 41.37 into a decimal number. Contextualizing the ‘decimal’ portion of this number was not obvious right away, but they were easily convinced once one of their classmates offered a rationale for it. I know that this is far from an earth-shattering ideas, but I also know that this is an idea that too many students are not exposed to in their high school experience and I am kind of pleased that I get to blow their minds a bit. Tomorrow we talk about the Mayans and the Babylonians and we wrestle with their numeration systems. A fun way to wind down the year.