On+Base+Twelve

= On Base Twelve =

Basic counting... (getting started)
On Monday 9/13, we counted together in **base twelve** for the first time. Just like in base five, base twelve means that we have a grouping unit that is not ten, and that we will use that grouping unit to build numbers. We counted up to one base as follows:

one, two, three, four, five, six, seven, eight, nine, _, _, _

We decided to call the number after nine "tee" and symbolize it with the capital letter T. We decided to call the number after T "eee" and symbolize it with the capital letter E. We decided to call the base "dozen," for obvious reasons! We have also decided to say that it's okay to abbreviate this verbally and in writing as "dough" or "do" (pronounced "dough").

So, the number word sequence is: one, two, three, four, five, six, seven, eight, nine, tee, eee, dozen And the digits for this sequence are: 1, 2, 3, 4, 5, 6, 7, 8, 9, T, E, 10 Now, of course, in base twelve "10" refers to one group of twelve and no additional tallies.


 * Can you keep going and count up to two-dozen, or 20?**

Note that when we kept counting on Wednesday 9/15, we decided to call a dozen dozens a "baker." This is symbolized by 100 in base twelve. **What does it look like?**

Just like in developing base five, to get to know base twelve it's important to: Can you count three less than each of the listed numbers (all in base twelve)?
 * 1) **Make numbers in base twelve.** For example, what is 19 (a base ten number) in base twelve? What is 27 (a base ten number)? What about 49 (a base ten number)? 100 (a base ten number)? Drawing out tally marks, writing the number word, and writing digits will help you get to know this base system.
 * 2) **Count!** There's no way around it--you have to count in a system to get to know it. Can you count one more than each of the listed numbers (the below are all numbers in base twelve)?
 * 1E
 * 29
 * 7D
 * 20
 * 32
 * 4E
 * DD
 * E0

Patterns in counting
It is also important to develop patterns in counting... what patterns have we noticed in class when counting by 3s in base twelve? By fours? By Ts? By 5s? [posting opportunity: Discuss one of these patterns __and try to explain it__.] Ashley Gilchrist: When counting by 4's in base 12, a definite pattern is developed. Couting by 4's in base 12 to 50 in base 12 looks as follows: 4, 8, 10, 14, 18, 20, 24, 28, 30, 34, 38, 40, 44, 48, 50. There is an apparent pattern when counting by 4's in base 12. There is a pattern with the ones digits of 4, 8, 0. This pattern can be explained because 4 is an even factor of a dozen. 4 goes into a dozen 3 times, which explains why the pattern repeats every 3 numbers. The ones digits form the pattern of 4, 8, and 0. There are 3 numbers in each dozen group which futhers the explantion that the pattern is formed becasue 4 goes into a dozen 3 times.
 * Patterns when counting by 3s:
 * Patterns when counting by 4s:
 * Patterns when counting by Ts:
 * Patterns when counting by 5s: