Common Core Math For Roman Numerals

Is Common Core Math good for anything? Probably not, but then again, maybe.

I had no experience with Common Core Math when I came across a short video on YouTube the other day. A real teacher was running down multiplication using the Common Core principles.

The problem was “35 x 12.”

She made a box on a white board (imagine the boxes; they don't copy-paste to other company's products):

                      Tens          Ones

          Tens/

          Ones/

The top line is for the “35,” (three tens, thirty, and five ones, five) and the side labels are for the “12,” (one ten and two ones).You multiply the left by the tops and fill in the intersecting box:

                      30              5

           10/      300             50

             2/      60               10

You need to work with me here. Ten times thirty is three hundred; ten times five is fifty; two times thirty is sixty; two times five is ten.

Then you put the four numbers into column formation, positionally, and add them up.

300

50

60

10

Adding them up, you get a total of 420.

Of course you do! Most adults just say, okay, 35 times ten is 350; two times 35 is 70; 350 plus 70 gives you the answer: 420.

I could see the pedagogy for this kind of introduction to multiplication, however misguided I believe it to be. Then I wondered: since Roman numerals are not positional, could this system make sense in that context?

What do we get if we try that?

XXXV times XII

The top of the box shows three tens, thirty (XXX), and five ones (V);

The side of the box shows shows one ten on top (X), and two ones on the bottom (II). When you multiply them out, this box is the result:

                       XXX              V

               X/     CCC              L

               II/     LX                X

Ten times thirty is 300 (CCC); ten times five is 50 (L);

Two times thirty is 60 (LX); two times five is ten (X).

You can make a column to be added, but positionality does not occur in Roman numerals.

CCC

L

LX

X

Adding them up, from top to bottom, just following them along in your head, you get a total of CDXX (420).

The box works for Roman numerals, but someone with more patience than I possess would have to multiply 127 x 1,795 to really see if it worked all the way out. It's so much easier to do the simple positional multiplication that we are all familiar with:

1,795

x 127

You know how that goes, so I won't bother. The calculator says 227,965. I'm going to take their word for it.

No wonder that the entire world uses Arabic numbers.* That positionality thing really comes in handy. And the zero! Those fellows were certainly onto something. The Romans did not know about the zero.

I have no idea how Romans did it, but they did. They could obviously perform complex calculations, I mean, just look at the architecture. Huge domes! Aqueducts! However they did it, they understood complex math, at least for engineering purposes.

*Thailand does not use the Roman alphabet. The Thai alphabet is unique to Thailand, although it is very similar to the Lao alphabet. Both are based on an Indian alphabet still used to write in Hindi. (The Indian words look so different because they put a line over the word, right across the tops of the letters.) Thai has its own numbers as well, probably also from India, but they are after the fashion of the Arabic numbers and therefor fully positional, and they do employ the zero. They function exactly like Arabic numbers. The Thai numbers would work fine for accounting and complex math, but they are slowly disappearing from Thai life. You see almost exclusively Arabic numbers, everywhere. I've spent several hundred days proctoring Thai university examinations, and the only subject where you are likely to encounter Thai numbers is Thai Language. I've never seen Thai numbers in test from a math class, or an accounting class.