## Thursday, April 22, 2010

### Reversing and Transposing Numbers

Reversing and transposing are both common math mistakes, but they are not the same thing.
• Reversing means writing the mirror image of a number.
• Transposing means writing multiple numbers out of order; changing the order of arrangement
REVERSE
Walking through our next-door-neighbor's parking lot this week, I noticed a 4 written in reverse on the curb:

NOTE - do you know how hard it is to set a number backwards on a web page? Not easy, I assure you!

I was surprised that the street painter would have the stencil upside down while painting. Writing numbers backwards is one thing, but painting a number stencil the wrong way around is a bit careless. Or maybe it was done on purpose? Who IS 24 and why don't they like her/him?

Kids often write their numbers backwards, sometimes even upside-down. To help alleviate that, we give them plenty of chances to practice. You may see this in our K and 1st grade materials:

Practice helps a lot, even for dyslexic folks. Maybe the curb painter is dyslexic and meant to paint this instead:

or this

( That introduces another math term - inverted. It means upside down, on its head. )

You can do a "reverse look-up" of a telephone number - you put in a number and get out the caller's information, rather than putting in a name and getting the phone number. This function is especially useful when you are getting those irritating calls from a person or business that always hangs up.

(Reminds me of yet another math term - recurring - things that keep happening over, and over, and over, and over, and over ... like those phone calls.)

TRANSPOSE
There are lots of complex ways of transposing numbers. One is changing the arrangement of data in a spreadsheet from rows to columns. I know there are functions that help you do this in spreadsheet software [copy/paste special/transpose], but I often find myself re-entering data because it's faster for me to retype small blocks of text than to remember the software process.
• Move data from rows to columns and vice versa
• Move a term from one side of an equation to the other (as long as you reverse its sign)
• Move music to another key (higher or lower)
REVERSE TRANSPOSE
If you are very clever, you can reverse transpose in a spreadsheet. That means re-sorting the order of the columns, then turning them into rows, or vice versa. In this usage it does not mean writing the numbers backwards.

I'm not going to tell you how to do this. The Excel Math blog isn't supposed to be about Excel spreadsheets. We are an elementary math curriculum, since 1976. Here's a brief history.