Today I had a couple problems on the warm-up dealing with things on sale. As we went over the problems, I realized I was doing this the same way I had learned. In fact, every time I teach this or do any problems, I always teach it the same way.
This is one of those topics that I always teach in one way. I do not show a second way of doing it. By this I mean, I have the students the cost by the percent discount and then subtract the product from the cost.
Example: You buy a $500 coat for 20 percent off. So 500 x .20 = $100 and $500 - $100 = $400. You paid $400 for the coat. This is the way I've always done it and its the way the books usually teach it.
As I was writing on the board, I realized I could easily teach it in at least two other ways.
First, I could have showed the students that if the store takes 20% off, you are actually paying 80% for the coat so its just as easy to multiply the original cost by 80% so that you don't have to subtract anything. I know this intellectually but I forget it when I'm teaching it. The nice thing about doing it this way is that it is extremely easy to create a visual representation. I often make a rectangle, divide it into 5 parts where each part represents 20%. I color in the 20% off part, leaving 80% uncolored so students can see where the 80% comes from.
Second, I could have shown them they could easily have divided the 500 by 5 so they know that each 20% represents $100. So if they take 20% off, they take $100 off the cost or 80% would be 4 - 100's or $400.
If we are teaching visualization of the concept as a way of improving understanding, why do we revert to the multiply and subtract method? Probably because its the way we learned and its our default way of doing things. I check out suggested ways of teaching percentages using visualization and the method I saw most often, used a 10 by 10 grid to represent 100%.
I am not sure how well that would work because the percentages used in high school are more often looking at either a mark-down such as when something is on sale or a mark-up for when you have your own business. So I don't think that a 10 by 10 grid would work unless there is a way to remove or add to it to represent discounts, sales tax, mark-ups etc.
So when I realized I was reverting to my usual way of teaching percentages, I made a conscientious decision to try teaching it more than one way. I need a poster that states "There is more than one way to do things!" that I can hang in my room as a reminder to me.