I Did It Again!!!!!!!!

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.

Percentages

  Its amazing how many of my students have trouble with the idea of percent being something per 100.  My father years ago told me that students do much better if you put it in terms of money rather than teach it as a decimal. 

So many times I remind them to think of 100 pennies and the percent is talking about how many pennies you have out of the 100.  I realize that its not precise but it helps my ELL students understand it better.

When I taught percentages at a community college, I learned to use the is/of = #/100 to solve those "What is 20% of 18" type problems.  It made it easier for students to solve that type of problem because they knew where to put the various numbers.

Better Lessons has a nice visual lesson on percents. This is a complete lesson plan that relies on a video, worksheets with percent model and a smartboard presentation. The video is more of a reflection but you do get enough information to present the lesson.

The one thing I love saving sales flyers from the Sunday paper for an assignment.  I have students "shop" for things and they have to calculate their savings from the shopping trip.  This makes it more realistic, especially if you are having them grocery shop.  Other times, I might have students plan to remodel a room and calculate the savings they received on the materials.

Another time, I had students decide to be a business.  They had to research the wholesale cost of the item and calculate the mark-up so they knew what they would have to sell it for so they could meet expenses. 

I just found a lovely article from George Mason University on using Art to help teach fractions, decimals and percentages. The idea is students use three colors of construction paper to create art on 10 by 10 grids much like the American artist Ellsworth Kelly from the 1950's.  Once they've created the art, they have to figure out the fraction, decimal and percentage of each color.   For more advanced students have them use an 8 by 8 grid. This makes it so they are not using a base of 100 for their percentage.

So now I have two new ideas for teaching percentages. The biggest issue my students have living in such a remote area is the lack of stores with sales.  The sales flyers I have to use are from the Bush Sales Flyer or the flyer from the supermarket in the hub two about 135 miles away.  The Bush Flyer is great because it includes sales info from Loews and Home Depot.  Its the best I can come up with so we make do with it.

Have fun trying the art activity.