From: Gail (for Teacher2Teacher Service)
Date: Jul 25, 2008 at 08:08:04
Subject: Re: Applications of Percents

Hi Andrea,

Have you tried giving them a proportional picture of the
problems?   Something like this:

0_________________________1/2 of total_______________________total
0%                           50%                             100%

Each problem we solve in my classroom, we use this same model.  Students
begin by filling in the data they know from the problem, and placing a
letter (unknown) at the spot where they are looking for a solution.  For
example, if the problem is "what percent of 60 is 12?" we would draw this:

0_________12________________30_______________________60
0%        n                50%                      100%

Now we can use proportional reasoning to solve the problem, or we can just
set up a proportion and cross multiply to solve it...

12/n = 60/100

12 x 5 = 60
n x 5 = 100
n = 20

If the problem were "40% of 56 is what number?" we would set it up this was:

0___________________n______28_______________________56
0%                 40%     50%                     100%

My students know how to determine 10% and 1% quickly, and would use those
skills to say that 10% of 56 is 5.6, so 40% of 56 is 4 times as great, or
22.4

The purpose of the visual is to check for reasonableness, and to give
students a framework for solving any percent problem that comes along.  They
have this one method that will work each time.   I hope this gives you
something to start with.  :-)  Gail


 -Gail, for the T2T service

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