Problem Solving Using Percentages

Thelma A. Rex                  Rosa L. Parks Middle School
                               147th and Robey Avenue
                               Harvey IL 60426
                               708-371-9575

Objectives: 

The student will be able to recognize the three basic types of Percentage 
Problems. 

The student will be able to:

      1.  Find what percent one number is of another.
      2.  Find a percentage of a number.                      
      3.  Find a number when the percent is known.
                                
Materials Needed:

      1-16 oz bag of plain M&M's; 19-4oz bags of M&M's; 19 plastic bags;
      1 black marker and 19 pencils; 19 student folders with plain writing 
        paper; 
      l9 M&M Math handouts and 19 calculators:  Overhead projector.
           
Strategy:

      All of the students are given a folder with a small plastic bag and one 
small bag of plain M&M's.  The students are asked to guess how many M&M's are in 
the bag.  They are asked to put their M&M's into sets by color and write the 
number of M&M's they have in each set.  They are also asked to use > or < or =, 
to show the relationship between these sets.  Students put l5 M&M's in front of 
them.  Then they are asked various questions, for example, how many piles of 
fours can you make?  What is left? 
    
      The teacher demonstrates three types of word problems on the board to find 
percents by using ratio and proportion.  The overhead projector is used to 
illustrate the same problems, but in a different way. For example: 
           
      a. The student is given the following information;  
        
         1.  the number of red M&M's in the small bag.
         2.  the total number of M&M's in the small bag.
         3.  the total number of M&M's in the big bag.
         The student is asked to find the number of red M&M's in the big bag.

      b.  A bicycle is on sale with a coupon for 25% off which is a $l5.00
savings.  How much is the bicycle without the coupon?

      c.  A set of stereo speakers is priced at $125.00.  The sales tax
is 8%.  What will be the total price of the speakers?

      d.  In a photo, Carlos measures 8 centimeters.  He is actually 56
inches tall.  In the photo his brother, Juan, measures 7 centimeters.  How tall
is Juan?
                                           
Performance Assessment:

      The students will be given a post-test.  The students will be able to
tell how many M&M's are in the big bag as compared to their small bag of
M&M's.  Students already know that there are 88 red M&M's in the big bag
and that there are a total of 527 M&M's in the big bag.

Multicultural Aspects:

      Percent comes from the Latin phrase per centum, which may be 
translated by the hundred, to the hundred, for each hundred.  The symbol
for percent is %.  Thus, 85% means the ratio 85 to 100 or 85/100.  Percent
is used for mathematical calculations throughout the world in everyday
living regardless of nationality.
 
References:

     Math and Science, A Solution. 1987, Aims Education Foundation.