Ratios and Proportions

Mamie P. Scott                 Edward Coles Elementary School
                               8440 South Phillips
                               Chicago, Il. 60617
                               312-535-6650

Objectives:

    The seventh grade student will:

        Review ratios and proportions.

        Determine the relationship between individual height and reach. 

        Find equal ratios.

        Solve word problems using ratios by trial and error.

        Practice finding pictorial expressions of fractions to   
        decode a message.

Materials:

    Measuring tapes or string
    Chart paper 
    Construction paper  (red, to make 15 Red beans; white, to make  
                         15 Black-eyed peas; and green, to make 15
                         Lima beans)
    Worksheet with pictorial expressions of fractions

Recommended Strategies:

   . Form small groups of three or four students.  
   . Distribute measuring tape or string to each group. 
   . Use the tape or string to measure and compare height to reach.
   . Record results on chart paper in this order:
   ________________________________________________________________
     Tall-Rectangle     Perfect-Square     Short-Rectangle         
    
       If the height > reach, record name under "tall-rectangle"
       If the height < reach, record name under "short-rectangle"
       If the height = reach, record name under "perfect-square"
 
   . Students whose names are in the "Perfect-Square" column will be the Chef
     Cook to make the "Three Bean Salads" for the first activity.
   . Distribute beans randomly (one per student).
   . Write salad recipe on the chalkboard. 
   . Call a Chef Cook to read and make the first salad by selecting beans
     (students) from any group.

      Each salad contains Red beans, Lima beans and Black-eyed peas
           
            #1 This salad contains:
               4 Red beans
               1/2 as many Black-eyed peas as Red beans
               10 beans in all
           
            #2 This salad contains:
               2 Lima beans
               Twice as many Red beans as Lima beans
               10 beans in all

            #3 This salad contains:
               An equal number of Red beans and Black-eyed peas
               5 more Lima beans than Red beans
               No more than 20 beans
       
   . Groups should be encouraged to make up 3 different salads
     and continue the activity.
 
   . Next, distribute worksheet to each student with fraction message:

              Students will solve problems, analyze which of the 
              coded solutions would best fit and, by substitution
              of the lettered answer, be able to decode the 
              message.
      
   . Discuss the message.               
       
References:

    Burns, Marilyn. The I Hate Mathematics Book. Boston, Mass.: 
    Little, Brown, and Company, 1975.

    National Council of Teachers of Mathematics, Fraction Message.
    Arithmetic Teacher 36 (December 1988): 32.

    Stenmark, Jean Kerr, Thompson, Virginia, and Cossey, Ruth.        
    Family Math. Berkley, Calif.: Lawrence Hall of Science, 1986.