Fickled Fractions

Elizabeth Chambers             Keller Gifted Magnet Center
                               3020 W. 108th St. 
                               Chicago IL 60655
                               312-535-2636

Objective:  (Grades 4-8)

To review the ways in which fractions are made real in our world
To show the relationship of cross multiplication and equivalent fractions
To reinforce fraction skills 

Materials Needed:

Measuring tape                  Construction paper
Pencil                          Equivalent fraction strips 
Crayons                         Ditto of a boy and girl doll

Recommended Strategy:

This lesson has been designed to enrich the students understanding of fractions 
after they have completed the study of fractions.  Now we will attempt to show 
that fractions indeed have a place in the real world. 
The students have learned to add, subtract, multiply, and divide fractions.  
They also know how to: 
                  -change mixed numbers to improper fractions.
                  -reduce fractions to lowest terms.
                  -change fractions to a decimal; to a percent; to a ratio.
                  -find the LCM and GCF.
                  -solve or make equivalent fractions.
The students will have a discussion about why fractions are so important and 
why students find understanding fractions so difficult.  How can we make 
fractions real to them?  Following the discussion, the students will do various 
activities:       -Label a doll that represents the students measurements.
                   (students will add, subtract, multiply, divide, and reduce 
                   fractions using their body measurements.)
                  -Use a calendar in order to do an activity that is a lead-in 
                   to cross multiplication and proportions.
                  -Play an equivalent fraction game to reinforce problem 
                   solving techniques.

Performance Assessment:   

Students will set up a proportion in order to solve word problems.

Multicultural Connections:  

The proportion property was recognized by the early Hindus as an arithmetic 
rule.  In the Seventh Century it was called the rule of three and was stated in 
words in the style of the times.  Merchants regarded the rule highly and used it 
widely as a mechanical procedure without explanation.  Prior to the Nineteenth 
Century the ability to use the rule of three was a mark of mathematical 
literacy.  This explains cross multiplication and also how to find an unknown in 
solving proportions.  Ex. a/b = c/d   therefore   aKd = bKc