The Generation Of Fractions

June Muhammad                  Park Manor School
                               7037 S. Rhodes
                               Chicago IL 60637
                               312-535-3070

Objectives:  

    To use a unique multiplication grid to help students realize that simple
    fractions (reduced fractions) may have many appearances, but have the same 
    value.
    To help students learn how to factor each denominator completely.
  
Materials needed:

    Group of four students      Four 5 x 8 1/2 white tag boards
    Ruler                       Red construction paper for apples
    Glue                        Green construction paper for trees
    Masking tape                Brown construction paper for tree trunks   
    Black marker                Make grids for multiplication tables

Strategy:

    Students will select fractions written on cut out apples from a bag. 
    To begin use only even number fractions. 
    Example:  The fraction 12/24 is selected by the students.  Students look
    at the multiples of two column, and then count down to 12 grids in the
    multiples of two.  The students stop on the sixth grid.  Ask students to
    record where have counted.  The students' final fraction should be 1/2.
    Remind the students that they must change multiples when the selected 
    fractions can be further reduced.
    The fraction 3/6 requires that they leave the multiples of two.  
    Students can visualize reduced terms and the final simple term.  When odd 
    fractions are selected students can compare how each fraction is divided by 
    one and itself. 

Performance Assessment:

    Students write five higher term fractions for one simplified fraction.  
    Teacher observes and records results.
    All higher terms and reduced fractions are hung on the tree.
    Odd fractions are hung on a crab apple tree.
  
Multicultural Aspect:

    Fractions were invented by the Ancient Egyptians.

Conclusions:
    
    This activity may be used for small or large groups of students.