Introduction To Equivalent Fractions

Rose Cartwright                Lyman Trumbull School
                               5200 North Ashland Avenue
                               Chicago IL 60640
                                312-534-2340

Objective:

To examine the part-whole relationship of numbers and to compare one fraction to 
another in order to discover their equalities. 

Materials Needed:

adding machine tape        fraction puzzle pieces 
crayons                    masking tape
paper

Strategies:

Each student will take a strip of adding machine tape that is 24 inches long.
They will measure the crown of their head.  Each tape will be labeled as halves,
thirds, fourths, etc.  These tapes will also be marked showing their fractional
parts.  Certain colors identify fractional parts--such as red marks 1/2, blue
marks 1/3, orange marks 1/4, etc.  After the measurements have been taken, each
student will place his/her tape on the chalkboard with masking tape.  From 
observation, students can clearly see that all of the red marks are aligned, as
well as all of the other colored marks, that divide each strip into equal parts.

After the students have compared the strips and have noticed the relationships,
they will begin a paper folding exercise that helps to develop the concept of 
how two fourths of the whole strip is equal to one half of the same strip.  To  
do this, fold a sheet of paper in half then color that half sheet of paper.  The
students will open the paper to the full sheet and they can see that one half
of the paper is colored.  The students will continue to fold the paper into
fourths, and as they unfold the paper, they can see that not only have they
folded the paper into four equal parts, but that half of the paper is the same 
space shaded as the two out of four parts.  The students will continue to fold
the paper into eighths and sixteenths.  They will continue using thirds, fifths,
etc.  The students will then use fraction puzzle pieces to create a square made
of equal fraction pieces.  Once a square has been completed, students can turn
the puzzle pieces over to see the numeric value of each fraction and discover
that the fractions that make up the square are equal to each other.

Performance Assessment:

Given twelve separate squares on a sheet of paper, the students will change
regions that have been divided in half into regions of fourths, eighths and
sixteenths.  Regions that have been divided into thirds, will be changed into
sixths and twelfths.  As an added discussion, students will be able to see,
looking at their original strips, how many students have the same or equal
head band sizes.


Reference:
         
Reys, Robert E., M. Suydam, and M. Lindquist.  How Children Learn Mathematics
Prentice Hall, 1989.