CECmath.39


TITLE:    EQUIVALENT FRACTIONS

AUTHOR:   Elizabeth Lofties, St. Charles Borromeo
          Elementary School, Oklahoma City, Oklahoma

GRADE LEVEL:   Appropriate for grades 3-5

OVERVIEW:  Most students will benefit from the use of
physical objects when they are introduced to the
concept of equivalent fractions.  This activity was
designed to show the students that the notion of
several names for a number is similar to the notion of
several names for a person.  One of them is the "given
name".  In the same way that we refer to "Rebecca
Smith, alias Becky Smith", we can refer to "1/2, alias
3/6".

OBJECTIVES:  Students will be able to:
1.  Write a fraction to tell what part of a region
    is shaded.
2.  Name the numerator and denominator of a
    fraction.
3.  Identify equivalent fractions.

RESOURCES/MATERIALS:
Teacher:  rectangular pieces of  paper, chalkboard,
chalk

Student:  crayolas

ACTIVITIES AND PROCEDURES:
1.   Provide each student with a piece of rectangular
     paper.  Fold the paper in half.  After you have
     folded the paper in half, instruct the students to
     do the same.  Explain that a fraction is a part of
     a whole.  You have divided a whole piece of paper
     into two equal parts.

     Instruct the students to color one of the two
     equal parts.  Ask a student to write 1/2 on the
     board to show that one out of the two equal parts
     is now shaded.

     Introduce the vocabulary words numerator and
     denominator. The numerator is the number of parts
     shaded and the denominator is the total number of
     equal parts.   (For those students who have
     difficulty remembering which is the numerator and
     which is the denominator, try this memory
     association technique----In a fraction, one number
     is UP above the line and one is DOWN below the
     line.  Numerator has an "u" in it and so does up;
     denominator begins with "d" and so does down.)

2.   Repeat the same activity with pieces of paper,
     demonstrating 1/4, 3/4, 1/3, 2/3, 1/8. Each time,
     a student should write the fraction on the board
     and identify the numerator and the denominator.
     If you prefer, project a rectangle on the overhead
     projector and divide the rectangle into the same
     fractions as those in the paper-folding
     demonstration.
3.   Equivalent Fractions:  Ask students to fold a
     rectangular sheet of paper in half and color one
     of the two equal parts.  Ask what fraction of the
     paper is colored (1/2).  Now have them refold the
     same paper and then fold it in half once again.
     Unfold.  How many equal parts now? (4)  What
     fraction is shaded (2/4 or 1/2)  Since the amount
     of shading has not changed, this means that 1/2 =
     2/4.  Tell students that 1/2 and 2/4 are two names
     for the same amount.  Therefore, they are
     equivalent.  Now have students refold the papers
     and then fold in half a third time.  Unfold.  What
     new fraction have they found that is equivalent to
     1/2 and 2/4?  (4/8)  These three fractions name
     the same amount.


TYING IT ALL TOGETHER:  Once students have a firm
understanding of equivalent fractions, they will be
ready to find "another name" for a fraction  by
multiplying or dividing the numerator and denominator
by the same (nonzero) number.  This emphasis on
equivalent fractions will pay dividends when you begin
teaching addition and subtraction of fractions with
unlike denominators.