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.