Activities using manipulatives help students equivalency in fractions.
Main Curriculum Tie:
Mathematics - 4th Grade
Standard 1 Objective 3
Model and illustrate meanings of multiplication and division of whole numbers and the addition and subtraction of fractions.
Painless Fractions, by Akyece B. Cummings; ISBN 10:0-7641-3439-6
Hecht, Steven Alan. (1998.) Toward an Information-Processing Account of Individual
Differences in Fraction Skills. Journal of Educational Psychology. 90. 545-59.
Background For Teachers:
Students should be familiar and comfortable with the concept of
what a fraction is and easily recognize and name fractions from halves
to twelfths. Students should be able to name equivalent fractions.
Intended Learning Outcomes:
1. Develop a positive learning attitude toward mathematics.
2. Become effective problem solvers by selecting appropriate methods,
employing a variety of strategies, and exploring alternative approaches to
Invitation to Learn
Have you ever wanted to be #1? How did you feel when you
were #1? Did you feel pretty powerful? Pretty cool? Pretty Smart?
Number ONE is the most powerful number! It can transform or
morph into an infinite number of forms of itself. To morph or
transform it must be in the “Magic Box”. (The magic box is a rectangle
divided in the middle with a fraction bar.) This is kind of like Clark
Kent went into a phone booth (a magic box) and came out as another
form of himself ----Superman!
POWER of ONE Skit—Brave teachers of Math will come dressed
in some superhero costume of their choice to represent the powerful
#ONE! It would be great to have a large box (e.g., one you could fit
into that would open and shut). On the outside of the box draw a
fraction bar. Prepare ahead of time fraction posters that are equivalent
to ONE (e.g., 2/2, 3/3, 4/4, 5/5 etc). ONE transforms himself or
morphs into the superhero he is needed to be at any moment for any
problem. Watch as he appears in his secret identity to save the day
for adding or subtracting fractions! Appear with the fractions that are
equal to ONE hung around your neck. Ham it up---the kids will love
it and they will remember it!
- Do Superhero Power of ONE skit. Include a costume if possible
and your Magic Box (phone booth) to transform into other form
of the number one.
- Give each student the Magic Box worksheet. Discuss that any
fraction that is written in the Magic Box must be equal to ONE
and therefore it will have the same numerator and denominator.
- Discuss and demonstrate with pattern blocks, fraction strips,
etc. that when a fraction is multiplied by another fraction that
equals ONE, the original fraction’s value does not change; it is
- Point out that when you multiply using the Magic Box and a
form of ONE, you are always being fair and just to all fractions
because you do the same thing to the numerator that you do
to the denominator. Everyone has been treated fairly and
numerators and denominators have been multiplied (or divided)
by the same number.
- Do several examples with manipulatives all together, in small
groups, and then have students do problems on their own.
- Place 12 objects on every student’s desk. Ask them to show
you 1/2? How do you know this 1/2? Use your hand to cover
1/2. Now cover 2/2. What is another name for 2/2?
- Separate your objects into thirds. How do you know they are
separated into thirds? Cover 1/3 of the objects. Now cover 2/3
of the objects. Now cover 3/3. Count and show me 1/3, 2/3,
3/3. What is another name for 3/3?
- Repeat with fourths, & sixths. What is another name for 4/4?
What is another name for 6/6?
- Review with Equivalent ONES worksheet.
- Have advanced learners teach struggling students the concepts.
- For learners with special needs, have them draw a super hero
ONE of their own to remind them about changing fractions
to equivalent fractions using the Magic Box and the Power of
- Compare and contrast with how things transform or change in
science (e.g., rocks change from sedimentary to metamorphic,
to igneous, etc). Have students brainstorm other things in
nature and in life that are powerful because of their ability to
- Have students teach their parents or a sibling about the
Power of ONE. Give extra credit for those that do this. If a
student can teach the concept to someone else, then they truly
understand. Have the make up their own problems to work
with parents. Have parents sign and return the note for credit.
- Have students work with someone in their family to use
the Power of ONE in a real life situation (e.g., recipes and
fractions). Write about it in their journal and share with the
- Do a cooperative learning assessment. After having been
taught the concept, have students assess their learning through
journal writing. Ask them to write a brief description of what
the have done. Have them describe how the activities with the
manipulatives and the idea of one being a powerful number
changed their perception of finding equivalent fractions.
- One way of getting students to think about the material they
have learned is to have them write their own test. Ask them to
imagine that they are the teacher. Instruct them as to exactly
what topics need to be covered (e.g., Why is one a powerful
number). Explain and give examples of how one changes
itself to different forms. You may want to require that the test
include one problem-solving situation, a reasoning question, or
other requirement. Ask students to solve their own problems.
Furner, J. M., & Duffy, M. L., (2001). Equity For All Students in the New Millennium:
Disabling Math Anxiety
Research by Jackson & Leffingwell (1999) has shown that only
7% of Americans have had positive experiences with math from
kindergarten through college. Similarly, Burns (1998) has contended
that 2/3 of US adults fear and loathe math. Whether it is 93% or 2/3
of Americans who have negative math experiences, a problem clearly
As teachers of mathematics, we need to make the learning
engaging, fun and varied. We need to individualize the learning and
the assessing to best meet the needs of each student in our class.
Created Date :
Jul 10 2008 12:19 PM