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1. |
Organize
class into groups of two and equip each group
with a BarCulator and PieCulator to be used
alternately by each person in the group. (If
necessary, students could be organized into
groups of four, with two students using one of
the tools) |
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2. |
Have
students put all of the pieces for the tool they
are using on the table with the tool, and
instruct each person (or pair of persons) to
fill the BarCulator or PieCulator, depending on
which they are using, with a certain color of
pieces until the total is 1. Be sure to
have the students “discover” that not only
are the pieces the same color, but the same
shape and size. As the students do this at their
desk, the teacher can demonstrate on the
overhead projector, as needed. |
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3. |
Have
the students count the number of pieces that it
took to fill the tool, and record it on their
paper, along with what it said on each piece.
For instance, if they had used the orange
pieces, they would write 4 and ¼ down on their
paper. |
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4. |
Continue
to have students follows steps two and three
with each of the different colors available in
both the BarCulator and PieCulator. Have them
exchange tools periodically to experience both
tools. |
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5. |
When
they have recorded all of the possible
combinations (2, ½; 3, 1/3; 4, ¼; 6, 1/6; 8,
1/8), ask them to notice the relationship
between the number of pieces that it took to
fill their calculator tool to 1, and the number
on the bottom of the fraction written on each
piece. |
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6. |
Lead
students to define the number on the bottom of
the fraction as the denominator, and that the
purpose of the denominator is to show the number
of equal pieces of a certain size must be used
to equal one unit. Lead students to see that
although, the shape of the PieCulator pieces and
the BarCulator pieces were different, each could
be used to equal one unit. |
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7. |
Extend
the understanding of the students of this
concept by asking for the number of pieces that
would be required if the pieces said other
fractions such as 1/5, 1/17, etc. |
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8. |
Show
the students that they can write that they have
8 pieces that are each 1/8 by writing 8/8, or if
they have 3 pieces that are each 1/3, by writing
3/3 and so on. |
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9. |
Have
the students fill the calculator with a certain
color of pieces again. If you have them use
yellow, ask them how to express that the
calculator is full. (6/6) Then ask them to
remove one piece and count how many are there
now. Ask them how they think they could
represent the fact that they now have 5 pieces
that say 1/6. (5/6) |
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10. |
Continue
with other examples of this until they realize
that the number on the top of the fraction tells
the number of pieces of a certain size that they
have. Define this number as the numerator. |
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11. |
Do a
test for understanding by filling the overhead
BarCulator and/or overhead PieCulator with a
certain color and having them express the
fraction and then partially filling the
calculator with same color pieces and having
them express the fraction. |
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12. |
Extend
their understanding by having them work page 1
of the Fraction Fun book, as you discuss the
questions as a class. You may choose to help
them with some of the questions and have them do
the rest with their group while you walk around
checking for understanding. Please note on this
step that some of the fractions have a numerator
bigger than the denominator, which allows you to
say that they have enough pieces to fill up the
calculator and have some left over. For
instance, if the fraction is 7/6, then they can
fill the calculator once (6/6) and have 1/6
left, so that is one and one sixth (1-1/6). |
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13. |
Notice
that this page also allows the students to move
from the use of manipulatives to the use of
pictures and then to the written representations
of the fractions, both numerical and in words.
Emphasize the use of words to help them when
they will experience word problems in the
future. |
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| Extensions: |
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1. |
Have
students complete page 2 of the Fraction Fun
book, as an independent practice. |
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2. |
If
desired, the concept of numerator and
denominator can be practiced by playing the Name
It game with a deck of FraCards. This game works
well with groups of four students. The
directions for playing the game are included
with the FraCard deck. |
