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Communicating about
Mathematics Using Games:
Playing Fraction Track
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Mathematical
games can foster mathematical communication as students explain and
justify their moves to one another. In addition, games can motivate
students and engage them in thinking about and applying concepts and
skills. This first part, Playing Fraction Track,
contains an interactive version of a game (based on the work of Akers,
Tierney, Evans, and Murray [1998])
that can be
used in the grades 3–5 classroom to support students' learning about
fractions. By working on this activity, students have opportunities
to think about how fractions are related to a unit whole, compare fractional
parts of a whole, and find equivalent fractions, as discussed in the
Number and Operations Standard.
In the second part, The Role of the Teacher, two video clips illustrate
communication about mathematics among a teacher and her students. The
third part, Communication among Students, shows how activities like
this allow students to use communication as a tool to deepen their understanding
of mathematics, as described in the Communication Standard. In the
fourth part, Reflecting on Practice, the teacher reflects on her own
mathematical learning that occurs as a result of using activities like
this game with her fifth-grade students.
The Game
Play the
Fraction Track game using the interactive board below. The first player
starts by moving one or more blue markers along the tracks, either forward
or backward, so that the positive and negative distances moved by all
markers add to the amount shown in the fraction box. When a piece is moved,
an outline is shown in its starting position for that turn. Clicking on
Finish Move will either let the next player take a turn if the markers
correctly add to the fraction shown on the box or display an error message
if the move was not correct. When a correct move has been entered, the
second player then similarly moves one or more red markers. If a player
cannot complete a move, a turn can be passed by clicking on the Pass button.
The first player to move all his or her markers to the right side of the
Fraction Track board wins!
[How
to Use the Interactive Figure]
[Stand-alone
applet]
Discussion
Prior to
playing this game, the game board itself should be explored. Teachers
can help students understand the relationships among the fractions on
the board by asking questions like "How was the game board constructed?"
and "How are various tracks on the board related?" The Fraction Track
board can be used as a visual model for comparing fractions and finding
equivalent forms. For example, which fraction is larger: 2/6 or 1/4? How
do the fractions 1/3 and 2/6 align on the board? Are they equivalent?
How do you know?
To extend
this game, students could make their own boards with different fractions,
with decimals, or with a combination of decimals and fractions.
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Take
Time to Reflect
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How can
playing a game like Fraction Track help a student build understanding
about the relative sizes of fractions?
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How can playing
a game like Fraction Track help a student build understanding
about the equivalence of fractions?
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What characteristics
of the classroom environment would support students as they
use a game like Fraction Track to help them deepen their understanding
of fractions?
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Reference
Akers,
Joan, Cornelia Tierney, Claryce Evans, and Megan Murray. "Name
That Portion: Fractions, Percents, and Decimals." A unit of the
curriculum Investigations in Number, Data, and Space. Parsippany,
N.J.: Dale Seymour Publications, 1998.
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