Below is an unusual pool table. The
dimensions are determined by the lengths of
the sides. When you click on the green flag a
yellow ball will start to roll at a 45 degree
heading and bounce off the opposite sides
until it ends up in a corner. The computer
will then tell you how many bounces the ball
made and in what corner it wound up in.
Your Challenge: See if you can come up with
a way to predict (1) what the number of touches will be
for any given size pool table and (2) which
corner the ball will end up in.
An example (4x7 table)
is done for you (above). Try the others using
the Scratch
tool* and see what you get.
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W
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L
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Touches
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Final Corner
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4
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7
|
9
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Upper Right
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8
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3
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|
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5
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4
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|
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10
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13
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|
|
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5
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10
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Try other number combinations. See what
conjectures or conclusions you come with.
(Use the data
sheets to help you collect more data.)
*The NCTM Illuminations paper pool app currently
has a problem. Until it is fixed use the Scratch
tool instead.
Source:
Original Version 1.0 developed at CIESE
Center for
Innovation in Engineering &
Science Education (2007)
Revised
11.1.21 currently under continued
revision
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