Transcript Hatsumon - The Math Forum @ Drexel

2nd Lesson
McAllen e-PCMI
July 19, 2007
Goal
th
(8
grade)
• For students to organize
data, recognize, and
predict patterns.
Texas TEKS
• (8.16) Underlying processes and mathematical tools.
The student uses logical reasoning to make conjectures
and verify conclusions.
• The student is expected to:
• (A) make conjectures from patterns or sets of examples
and nonexamples; and
• (B) validate his/her conclusions using mathematical
properties and relationships.
Texas TEKS
• 8.14) Underlying processes and mathematical tools.
The student applies Grade 8 mathematics to solve
problems connected to everyday experiences,
investigations in other disciplines, and activities in and
outside of school.
• The student is expected to:
• (C) select or develop an appropriate problem-solving
strategy from a variety of different types, including
drawing a picture, looking for a pattern, systematic
guessing and checking, acting it out, making a table,
working a simpler problem, or working backwards to
solve a problem;
Previous Knowledge
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greatest common factor
prime numbers
odd & even numbers
division
organizing data in a table/list
angle measures
dimensions
Major Focus
• Recognizing patterns
Questioning
• How can you predict the number of hits
and the pocket the ball will land in, for any
dimensions of the pool table?
Guiding Questions
• How many times would you simulate the
problem?
• What dimensions would you use?
• Do the dimensions 2,1 and 1,2 have the
same outcome? (Does order matter?)
• How many patterns do you see?
Guiding Questions
• Do all the patterns matter?
• What rule can be used to predict the
number of hits?
• What observations did you make about the
number of hits that occur on tables of
various sizes?
• How would you organize your data?
Anticipating Students Responses
• Students say if length is even pocket B,
without sufficient examples.
• There is no pattern to predict the pocket.
• Add the dimensions without simplifying
them to predict the hits.
• It’s impossible to organize data, too much
info.
Facilitate Discussion
• What are the different ways to organize
your data?
• Is there only one best way to organize
data?
• What patterns seem to occur in the
simulations? (hits/pockets)
• How or what dimension should you
change?
McAllen Team
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Meiling Dang
Steve Ferguson
Raul Hinojosa
Louis Shoe
Armando Soto
Dai Tolkov
Dr Monty Taylor as table advisor