Discussion:  Research Area 
Topic:  Colored multiplication patters and conservation laws 
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Subject:  Colored multiplication patters and conservation laws 
Author:  Sonny 
Date:  Jun 11 2004 
Science Fair competition for island of Puerto Rico with exhibit of this. In
2002, put ONLINE, listed Frontpage, URL
http://members.fortunecity.com/jonhays/elementary.htm. Decimal notation has
basis ten, and 10 = 2 x 5. So patterns of tens, hundreds, thousands, ten
thousands, etc., also patterns of fives, twnetyfives,
onehundredtwentyfives, etc., become obvious. (I relate coloring these
patterns to discovery of chromosomes and DNA.) Purposes: (1)learning arithmetic;
(2)link to physics conservation laws; (3)link to observation of French
anthropologist that people "feel need for
their lives to fit a pattern". Under (2): PROPERTY OF TWONESS (OR
NONTWONESS) IS CONSERVED UNDER TRANSFORMATION OF ADDING TEN TO NUMBER.
PROPERTY OF FOURNESS (OR NON...) IS CONSERVED UNDER TRANSFORMATION OF
ADDING ONE HUNDRED TO NUMBER. PROPERTY OF EIGHTNESS (OR NON...) IS
CONSERVED ... OF ADDING ONE THOUSAND .... Etc. Also, PROPERTY OF FIVENESS (OR
NON...) IS CONSERVED UNDER THE TRANSFORMATION OF ADDING TEN TO NUMBER.
PROPERTY OF TWENTYFIVENESS (OR NON...) IS CONSERVED ... OF ADDING ONE
HUNDRED .... Etc. Two more obvious patterns: "neighbors of ten", namely, nine
and eleven (rightdiagonal and leftdiagonal gridpatterns), invoking
"casting out nines and elevens" amd "bookkeeper's check". In octal numeration,
these roles are assumed, respectively, by seven and nine; in polynomial algebra,
resp., by x  1, x + 1. I
describe teaching this to class of 25 ThirdGraders.
 
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