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 Discussion: All Topics Topic: Colored multiplication patters and conservation laws

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 Subject: Colored multiplication patters and conservation laws Author: Sonny Date: Jun 11 2004
Developed 1963, taught this to son, Tim, who won First Mathematics Prize in
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, twnety-fives,
one-hundred-twenty-fives, etc., become obvious. (I relate coloring these
patterns to discovery of chromosomes and DNA.) Purposes: (1)learning arithmetic;
anthropologist that people "feel need for
their lives to fit a pattern". Under (2): PROPERTY OF TWO-NESS (OR
NON-TWO-NESS) IS CONSERVED UNDER TRANSFORMATION OF ADDING TEN TO NUMBER.
PROPERTY OF FOUR-NESS (OR NON-...) IS CONSERVED UNDER TRANSFORMATION OF
ADDING ONE HUNDRED TO NUMBER. PROPERTY OF EIGHT-NESS (OR NON-...) IS
CONSERVED ... OF ADDING ONE THOUSAND .... Etc. Also, PROPERTY OF FIVE-NESS (OR
NON-...) IS CONSERVED UNDER THE TRANSFORMATION OF ADDING TEN TO NUMBER.
PROPERTY OF TWENTY-FIVE-NESS (OR NON-...) IS CONSERVED ... OF ADDING ONE
HUNDRED .... Etc. Two more obvious patterns: "neighbors of ten", namely, nine
and eleven (right-diagonal and left-diagonal grid-patterns), 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 Third-Graders.