| 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 |
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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;
(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 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.
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