TEACHING HOPPY TO MULTIPLY BY "BUILDING-TABLE ALGORITHM"
HOPPY Multiplies, by COUNTS, (say) 3 X 4
- For first multiplier (3), HOPPY constructs a column with 3 ROWS
of DISRIBUTED COUNTERS, say, bottle-tops or stones or asterisks).
*
*
*
- For second multipler (4), HOPPY MAKES 4 COPIES of this COLUMN, STACKING THEM SIDE BY SIDE
* * * *
* * * *
* * * *
- To complete the calculation, HOPPY COUNTS the COUNTABLES to obtain
a COUNT of 12.
- So HOPPY ANNOUNCES the PRODUCT: 3 X 4 = 12 TO THE PRINTER.
FLOWCHART FOR HOPPY'S "TABLE MULTIPLICATION TRICK"
\=========/
\ START /
\ /
\ /
\_/
|
v
|
----------------------------------------
|[LEFT MULTIPLIER] X [RIGHT MULTIPLIER]|
|______________________________________|
|
v
___________|_______________
|CONSTRUCT COLUMN OF LEFT |
|MULTIPLIER COUNTABLES |
------------------------
|
v
__________|___________
|MAKE COPY OF LEFT |
------------->|MULTIPLIER-COLUMN |
| |BESIDE 1ST COLUMN |
| ----------------------
| |
| V
^ |
| /\
| / \
| /DOES\
| /NUMBER\
| /OF COL- \
| /UMNS EQUAL\ _____________ _______________
----<---NO--------\RIGHT MUL-/--->----YES---|COUNT TABLE|---->---|PRINT PRODUCT|
\TIPLIER?/ ------------- ---------------
\ / |
\ / v
\ / |
\/ / \
/ \
/STOP \
-------
EXAMPLE with STAGES and (UNFOLDED) FLOWCHART.
ANTITONIC DIAGRAM OF MULTIPLICATION BY TABLE-ALGORITHM
^ |
MAXTONE: ADJOINING| |MINTONE: DIFFERENCE BETWEEN
COLUMN COPIES | |NUMBER OF COLUMN COPIES AND
| vVALUE OF RIGHT MULTIPLIER