on May 20, 2003
Cracker - dollar ? Dollar - cracker ? Hmmmm
This is an interesting question - what are the mathematical differences
between a cracker and a dollar ?
These ideas come to mind:
-- cracker is mostly visualized as a "whole" while (at least for me and
I think for kinds of this age) a dollar carries simultaneous images of
a whole piece of paper (not able to be broken up in any meaningful
way)- a set of 4 quarters - a set of 10 dimes - etc.
-- because of their familiarity with money the image of 4 quarters
"standing in for a dollar" and 3 quarters representing an amount may
have more meaing
-- using dollars allows us to more easily make the connection between
3/4 and .75, etc.
-- the cracker on the other hand allows us to keep the image of "whole"
as we break the cracker apart - it forces us to "see" and think in
fractional parts where interchanging the paper dollar with a variety of
coins makes it much harder to "see"
-- cracker (at least when drawn on a board) can be broken in to an
infinited number of pieces - dollars (cents) can only meaningfully be
broken into 100 pieces
Boy, this would have been really important to have considered before
this lesson. Especially since, as a teacher you probably plan the
perfect lessons and decide on the appropriate contexts to illuminate
the mathematics you wanted to focus on - but you know, then you let the
kids in on it and darned if they don't pick a different example or