# Discussion: Keynote Part 2

 posted by: Judith Fonzi on May 20, 2003 at 7:37AM subject: 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 andI think for kinds of this age) a dollar carries simultaneous images ofa whole piece of paper (not able to be broken up in any meaningfulway)- 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 mayhave more meaing-- using dollars allows us to more easily make the connection between3/4 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 infractional 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 aninfinited number of pieces - dollars (cents) can only meaningfully bebroken into 100 piecesBoy, this would have been really important to have considered beforethis lesson. Especially since, as a teacher you probably plan theperfect lessons and decide on the appropriate contexts to illuminatethe 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 orcontext !
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