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Q&A #16511


Modeling Subtraction of Integers using Red and Yellow Counters

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From: Mimi <mimisolis@comcast.net>
To: Teacher2Teacher Service
Date: Jan 14, 2006 at 03:19:12
Subject: Modeling Subtraction of Integers using Red and Yellow Counters

Modeling -7 - 5 using red(-) and yellow(+) counters is a difficult concept
to instruct.  How can this best be described so that students can fully
understand, therefore, accept the answer as -12 and not -2, -7 or some other
integer?  Students understand that they are subtracting 5 positive counters
from 7 negative counters, but they don't want to accept -- for they don't
understand -- that they have to add both red and yellow counters to the
model so that it doesn't change the value of the number they are
subtracting (in this case -7).

My model would show 7 red counters and then 5 red and 5 yellow counters to
illustrate that the value of -7 remains the same.  When I explain this, I get
perplexing facial expressions. They simply want to show 7 negative counters
and 5 positive counters. They understand the concept of additive inverse, but
they don't know that they need to apply it when subtracting a positive
integer from a negative one. They really don't understand the idea of why the
value of -7 in this problem must remain the same.  They just don't understand
what I am talking about here. How can I better describe this when modeling
subtraction of integers using red and positive counters so that they
understand that they are subtracting a positive number from a negative
number?

Thank you for helping!
Mimi

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