Q&A #561

Teachers' Lounge Discussion: Borrowing in mathematics

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From: Gail

To: Teacher2Teacher Public Discussion
Date: 2000052512:08:12
Subject: Re: Regrouping

Here is a questions and reply from the past that might give you an

>Now I am looking for resources, websites, and any other helpful
information on teaching the concept of subtraction with borrowing to a
6th grade child with severe learning challenges (she functions on a
2nd grade math level). My inquiry is two-fold:

1)  What is the basic knowledge that she needs in order to progress to
the line of thinking required to regroup?  Is place value enough?

2)  Are there any techniques which may help to teach this concept to
her? It has been very difficult so far.

Thanks for your help, I appreciate the information!

I am not sure what approach your text suggests, but you might try
having this student return to using manipulatives, and modeling the
problems, if you have moved on to pencil and paper work.  It is likely
that your student is having trouble thinking abstractly about the math
you are doing. It seems so simple to us...   but it really isn't.

This was made very clear to me last summer when I took a Math - A Way
of Thinking workshop.  We did all the operations, but in base six. 
Suddenly something I had been doing all my life was a struggle (and I
am good at arithmetic, so this was not something I was at ease with

We were encouraged to use beans, cups and buckets to model the numbers
(place value materials), and ever time I tried to abandon them, prior
to the point where I had really internalized the number system, I fell
on my face.  The most important thing it taught me was that what I
think about second-nature, my students DON'T think abut with facility
at all...   and no amount of pencil and paper helped me...   it was
working with those place value materials, regrouping to subtract, and
when I added, that get me the frame of reference I needed.

There are chip trading games out there, too, but I am not sure who
sells them. You assign a value to each color, using the place value
amounts (I would use a different base at first, just to make it
quicker).  So if you were using base 4, then yellow might be 1, blue
might be worth one four, red worth four squared (16), and black worth
4 cubed (64) etc., just like our tens system goes.

Then you roll a die, and take that many yellow chips.  When you have
enough, you trade for a blue.  The first person to read the black chip
wins.  You can reverse it by starting with the black chip, and
regrouping to subtract the amount you roll.  Then you are racing back
to 0.

If you would like more specific instructions for this game, I would be
happy to go into more detail.  :-)

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