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Topic: [math-learn] Other Subtraction methods, beyond borrowing?
Replies: 14   Last Post: Sep 29, 2010 8:13 PM

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Jon Wilson

Posts: 56
Registered: 9/25/05
[math-learn] Re: Other Subtraction methods, beyond borrowing?
Posted: Sep 29, 2010 10:40 AM
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Ron!

Just as a follow up to my last post back to you, I feel this method will result in a better "teachable moment" for these student's who currently struggle with the borrowing method.

Nice examples. Thank you very much!
Jon



--- In math-learn@yahoogroups.com, "Ron" <Ronald_Ferguson@...> wrote:
>
> If any wonders where this delayed borrowing came from, I adapted it from the method I like to use for adding signed numbers before formulating the "rules."
>
> 8+3 = 11 (known info for counting numbers. The rest makes use of additive inverses and 0)
> 8 + (-3) = 5+ 3+(-3) = 5 + 0 = 5
> -8+ (3) = -8 +(-5)+5 + (3) = -8+ (-5) + 8 = 0 + (-5) = -5
> -8+(-3) = (-8) + (-3) + 11 + (-11) = -8 +(-3) + 8 + 3 + (-11) = 0 + 0 + (-11) = -11
>
> If no one wondered, I apologize for wasting bandwidth.
>
> cordially,
> -Ron
>
>
> From: Ron
> Sent: Tuesday, September 28, 2010 9:50 PM
> To: math-learn@yahoogroups.com
> Cc: math-learn@yahoogroups.com
> Subject: Re: [math-learn] Other Subtraction methods, beyond borrowing?
>
>
>
> You can try delayed borrowing: Consider
>
> 52 50 + 2
> 37 30 + 7 subtract
> === ======
> ?? ? + ?
>
> Now add 10 to the subtrahend and subtract 10 from the difference to rebalance (this way you get to use a nice property of 10-10 = 0)
>
> 50 + 2 + 10 50 + 12
> 30 + 7 30 + 7 subtract
> ========= =======
> ? ? - 10 20 + 5 -10 = 10+ 5 = 15
>
> 52
> 37 subtract
> ==
> 15
>
> 463 400+ 60 + 3
> 174 subtract 100 +70 +4
> ==== ==========
> ??? ? + ? + ?
>
> Add 100 + 10 to the subtrahend and subtract 100+10 from the difference:
>
> 400 + 60 + 100 + 3 + 10 400 + 160 + 13
> 100 + 70 + 4 100 + 70 + 4
> =================== =============
> ? + ? + ? 300 + 90 + 9
> subtract 100 + 10 100 + 10
> =============
> 200+80 + 9
> 289
>
> I'm not suggesting that this is a great way to subtract because it takes quite a bit of space, but it does reveal some properties of the base ten numeration system and inserts the usefulness of the number zero. There may be some cases for which the technique is exceptionally clumsy, but then perhaps students will better appreciate the compact form of borrowing a bit better when you demonstrate it. The advantage here is that delayed borrowing isolates the two steps in the borrowing process.
>
> I've never seen this in a textbook and perhaps there's a good reason for that.
>
> cordially,
> -Ron
>
> From: Robert Hansen
> Sent: Tuesday, September 28, 2010 9:15 PM
> To: math-learn@yahoogroups.com
> Cc: math-learn@yahoogroups.com
> Subject: Re: [math-learn] Other Subtraction methods, beyond borrowing?
>
> Google "subtraction and regrouping". The idea is that the student is actively borrowing from the left by looking at it's true value (x10) rather than mechanically at its face value as just a digit. The key is a good understanding of place value.
>
> On Sep 28, 2010, at 9:47 PM, "jjaywilson2004" <jjaywilson2004@...> wrote:
>

> > We all know about the borrowing method used in teaching and applying subtraction.
> >
> > Does anyone have a suggestion, link or method that could be a substitute for the borrowing method?
> >
> > Jon
> >
> >

>
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