peacefully Posted July 28, 2011 Share Posted July 28, 2011 My 6yo is fascinated with negative numbers and has been for a while. The last few days he has been wanting to do his mental subtraction problems this way. Example: 62-38= (60-30)+(2-8)= 30+(-6)=24 He worked this out himself, and he insists that this is an acceptable way to work subtraction with regrouping problems ("It totally makes sense this way, Mom!"). I am not a mathy person at all. It seems to me that this should be okay, but what the heck do I know? Is there any reason why he shouldn't use this method? Is it going to cause confusion later on down the road? For example, the only way I can figure out a problem like this requires so many more steps. It seems so inefficient compared to the standard algorithm (with vertical subtraction). 2457-1989= (2000-1000)+(400-900)+(50-80)+(7-9) 1000-500-30-2 500-30-2 470-2 468 Do I let him continue to use his method? Just for mental math? I'm really out of my element here so any input would be helpful. Quote Link to comment Share on other sites More sharing options...
wapiti Posted July 28, 2011 Share Posted July 28, 2011 If it makes you feel any better, ds8 does something similar quite often (he'll do anything to avoid having to write it down LOL). Quote Link to comment Share on other sites More sharing options...
peacefully Posted July 28, 2011 Author Share Posted July 28, 2011 I'm glad I'm not the only one in this boat. :) The thing is, he doesn't have to write down any steps anyway. Ds does mental math problems as warm-ups, and every once in a while, I ask him to explain how he got an answer. Sometimes I also make him show me how to represent his solution with manipulatives. He has to do this whether his answers are right or wrong. It's just part of our math lesson. That was when I first learned that he was working out his subtraction problems this way. At first, I could not for the life of me figure out what he was doing with his units. I think the problem was 40-15, and I actually said, "No, you can not take 5 from a zero," to which he replied, "Yes, you can, Mom, and it's negative 5 units." :001_huh: Then he said that he has 3 tens and negative 5, so the answer is 25. Because I grew up on the standard "borrowing" algorithm, it took me several minutes to figure out that he might be on to something, but I'm concerned that his way is really only workable for 2-digit problems. Maybe I should just let it go? Perhaps he'll figure out a different solution when we start doing mental math problems with bigger numbers. Quote Link to comment Share on other sites More sharing options...
KAR120C Posted July 28, 2011 Share Posted July 28, 2011 I'm glad I'm not the only one in this boat. :) The thing is, he doesn't have to write down any steps anyway. Ds does mental math problems as warm-ups, and every once in a while, I ask him to explain how he got an answer. Sometimes I also make him show me how to represent his solution with manipulatives. He has to do this whether his answers are right or wrong. It's just part of our math lesson. That was when I first learned that he was working out his subtraction problems this way. At first, I could not for the life of me figure out what he was doing with his units. I think the problem was 40-15, and I actually said, "No, you can not take 5 from a zero," to which he replied, "Yes, you can, Mom, and it's negative 5 units." :001_huh: Then he said that he has 3 tens and negative 5, so the answer is 25. Because I grew up on the standard "borrowing" algorithm, it took me several minutes to figure out that he might be on to something, but I'm concerned that his way is really only workable for 2-digit problems. Maybe I should just let it go? Perhaps he'll figure out a different solution when we start doing mental math problems with bigger numbers. (And at that age I was fascinated with negative numbers too! :)) The only downside I think is what you've already noticed - the number of steps. As problems get bigger, he'll have more to remember... but not really more than borrowing/regrouping would require. And actually... when he gets to polynomial addition and subtraction (guess what one of my tutoring kids is working on this week? LOL) this is exactly the right method. I actually do a variation on it myself - instead of figuring each column as a positive or negative number, I go with something like 62-38 = 62-(40-2) ........ = 62-40+2 ........ = 22+2 ........ = 24 (but I would do that in my head, not on paper) I think the only thing I would do is occasionally ramp up the number of digits to a point where he needs to jot down each column's positive or negative difference to keep track of them. At six I wouldn't worry too much about the "showing his work" part in general, but when he does need to, it's worth spending some time on being efficient about it. Quote Link to comment Share on other sites More sharing options...
boscopup Posted July 28, 2011 Share Posted July 28, 2011 I think it's fine for him to do that (mine loves negative numbers too). When you get to teaching the standard algorithm in your math program, you can just show him "another way of doing it". When introducing the SA, instead of saying "Can we take 5 from 0?", say "Can we take 5 from 0 without going negative?" My son had no problem understanding that, and he picked up the SA in the first lesson and applied it to 5-digit numbers the next day. He can still use negative numbers also. Just another tool in his toolbox. :D I wouldn't discourage his current method, as it's a good mental math method. Quote Link to comment Share on other sites More sharing options...
kiana Posted July 28, 2011 Share Posted July 28, 2011 There's nothing mathematically wrong with what he's doing, and it's more efficient for mental math imho. I do something similar myself. I know and can demonstrate the standard algorithm, but I almost never use it. For example, with 2457 - 1989, I'd do 2457 - (2000-11) = 2457 - 2000 + 11 = 457 + 11 = 468. It also sounds like he has a great understanding of place value :D Quote Link to comment Share on other sites More sharing options...
peacefully Posted July 28, 2011 Author Share Posted July 28, 2011 Whew! Thanks for the help, everyone. I'm going to just go with it. Ds is 2E in ways that I'm just now starting to figure out. I was not expecting him to have this kind of insight into math, and I'm a little stumped by some of his approaches. I'm the kind of learner who likes to follow the steps in the textbook. And he's... not. :001_huh: Quote Link to comment Share on other sites More sharing options...
jenbrdsly Posted July 29, 2011 Share Posted July 29, 2011 This is super cool!!! Your 6year old is approaching math in a Constructivist way. This specific strategy he has created is mentioned in Right Start as: "Terry's way". That is really awesome that he came up with it on his own. I have some more ideas about subtraction with regrouping without the traditional algorithm on my blog, in case you are interested. Quote Link to comment Share on other sites More sharing options...
Critterfixer Posted July 29, 2011 Share Posted July 29, 2011 Why is it that negative numbers just seem to fascinate this age group? My boys discovered them the other day in the course of this question from my ds7 hFA, "Mom, what happens on the other side of zero?" Quote Link to comment Share on other sites More sharing options...
peacefully Posted July 29, 2011 Author Share Posted July 29, 2011 Seriously! Ds is also fascinated by huge numbers. The other week, I caught him having a discussion with an older cousin, where the cousin was trying to explain exponential notation to my ds. When I asked what was going on, ds said with feverish excitement, "Mom, [cousin] is going to show me the difference between a googol and a googolplex!" :001_huh: Quote Link to comment Share on other sites More sharing options...
Spy Car Posted July 30, 2011 Share Posted July 30, 2011 I think it's fine for him to do that (mine loves negative numbers too). When you get to teaching the standard algorithm in your math program, you can just show him "another way of doing it". When introducing the SA, instead of saying "Can we take 5 from 0?", say "Can we take 5 from 0 without going negative?" My son had no problem understanding that, and he picked up the SA in the first lesson and applied it to 5-digit numbers the next day. He can still use negative numbers also. Just another tool in his toolbox. :D I wouldn't discourage his current method, as it's a good mental math method. :iagree: I was scrupulous in always qualifying subtraction question that might otherwise require re-grouping with the disclaimer "without going into negative numbers." My son must have heard it hundreds of times. Finally one day he demands to know what these negative numbers I keep mentioning are all about. He caught onto them right away and he too went through a phase (mostly passed) of making negative numbers part of his active mental math strategy. I would take it as an excellent sign that he has put this knowledge into an active strategy. It shows he understands mathematics and is creative. If it proves to be inefficient I suspect he will move to alternative mental math strategies of his own accord. Bill Quote Link to comment Share on other sites More sharing options...
RahRah Posted August 2, 2011 Share Posted August 2, 2011 :iagree: I was scrupulous in always qualifying subtraction question that might otherwise require re-grouping with the disclaimer "without going into negative numbers." My son must have heard it hundreds of times. Finally one day he demands to know what these negative numbers I keep mentioning are all about. He caught onto them right away and he too went through a phase (mostly passed) of making negative numbers part of his active mental math strategy. I would take it as an excellent sign that he has put this knowledge into an active strategy. It shows he understands mathematics and is creative. If it proves to be inefficient I suspect he will move to alternative mental math strategies of his own accord. Bill :iagree: My DS is now getting past the negative number obsession and like the OP's child, he was setting up his mental math formula very similarly. Now he does a quick re-group in his head that from what he's said aloud to me looks like this: 62-38 12-8 = 4 50 - 30 = 20 answer is 24 Basically he'll take the tens place over to his subtraction in his head, leaving the rest in the tens place to subtract that after subtracting the ones. So far he can do it to the thousands place pretty well (shocks me), his latest was yesterday....2367-1658, which he orally did as: 17-8 = 9 50-50 = 0 1300-600 = 700 1000-1000 = 0 answer = 709 On paper he does the standard steps to figure out the answer - he only does this mental gymnastics approach in his head. Quote Link to comment Share on other sites More sharing options...
chepyl Posted August 2, 2011 Share Posted August 2, 2011 My son was fascinated with negative numbers last year too. He loved the idea and played around with math that way. I thought it was just him. Quote Link to comment Share on other sites More sharing options...
Rebookie Posted August 2, 2011 Share Posted August 2, 2011 This is such a cool thread! I had to subscribe to it. =P Quote Link to comment Share on other sites More sharing options...
jenbrdsly Posted August 2, 2011 Share Posted August 2, 2011 62-38 12-8 = 4 50 - 30 = 20 answer is 24 Basically he'll take the tens place over to his subtraction in his head, leaving the rest in the tens place to subtract that after subtracting the ones. Very cool!!!! Quote Link to comment Share on other sites More sharing options...
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