newlifemom Posted July 14, 2010 Share Posted July 14, 2010 When rew addition problems to my dd (rising 7th grade), I am mindful of the fact that she really needs to go beyond the basic. Add 8+4 =12 carry the one etc. So I have been talking ala Liping Ma and using terms like composing a unit and really stressing that when you are adding numbers in the tens column, you are not adding 1+3+5, but 10+30+50. Are you with me so far. When we put the answer into the tens column we are using the identity law of addition. We know the answer is 90, but we only put 9 b/c the zero is added to the 2 from above and 0+2 = 2. Now please know that math was not and is not my strong suit, so please be gentle. Is this a valid way to integrate the identity law of addition into a problem? I can see how it would be done in higher level math, but I want to discuss it here as well and this is the best way I can think of at the moment. Thank you oh so wise and powerful mathematicians. I do not deserve to share cyberspace with you. :tongue_smilie: Quote Link to comment Share on other sites More sharing options...
Perry Posted July 14, 2010 Share Posted July 14, 2010 (edited) when you are adding numbers in the tens column, you are not adding 1+3+5, but 10+30+50. When we put the answer into the tens column we are using the identity law of addition. We know the answer is 90, but we only put 9 b/c the zero is added to the 2 from above and 0+2 = 2. I'm not really following... where are you getting the 2? In general, I wouldn't be using a problem like this to discuss the identity property of addition. I'd think it would be confusing. Edited July 14, 2010 by Perry Quote Link to comment Share on other sites More sharing options...
Denisemomof4 Posted July 14, 2010 Share Posted July 14, 2010 I'm not really following... where are you getting the 2? In general, I wouldn't be using a problem like this to discuss the identity property of addition. I'd think it would be confusing. I've never heard of identity property being discussed before. We call it place value. I understand that the 2 is from the 12, although I didn't at first. Still, I think the way this is all presented might be very confusing for your dd. Is it? Quote Link to comment Share on other sites More sharing options...
newlifemom Posted July 14, 2010 Author Share Posted July 14, 2010 So if the problem is 3132 256 + 4 _____ While I was explaining that you don't really 'carry' the one as much as you have composed a unit of 10 and need to put it in the right place, it seems to me [woefully ignorant of math] that the reason you don't use the 0 is because of the identity law. Instead of writing out the answer like 3000+300+90+2 You write 3,392 Does that make more sense? And yes I like to complicate things. It's in my nature. Hopefully my children will forgive me. :tongue_smilie: Quote Link to comment Share on other sites More sharing options...
Perry Posted July 14, 2010 Share Posted July 14, 2010 While I was explaining that you don't really 'carry' the one as much as you have composed a unit of 10 and need to put it in the right place, it seems to me [woefully ignorant of math] that the reason you don't use the 0 is because of the identity law. No, I don't really think it's appropriate to incorporate the identity property in this situation. So if the problem is 3132 256 + 4 _____ Instead of writing out the answer like 3000+300+90+2 You write 3,392 While 3000+300+90+2 is a good way of representing the number 3392, I think you are trying to do too many different things with the problem. 3000+300+90+2 doesn't really have anything to do with the actual addition problem. If you want to demonstrate place value, I'd be doing it differently: Add the Ones: 2+6+4 = 12 Add the Tens: 30+50 = 80 Add the Hundreds: 100+200 = 300 Add the Thousands: 3000 = 3000 ------ 12 + 80 + 300 + 3000 = 3392 Quote Link to comment Share on other sites More sharing options...
Dana Posted July 14, 2010 Share Posted July 14, 2010 So if the problem is 3132 256 + 4 _____ While I was explaining that you don't really 'carry' the one as much as you have composed a unit of 10 and need to put it in the right place, it seems to me [woefully ignorant of math] that the reason you don't use the 0 is because of the identity law. Instead of writing out the answer like 3000+300+90+2 You write 3,392 Does that make more sense? And yes I like to complicate things. It's in my nature. Hopefully my children will forgive me. :tongue_smilie: No, that's place value. 3000 + 300 + 90 + 2 is expanded form of a number while 3392 is the standard form of the number. At a basic level, some systems have an identity property. With addition and the real numbers, the identity element is 0. This means that you can add 0 to any number and the number stays the same: 0 + 5 = 5 + 0 = 5 (for example). With multiplication, the identity element is 1. (1)(9) = (9)(1) = 9. You use the identity property of multiplication every time you get equivalent fractions. Quote Link to comment Share on other sites More sharing options...
newlifemom Posted July 14, 2010 Author Share Posted July 14, 2010 Alright, I guess I will wait for trig before identity of addition gets play. Of course at that point I won't be teaching anyone at that level. I tried :D Quote Link to comment Share on other sites More sharing options...
GraciebytheBay Posted July 14, 2010 Share Posted July 14, 2010 (edited) We know the answer is 90, but we only put 9 b/c the zero is added to the 2 from above and 0+2 = 2. I am certainly no mathemetician, but I don't think the identity law applies here. If you're trying to explain to her why you only put the one number in the column and "carry" the other, this seems fine. I may be confused, though. In your example above, wouldn't you write the 0 and add (carry) the 9 to the column to the left? Actually, the more I think about it, I think I am surely am confused as to what is being asked. Sorry I can't be more helpful! :001_unsure: Edited July 14, 2010 by GraciebytheBay Quote Link to comment Share on other sites More sharing options...
newlifemom Posted July 14, 2010 Author Share Posted July 14, 2010 I am certainly no mathemetician, and I'm not sure what the identity law of addition is. (I've heard of other laws of addition, but not this one.) However, if you're trying to explain to her why you only put the one number in the column and "carry" the other, this seems fine. I may be confused, though. In your example above, wouldn't you write the 0 and add (carry) the 9 to the column to the left? Actually, the more I think about it, I think I am surely am confused as to what is being asked. Sorry I can't be more helpful! :001_unsure: I have that effect on people. ;) Quote Link to comment Share on other sites More sharing options...
EKS Posted July 14, 2010 Share Posted July 14, 2010 If you're interested in getting a kid to really think clearly about place value, doing simple arithmetic in different bases and converting back and forth between them and base 10 works great. Quote Link to comment Share on other sites More sharing options...
newlifemom Posted July 14, 2010 Author Share Posted July 14, 2010 If you're interested in getting a kid to really think clearly about place value, doing simple arithmetic in different bases and converting back and forth between them and base 10 works great. Great. Throw another wrench into my school plans. :tongue_smilie: Quote Link to comment Share on other sites More sharing options...
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