SorrelZG Posted August 30, 2013 Share Posted August 30, 2013 This is making me feel stupid. Not because I can't do math but because I do it without thinking and teaching is requiring me to think and have names and reasons for things I haven't needed for my own purposes and understanding. So, in advance, please forgive me for my apparent ditziness. DS was just introduced to parenthesis and their place in the order of operations. He was having to do problems such as (10-5) x 4 and he had solved several problems before this one without issue (ie. 5 x (9+1) = 5x10 = 50) so he showed that he understood the concept of solving the parenthesis. It was a simple lesson ... sort of. My question is: is there a name for the approaching such a problem so that instead of doing it as in the example you solve it as 5x9 + 5x1 and when is solving it that way useful? When is that taught? I remember doing that in math but .. Maybe just in algebra? I don't recall why it would need to be done that way unless there is an unknown that needs to be broken out of the parenthesis. Anyway, I'm just curious. DS just bamboozled me by my suddenly turning (10-5) x 4 into 40 - 5 - 5 - 5 - 5 = 40 - 4x5 = 40-20 = 20. I went over it with him to point out how many mental steps that took in comparison to what he had been actually taught to do but I got to thinking that it seemed like a bit of a leap to recognize off the bat like that that (10-5) x 4 was 40-20. The problem we're having with the lesson is that since then he now keeps approaching every problem without parenthesis as if there are parenthesis, so we have to step back and reinforce how to read an equation that has no parenthesis. Oh well. :-/ Quote Link to comment Share on other sites More sharing options...
zoo_keeper Posted August 30, 2013 Share Posted August 30, 2013 Are you talking about the distributive property? Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted August 30, 2013 Author Share Posted August 30, 2013 Maybe. Imagine I'm seven and explain it to me. Please. lol ETA: Yes! That is it! (I googled. Now I really feel ditzy.) Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted August 30, 2013 Author Share Posted August 30, 2013 Now I'm all wondering how a child manages to get confused by the order of operations but intuitively comprehend the distributive property. Quote Link to comment Share on other sites More sharing options...
freerange Posted August 30, 2013 Share Posted August 30, 2013 Because order of operations is a rule created by mathematicians, whilst the distributive property is a naturally occurring feature of mathematics. I have 2 children with brains wired the same way as your DS and it can be fascinating to observe what they can intuit. Quote Link to comment Share on other sites More sharing options...
kiana Posted August 30, 2013 Share Posted August 30, 2013 Using the distributive property is exactly what we are doing in the standard long multiplication, fwiw. If we're doing something like 123x45, that's 123x(40+5). We put 123x5 on the first row, 123x40 on the second row, and then add them up to get the answer. Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted August 30, 2013 Author Share Posted August 30, 2013 Because order of operations is a rule created by mathematicians, whilst the distributive property is a naturally occurring feature of mathematics. I have 2 children with brains wired the same way as your DS and it can be fascinating to observe what they can intuit. I had to talk this through with DH before I was sure I comprehended what you meant but now it makes so much sense. :D I'm impressed on one hand and a little discouraged on the other. I have been trying to work through this material until I find the point where I'm not just mostly review stuff he's already figured out and then he busts out with comprehension of something we're just not near yet which gives me the feeling that I may be in this mode for a while still to come. Quote Link to comment Share on other sites More sharing options...
SorrelZG Posted August 30, 2013 Author Share Posted August 30, 2013 Using the distributive property is exactly what we are doing in the standard long multiplication, fwiw. If we're doing something like 123x45, that's 123x(40+5). We put 123x5 on the first row, 123x40 on the second row, and then add them up to get the answer. I'm not entirely sure that I ever consciously made that connection. Thank-you so much for mentioning it! Quote Link to comment Share on other sites More sharing options...
mathwonk Posted August 30, 2013 Share Posted August 30, 2013 it's also a trick for mental multiplication. to do 4 times 123 in your head, you do 4 times 100 then 4 times 20 and then 4 times 3 and add to get 400 + 80 + 12 = whatever it is. (I guess 492, but i enjoy the process more than the answer.) associativity is useful too. i.e. (ab)c = a(bc), and c/(ab) = (c/a)/b. e.g. the NFL offered 765 million to over 4,000 concussion victims yesterday. =how much per victim? we.. round down to 760 million and divide by 4000. first divide by 1000, getting 760,000, then divide by 4 getting 190,000 (i.e. 760,000 = 76 plus 4 zeroes, so divided by 4 its 76/4 = 19 plus 4 zeroes.) The point is, with this tick, if you can divide 76 by 4, you can just as easily also divide 760,000,000 by 4,000. so its 190,000 per person for high income people, some who lost years of work, and some of whom have serious head in juries. Quote Link to comment Share on other sites More sharing options...
freerange Posted August 31, 2013 Share Posted August 31, 2013 it's also a trick for mental multiplication. to do 4 times 123 in your head, you do 4 times 100 then 4 times 20 and then 4 times 3 and add to get 400 + 80 + 12 = whatever it is. (I guess 492, but i enjoy the process more than the answer.). s. I'd do it as 100 x 4 + 25 x 4 - 2 x 4. I'm sure there are lots of other ways to group the numbers. And I agree about enjoying the process the most. :-) Quote Link to comment Share on other sites More sharing options...
kiwik Posted August 31, 2013 Share Posted August 31, 2013 It is just expanding out the brackets isn't it? Like the quadratic equation. Quote Link to comment Share on other sites More sharing options...
dbmamaz Posted August 31, 2013 Share Posted August 31, 2013 I'm impressed on one hand and a little discouraged on the other. I have been trying to work through this material until I find the point where I'm not just mostly review stuff he's already figured out and then he busts out with comprehension of something we're just not near yet which gives me the feeling that I may be in this mode for a while still to come. Its probably not everything, though. When I was in middle school, my mom brought out her study book for the GREs, and I had a blast doing some of the math problems. She was flabbergasted. OTOH, there was still plenty of high school math i didnt know. But depending on age, you might want to look at Art of Problem Solving, since he seems to be a kid who does not need a lot of direct teaching Quote Link to comment Share on other sites More sharing options...
kiana Posted September 1, 2013 Share Posted September 1, 2013 I'd do it as 100 x 4 + 25 x 4 - 2 x 4. I'm sure there are lots of other ways to group the numbers. And I agree about enjoying the process the most. :-) I'd be doing 125x4 - 2x4 as well -- 125x4 is something I recognize because of .125 being 1/8. Quote Link to comment Share on other sites More sharing options...
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