ElizabethB Posted January 1, 2014 Share Posted January 1, 2014 I wish there was a HIG for Singapore 6! The teacher's manual was more than twice as expensive and is almost worthless. I have found a fairly decent explanation that explains subtracting a negative, but a few more would be helpful. But, I have not found a good explanation for multiplying 2 negatives. With other topics in Singapore 6 that I have needed better explanations for, my Dolciani Pre-Algebra or online searching was helpful. I'm hoping for some good links or explanations for multiplying 2 negatives. The other cases all make sense to me, this one does not and I have not found a great explanation why when searching. (Ours in not to reason why, just move the sign and multiply is pretty much what I've found so far.) Thanks! Quote Link to comment Share on other sites More sharing options...
MomatHWTK Posted January 1, 2014 Share Posted January 1, 2014 Try Khan Academy, it helped me (a little). Pretty much for negatives, I just have to memorize the rules. Quote Link to comment Share on other sites More sharing options...
ErinE Posted January 1, 2014 Share Posted January 1, 2014 I don't know if this is the perfect theoretical explanation, but here's how I explained it to DS: Multiplying two positives is repeated addition. 2 * 3 = 2+2+2 = 6 Multiplying a negative and a positive is the same as adding a negative number the shown amount or subtracting a positive number the given amount. -2 * 3 = (-2) + (-2) + (-2) = - 2 - 2 - 2 = -6 I also showed the equation as: -2 * 3 = - 3 - 3 = - 6 [i noted it was the same answer as above] Therefore, multiplying two negatives is the same as subtracting a negative number the given amount: (-2) * (-3) = - (-2) - (-2) - (-2) [subtract -2 three times] = 2 + 2 + 2 [subtracting a negative from a negative is the same as adding] = 6 Also shown as: (-2) * (-3) = - (-3) - (-3) = 3 + 3 = 6 DS and I did this lesson a few times and it seemed to help his understanding so I hope this helps. Quote Link to comment Share on other sites More sharing options...
ElizabethB Posted January 1, 2014 Author Share Posted January 1, 2014 Therefore, multiplying two negatives is the same as subtracting a negative number the given amount: (-2) * (-3) = - (-2) - (-2) - (-2) [subtract -2 three times] = 2 + 2 + 2 [subtracting a negative from a negative is the same as adding] = 6 Also shown as: (-2) * (-3) = - (-3) - (-3) = 3 + 3 = 6 DS and I did this lesson a few times and it seemed to help his understanding so I hope this helps. That is very helpful, thanks! I think this will make sense to her. Quote Link to comment Share on other sites More sharing options...
RootAnn Posted January 2, 2014 Share Posted January 2, 2014 It was almost too quick to notice, but I liked when the snotty girl in this said to her mom, "So, three weeks ago, you were fifteen pounds heavier. Negative three times negative five equals positive fifteen." (Start at 2:10 on the video to get the context. Snotty comment is at 2:32.) Not really helpful for an explanation (as they don't explain the why), but an interesting "real world" example. :laugh: Quote Link to comment Share on other sites More sharing options...
Lara in Colo Posted January 2, 2014 Share Posted January 2, 2014 here is a good place to start-- he really explains things well. If you look though his other videos, (in the same chapter) you will find multiplication of negatives as well (IIRC) http://www.artofproblemsolving.com/Videos/external.php?video_id=22 Quote Link to comment Share on other sites More sharing options...
avilma Posted January 2, 2014 Share Posted January 2, 2014 I like what MEP does. See page 27, exercises 4 & 5 in year 6: http://www.cimt.plymouth.ac.uk/projects/mepres/primary/pb6a_1.pdf According to the lesson plans the students should be given 5 mins at the end of a class to discover by themselves the rules of multiplying by negative numbers using those 2 exercises. My take on this is that MEP is trying to make the introduction of the rules a low key affair. What is important is what the rules are and sure enough there will be plenty of exercises to make sure the rules are not forgotten. The student should accept the rules without much resistance. Clearly what MEP is doing is not proof of the rules as the proof is way beyond middle school math. Contrast that with my own experience when I learned those rules in grade 7. My math teacher actually tried to prove those rules to us using number lines. I think I was a pretty good student but after the teacher spent 45 minutes explaining the proofs I was left extremely confused and not at all convinced of the validity of the rules. This actually made me have difficulty applying the rules because anytime a multiplication with a negative number came up I would try to work out the rule by myself without much success. Quote Link to comment Share on other sites More sharing options...
arborite Posted January 2, 2014 Share Posted January 2, 2014 Subtracting a negative is like taking away a debt. Quote Link to comment Share on other sites More sharing options...
kiana Posted January 2, 2014 Share Posted January 2, 2014 Proof is not really that bad. Here's a website with a bunch of explanations and some proofs. http://jwilson.coe.uga.edu/EMAT6680/Brown/6690/negneg.htm Quote Link to comment Share on other sites More sharing options...
Ellie Posted January 2, 2014 Share Posted January 2, 2014 Negative numbers are evil. The "rules" remind of the rules for the card game Fizbin. Actually, they seem more like guidelines than rules. Sorry. I manged to get through Algebra 1, but it never, ever made sense to me. Quote Link to comment Share on other sites More sharing options...
ThatHomeschoolDad Posted January 2, 2014 Share Posted January 2, 2014 http://youtu.be/DR70VG2V1Rs Quote Link to comment Share on other sites More sharing options...
dbmamaz Posted January 2, 2014 Share Posted January 2, 2014 fwiw, my mathy youngest, when asked to explain this last year for a post, just said 'they are opposite' . . so adding them is like subtracting and subtracting them is like adding. and with multiplying, multiplying by a negative 'flips' the sign of the other - after all, -8 is the same as 8 * (-1). so (-8) * (-3) is the same as (-1)*(8)*(-1)*(3) which is (8*3)*(-1*-1) . . . . -1 times anything switches its sign, so -1*-1 is 1. so you just have 8*3. Quote Link to comment Share on other sites More sharing options...
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