rose Posted January 18, 2018 Share Posted January 18, 2018 I'm working on teaching my older dd the basics of algebra. Today she had this problem: 2x-3=7x-58 I can easily solve this problem but what I couldn't grasp was how to adequately explain why the 'minus 3' becomes 'negative 3' when you subtract 2x from both sides. I understand it almost intuitively. It just has to be but that's not a very adequate explanation, iykwim. Can you explain this better? 2x-3-2x=7x-58-2x -3=5x-58 Quote Link to comment Share on other sites More sharing options...
Caroline Posted January 18, 2018 Share Posted January 18, 2018 2x-2x=0 so you end up with 0-3. 0-3=-3 7 Quote Link to comment Share on other sites More sharing options...
justasque Posted January 18, 2018 Share Posted January 18, 2018 I'm working on teaching my older dd the basics of algebra. Today she had this problem: 2x-3=7x-58 I can easily solve this problem but what I couldn't grasp was how to adequately explain why the 'minus 3' becomes 'negative 3' when you subtract 2x from both sides. I understand it almost intuitively. It just has to be but that's not a very adequate explanation, iykwim. Can you explain this better? ... Once she understands the "why", she might find it useful to change all minus operations to "plus the opposite" before trying to move things around. One of my students coined the term "doing the boom booms" for this technique. If it's minus a positive, you use two pen strokes - one to change the minus to a plus ("boom"), and one to draw a negative sign in front of the term ("boom"). If it's minus a negative, you also use two pen strokes - one to change the minus to a plus ("boom"), and one to change the negative to a positive/plus ("boom"). Thus, regardless of what comes after the minus sign, you need two strokes to change it appropriately - boom boom. It's silly of course, but by verbally or mentally saying "boom" with each stroke, you build the habit of remembering both. And by changing minus to plus before moving things, you're much less likely to make a mistake or drop a negative. 5 Quote Link to comment Share on other sites More sharing options...
wendyroo Posted January 18, 2018 Share Posted January 18, 2018 Once she understands the "why", she might find it useful to change all minus operations to "plus the opposite" before trying to move things around. One of my students coined the term "doing the boom booms" for this technique. If it's minus a positive, you use two pen strokes - one to change the minus to a plus ("boom"), and one to draw a negative sign in front of the term ("boom"). If it's minus a negative, you also use two pen strokes - one to change the minus to a plus ("boom"), and one to change the negative to a positive/plus ("boom"). Thus, regardless of what comes after the minus sign, you need two strokes to change it appropriately - boom boom. It's silly of course, but by verbally or mentally saying "boom" with each stroke, you build the habit of remembering both. And by changing minus to plus before moving things, you're much less likely to make a mistake or drop a negative. :iagree: Subtractions signs are the root of all sorts of algebra mistakes. The other day my son was working on 10 - (x + 3) = 11 - 3x He kept subtracting 10 from each side, but then not knowing what to do with the subtraction sign left floating in front of the parenthesis. What does it mean to subtract (x + 3) from nothingness? Well, obviously it means negative (x + 3), but he was just soooooo tempted to ignore that subtraction sign now that there was nothing to subtract from. I kept reiterating that I don't help trouble shoot until all subtraction has been changed into addition of the negative. Lo and behold, once that "subtraction" sign was changed into a negative and nestled right up against that parenthesis, DS could clearly see the need to distribute and the rest of the problem went smoothly. Wendy 3 Quote Link to comment Share on other sites More sharing options...
Kote Posted January 20, 2018 Share Posted January 20, 2018 (edited) Hi Rose. If you couldn't grasp was how to adequately explain why the 'minus 3' becomes 'negative 3' when you subtract 2x from both sides you just should ask professionals. Edited January 20, 2018 by emzhengjiu Removed links Quote Link to comment Share on other sites More sharing options...
El... Posted January 20, 2018 Share Posted January 20, 2018 I don't think that is a dumb question. It goes to the meaning of subtraction. To subtract is to add the negative. For example, 2-2 can also be written 2 + (-2). Rewriting the problem with this format can clarify it. I hope others will chime in, or that you will find the right section of the textbook to review. 2 Quote Link to comment Share on other sites More sharing options...
Paige Posted January 20, 2018 Share Posted January 20, 2018 I cover this in 2 ways. I tell them that there's really no such thing as subtraction; only addition of positive and negative numbers. We teach "subtraction" to younger children because it's an easy shortcut, but when they are older they learn that subtraction is really just another way to add. I also tell them that +/- signs are married to the number to their right. They move together and a sign is never ever independent of it's number to the right. In the case above with parentheses, the sign is married to an invisible 1. When we put the 1 back in, which was just left out from convention and laziness, the problem clearly becomes a multiplication problem that should be distributed out. Some of my kids like to rewrite the problems with all the invisible ones and sometimes rewrite all subtraction as addition. It annoys me because I think it looks cluttered but I bite my tongue because whatever works for them is fine. I actually taught them to do that, but I figured they'd stop once they got the concept. 2 Quote Link to comment Share on other sites More sharing options...
Monica_in_Switzerland Posted January 20, 2018 Share Posted January 20, 2018 I wrote all terms in boxes it’s their associated signs. Then told DS they were all combined (summed) if they were on the same side of the equal sign. I think we even did a few problems where we wrote each term on its own post it note. 1 Quote Link to comment Share on other sites More sharing options...
Tanaqui Posted January 20, 2018 Share Posted January 20, 2018 What worked with the older kiddo was repetition and putting each term on its own little slip of paper (with a + in front of the leading term, if it was positive). The sign sticks with the term. We can shift them around and have the same expression, but the sign sticks with the term. The younger kiddo hasn't had that problem, but she has other ones. Weird how different kids are different. 1 Quote Link to comment Share on other sites More sharing options...
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