I like the way this teacher uses different symbols for subtraction and negative signs. (Is there also a different symbol for the opposite sign?)
I think that might have something to do with what’s going on here, too. In other words, a lot of us would write work like this and then on the next line write “-b = 2”, with a subtraction sign magically changing into an opposite sign. I wonder if in an algebra 1 class we ought to write “0 – b = 2” first and then “-b = 2” … perhaps with a different symbol for the subtraction and the opposite operator. Anyway for this student I would emphasize that 0 is not nothing, and get them to write that “0 – b = 2” if I could manage to lead them that way. Alternatively, I’d work on the habit of replacing subtraction with adding the opposite and see if that helped.
I’ve seen this mistake so many times. I think students are making one of two mistakes here: they forget the – sign, they think it is unimportant, or they just ignore it because they don’t know how to handle it.
David, I agree. They see the – sign but because it is next to a variable they disregard it. I sent this in because most students got it wrong on the semester exam. Then it showed up on the worksheets from the “facing math” book and the majority of the student got it wrong. When we go over multiplying both sides by -1 they say “I didn’t know we could do that”. Which makes me wish I would have video taped myself teaching it to them….so I could put it on a replay loop …. over and over and over….
But David, what I want to know is what you say to the kids when you see this mistake! I need more ideas!
@Joshua
Perhaps an idea to work with here is to be in the (silly) habit of including coefficients of 1 and -1 next to a variable during an introductory phase of the unit. I think that this would increase the sense of importance of that – sign in front of the variable and it might address Anne’s students as well who ‘claim’ that they had ‘no idea’ that they could multiply each side of the equation. It’s been a while since I spent much time on equations at this level so I am not sure how good an idea this is.
I have them re-write it as +(-b) at first. It’s helped them catch on that the negative goes with the b, once they get that they can solve without re-writing it.
I like the ideas here; i will have to use the 0– b idea more the next time I teach this. One idea is to use algae locks or algetiles or algeblocks. There is an electronic version at nlvm.
This student understands the step for finding b, but the student does not fully understand b is negative and not positive. I can see why the student is confused about this because the minus sign can confuse the student. In the student’s mind by adding 8 on both sides the minus sign goes away. I would help the student by rewriting the problem as -8 + (-1b) = -6. By doing this the student will see that b is a negative number and not a positive number. I added the 1 in front of b because the 1 is always there but it is never written out in a problem. So when the student adds 8 on both sides, that leaves the left side with –b = +2. Then you will divide both sides by -1 to find the value of b, with is -2.
8 replies on “Solving Simple Equations”
I like the way this teacher uses different symbols for subtraction and negative signs. (Is there also a different symbol for the opposite sign?)
I think that might have something to do with what’s going on here, too. In other words, a lot of us would write work like this and then on the next line write “-b = 2”, with a subtraction sign magically changing into an opposite sign. I wonder if in an algebra 1 class we ought to write “0 – b = 2” first and then “-b = 2” … perhaps with a different symbol for the subtraction and the opposite operator. Anyway for this student I would emphasize that 0 is not nothing, and get them to write that “0 – b = 2” if I could manage to lead them that way. Alternatively, I’d work on the habit of replacing subtraction with adding the opposite and see if that helped.
I’ve seen this mistake so many times. I think students are making one of two mistakes here: they forget the – sign, they think it is unimportant, or they just ignore it because they don’t know how to handle it.
David, I agree. They see the – sign but because it is next to a variable they disregard it. I sent this in because most students got it wrong on the semester exam. Then it showed up on the worksheets from the “facing math” book and the majority of the student got it wrong. When we go over multiplying both sides by -1 they say “I didn’t know we could do that”. Which makes me wish I would have video taped myself teaching it to them….so I could put it on a replay loop …. over and over and over….
But David, what I want to know is what you say to the kids when you see this mistake! I need more ideas!
@Joshua
Perhaps an idea to work with here is to be in the (silly) habit of including coefficients of 1 and -1 next to a variable during an introductory phase of the unit. I think that this would increase the sense of importance of that – sign in front of the variable and it might address Anne’s students as well who ‘claim’ that they had ‘no idea’ that they could multiply each side of the equation. It’s been a while since I spent much time on equations at this level so I am not sure how good an idea this is.
I have them re-write it as +(-b) at first. It’s helped them catch on that the negative goes with the b, once they get that they can solve without re-writing it.
I like the ideas here; i will have to use the 0– b idea more the next time I teach this. One idea is to use algae locks or algetiles or algeblocks. There is an electronic version at nlvm.
http://nlvm.usu.edu/en/nav/frames_asid_189_g_4_t_2.html?open=activities&from=category_g_4_t_2.html
This student understands the step for finding b, but the student does not fully understand b is negative and not positive. I can see why the student is confused about this because the minus sign can confuse the student. In the student’s mind by adding 8 on both sides the minus sign goes away. I would help the student by rewriting the problem as -8 + (-1b) = -6. By doing this the student will see that b is a negative number and not a positive number. I added the 1 in front of b because the 1 is always there but it is never written out in a problem. So when the student adds 8 on both sides, that leaves the left side with –b = +2. Then you will divide both sides by -1 to find the value of b, with is -2.