# Need help teaching algebraic equations

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I completely and totally frustrated and don't know what to do here.

So, this year we are using teaching textbooks. I needed something more hands off for the year and so chose this. DS was doing well with the program until he hit ch. 9: Longer Algebraic Equations. He went through the ch. once and was struggling. I worked with him and he seemed to be doing better but then bombed the ch. test.

So, we went back through the ch. I sat down with each day and he worked through the problems. He seemed to get it. He passed the test. He continued on with his lessons and was making 100% each day. Today I sat to down to work with him. I had him do his equations on the board. Only, he didn't do them because he doesn't know how.

He just stood there staring at the equation. He had no idea what go do first. I asked how he had managed 100% on his lessons. He used his calculator. A regular old calculator. But he couldn't tell me how he got them right that way either.

I don't know what's going on.

He says the rules for isolating x do not make sense. For example, in the problem

-13-5x=-12

He thinks you should subtract 13 first. We talk about doing the opposite operation but he says it does not make sense to do that. He doesn't understand why you would add and not subtract. I don't know how to explain. I have worked the problems out on the board (many, many problems). I have let him do it the wrong way and get the wrong answer. But, no, it doesn't make sense to him. He refuses to just accept that it just is and overthinks it.

I feel like I have gone over this a zillion times. I have explained it til I'm blue in the face and in every way I can think to. Algebra is sooo easy. It's frustrating to me that I can't explain in a way that makes it click. It's scaring me that he doesn't get it either.

Does anyone have ideas on what I could do or how to explain it?

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I discribe it as "undoing the equation." You add 13 to "undo" the subtracting. What you do to one side you have to do to the other. Then you have to "undo" the multiplication by dividing. What you do to one side you have to do to the other.

Another way I have explained it is that you are given the answer and have to go back to the beginning. You are the math detective. What happened? It looks like someone had a number, multiplied it by negative five, and then tried to take away 13. All that came out to be -12 . How can you go backward to find what the number was? If it is saying subtract 13, you have to go backwards and add 13. If it is saying multiply 5, you have to go backwards and divide 5. By going backward, you get to the original number that x was.

I do not know if either of those help, but for many kids a story format helps them see the chronological order in math.

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TT teaches it as undoing, as well. I see you use AoPS. I bought their pre-algebra book and have never used it. I was thinking about breaking it out and seeing if it might work for him. Maybe it would be the right kind of explanation?

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With AoPS there are very few "explanations". That is sort of the point. However, they give you tiny, bite sized pieces to work through so you can make the connection. It allows the student to find their own path based on the proof. It is worth a shot. My Ds does not follow traditional math methods very well and AoPS really worked for him.

If you go online, there are videos on the AoPS website. They might be your best bet. Khan also has videos and plenty of practice.

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Does it help to factor out the -1?

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If the equation was 13 + 5x = 12, would he know how to do it? If yes, would he still be able to solve it if the equation was 5x - 13 = 12?

Edited by Tanaqui
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I completely and totally frustrated and don't know what to do here.

So, this year we are using teaching textbooks. I needed something more hands off for the year and so chose this. DS was doing well with the program until he hit ch. 9: Longer Algebraic Equations. He went through the ch. once and was struggling. I worked with him and he seemed to be doing better but then bombed the ch. test.

So, we went back through the ch. I sat down with each day and he worked through the problems. He seemed to get it. He passed the test. He continued on with his lessons and was making 100% each day. Today I sat to down to work with him. I had him do his equations on the board. Only, he didn't do them because he doesn't know how.

He just stood there staring at the equation. He had no idea what go do first. I asked how he had managed 100% on his lessons. He used his calculator. A regular old calculator. But he couldn't tell me how he got them right that way either.

I don't know what's going on.

He says the rules for isolating x do not make sense. For example, in the problem

-13-5x=-12

He thinks you should subtract 13 first. We talk about doing the opposite operation but he says it does not make sense to do that. He doesn't understand why you would add and not subtract. I don't know how to explain. I have worked the problems out on the board (many, many problems). I have let him do it the wrong way and get the wrong answer. But, no, it doesn't make sense to him. He refuses to just accept that it just is and overthinks it.

I feel like I have gone over this a zillion times. I have explained it til I'm blue in the face and in every way I can think to. Algebra is sooo easy. It's frustrating to me that I can't explain in a way that makes it click. It's scaring me that he doesn't get it either.

Does anyone have ideas on what I could do or how to explain it?

Can he use trial and error to figure out 'x'? i.e. What value of x will satisfy -13-5x=-12. This might take a long long time, but will drive home the need for a consistent method or strategy.

fwiw, When any kid doesn't know where to begin given an equation, I review the following concepts quickly. Maybe these concepts are individually very basic, but many kids trip when all of them need to be applied together.

1- Additive inverse: In this case: what number when added to -13 equals 0?

2- Integer operations.: adding and subtracting integers.

3- Operations on negative fractions.

4- What is: a term, like and unlike terms, and algebraic expression.

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You could try this type of conversation. (This is how these conversations go with my little kids.)

The = sign is the middle of a teeter totter. Your job is to keep this teeter totter totally level. If you make one side heavier or lighter, the = sign is broken. The only way to keep it equal,is to think about keeping the teeter totter Balanced. If you add something to one side it will make that side heavier. You need to add it to both sides to keep it balanced. Same with subtracting.

With the -13, that is like someone owing you \$13. The only way they can get back to zero is by paying you back \$13. If they borrow \$13 more dollars, they now owe you \$26!! Not \$0. So imagine that the - sign means your teeter totter has a hole with your piggy bank hanging from the bottom. When they borrow the money, there is a hole going down into the bank. When they pay you back it fills your bank back up; it does not make your bank emptier.

If they pay you back the \$13, then you need to add the \$13 to both sides of the teeter totter to keep it level bc you can't do something to just one side. You have to do it to both.

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I completely and totally frustrated and don't know what to do here.

So, this year we are using teaching textbooks. I needed something more hands off for the year and so chose this. DS was doing well with the program until he hit ch. 9: Longer Algebraic Equations. He went through the ch. once and was struggling. I worked with him and he seemed to be doing better but then bombed the ch. test.

So, we went back through the ch. I sat down with each day and he worked through the problems. He seemed to get it. He passed the test. He continued on with his lessons and was making 100% each day. Today I sat to down to work with him. I had him do his equations on the board. Only, he didn't do them because he doesn't know how.

He just stood there staring at the equation. He had no idea what go do first. I asked how he had managed 100% on his lessons. He used his calculator. A regular old calculator. But he couldn't tell me how he got them right that way either.

I don't know what's going on.

He says the rules for isolating x do not make sense. For example, in the problem

-13-5x=-12

He thinks you should subtract 13 first. We talk about doing the opposite operation but he says it does not make sense to do that. He doesn't understand why you would add and not subtract. I don't know how to explain. I have worked the problems out on the board (many, many problems). I have let him do it the wrong way and get the wrong answer. But, no, it doesn't make sense to him. He refuses to just accept that it just is and overthinks it.

I feel like I have gone over this a zillion times. I have explained it til I'm blue in the face and in every way I can think to. Algebra is sooo easy. It's frustrating to me that I can't explain in a way that makes it click. It's scaring me that he doesn't get it either.

Does anyone have ideas on what I could do or how to explain it?

Here are a few random thoughts, fwiw:

Is your son able to combine positive and negative numbers when combining like terms?  I have tutored many students who have a difficult time understanding the concept of a negative number.  With these students, I have found that drawing out a number line, including both positive and negative numbers helps quite a bit.  For example, some kids don't understand why 5 - 13 doesn't equal 8.  When I work the problem using the number line, I have them start at 5 and move in the negative direction 13 spaces to land on -8.  Also, instead of viewing the "-" sign as "subtraction", it sometimes helps some kids to view the "-" sign as "adding a negative number".

I would also consider using "Hands-on-Equations"  to help your son understand better understand the process of isolating the variable.  This hands-on approach has helped many of my students.

Good luck

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Does it help to factor out the -1?

I tried this. I think I made it worse. Deer in headlights.

If the equation was 13 + 5x = 12, would he know how to do it? If yes, would he still be able to solve it if the equation was 5x - 13 = 12?

He would be able to do the first and maybe the second. He thinks it is different depending on which side of the x. I have no idea why.

Can he use trial and error to figure out 'x'? i.e. What value of x will satisfy -13-5x=-12. This might take a long long time, but will drive home the need for a consistent method or strategy.

fwiw, When any kid doesn't know where to begin given an equation, I review the following concepts quickly. Maybe these concepts are individually very basic, but many kids trip when all of them need to be applied together.

1- Additive inverse: In this case: what number when added to -13 equals 0?

2- Integer operations.: adding and subtracting integers.

3- Operations on negative fractions.

4- What is: a term, like and unlike terms, and algebraic expression.

We go through the steps but he is stuck at the first one. I think he is overwhelmed by seeing all the steps together. I really need to emphasize dealing with the equation in parts.

You could try this type of conversation. (This is how these conversations go with my little kids.)

The = sign is the middle of a teeter totter. Your job is to keep this teeter totter totally level. If you make one side heavier or lighter, the = sign is broken. The only way to keep it equal,is to think about keeping the teeter totter Balanced. If you add something to one side it will make that side heavier. You need to add it to both sides to keep it balanced. Same with subtracting.

With the -13, that is like someone owing you \$13. The only way they can get back to zero is by paying you back \$13. If they borrow \$13 more dollars, they now owe you \$26!! Not \$0. So imagine that the - sign means your teeter totter has a hole with your piggy bank hanging from the bottom. When they borrow the money, there is a hole going down into the bank. When they pay you back it fills your bank back up; it does not make your bank emptier.

If they pay you back the \$13, then you need to add the \$13 to both sides of the teeter totter to keep it level bc you can't do something to just one side. You have to do it to both.

Dh tried this explanation with him. He says he understands but I get the sense that there are still problems.

Here are a few random thoughts, fwiw:

Is your son able to combine positive and negative numbers when combining like terms?  I have tutored many students who have a difficult time understanding the concept of a negative number.  With these students, I have found that drawing out a number line, including both positive and negative numbers helps quite a bit.  For example, some kids don't understand why 5 - 13 doesn't equal 8.  When I work the problem using the number line, I have them start at 5 and move in the negative direction 13 spaces to land on -8.  Also, instead of viewing the "-" sign as "subtraction", it sometimes helps some kids to view the "-" sign as "adding a negative number".

I would also consider using "Hands-on-Equations"  to help your son understand better understand the process of isolating the variable.  This hands-on approach has helped many of my students.

Good luck

I thought it was a negative number issue. We worked with negative numbers yesterday using the number line. He was insulted. <_<

I don't understand quite how his brain works. He definitely processes things differently than I do. I think, more than anything, he overthinks things. I think he needs to know the why behind it. We did a few problems first thing this morning and he did them right. But, he does this. Monday, it makes sense. Tuesday, it doesn't. I know that is normal when you are learning something new but he is really stuck here. I'm going to bring out AoPS today and see how that goes. It will repeat some concepts he has already covered but I am thinking it might cement some of the basics.

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So you worked with negative numbers and he breezed through all the problems? Did you try giving him some really tricky ones with multiple numbers and steps? I also had a hunch that this was a problem understanding negative numbers. And I thought 8's explanation of how to teach it was good. Or to just do a bunch of stuff with negative numbers in general. Jousting Armadillos has a thing where it teaches it with black and white balls that I liked, where the balls are always canceling each other out. And MEP has a thing where a car can turn around either way to add or subtract on the number line that really worked for one of my boys.

Has he played Dragonbox? Or have you ever tried Hands on Equations? Both of those might be useful as well. HoE basically does the same thing as the black and white balls that I mentioned above but with different colored pegs.

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I totally empathize with him, and I'm trying to think of how I finally "got" it. I seize up with "the rules". It helps me to know what's going to happen if I do the wrong step first. Brackets are a tremendous help to me to see the steps. For example, I will always forget that x is really 1x if i don't write it there. Writing 1(x) is even more helpful, especially if I'm going to have to divide. So for me, I'd take that -1 out, so I'd have -1(13+5x)=12. Then I'd divide both sides by -1, so I'd have 13+5x= -12. Then I'd subtract 13 from both sides. 5x= -25 Then divide both sides by 5.

For me, repeating the language of doing this to both sides helps. I totally get how frustrating it is to have done a thousand problems the same way, then you look at one and have no idea where to start.

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/snip

I thought it was a negative number issue. We worked with negative numbers yesterday using the number line. He was insulted. <_<

I don't understand quite how his brain works. He definitely processes things differently than I do. I think, more than anything, he overthinks things. I think he needs to know the why behind it. We did a few problems first thing this morning and he did them right. But, he does this. Monday, it makes sense. Tuesday, it doesn't. I know that is normal when you are learning something new but he is really stuck here. I'm going to bring out AoPS today and see how that goes. It will repeat some concepts he has already covered but I am thinking it might cement some of the basics.

Sounds like pubertal brain fog to me. Could it be? In any case, no harm in going over the concepts until he's comfortable applying them. Good luck!

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He can subtract, but the number to subtract is not 13, it is negative 13.  Rewriting the problem with parenthesis around the negative numbers might make things clearer for him.

-13 - 5x = -12

(-13) + (-5)x= (-12)

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Algebra tiles is another good way. It does the canceling out of colors like JA too. See here for info:

.

We've loved using them and Algeblocks to work with algebra kinetically. It's hard to find manipulatives for algebra!

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The Dragonbox app (5+) is helpful. You let him work through the whole thing. When the whole thing is unlocked, I think there is an option to go back through some or all of the levels with numbers instead of pictures.

Hands On Equations is good, too, but Dragonbox is a better starter since it is so obviously a game. (He is really old for it, but I think it will help drop the overwhelmed aspect.)

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