Current Events > ... Why can't we just isolate the variable? Grade 8 math ITT

(+) Yeah! (+)

https://imgur.com/4n938A0
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Who comes up with these bullshit methods?
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What the hell...?
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I am supposed to teach this to my students. I can't not teach them this method cause there are questions involving making these pictures.

Ugh.
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BTW, I am a sub so I can't make sweeping changes to what they are doing.
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The point of these "bullshit" methods is so people actually understand what they're doing and not just blindly following steps.

What that just showed you visually is exactly what you do with the regular method. People who complain about this probably has a bad grasp of math to begin with.
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What was the point of the boxes when they literally just rewrote the equation afterwards?
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That's asinine.
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Squall28 posted...

What that just showed you visually is exactly what you do with the regular method. People who complain about this probably has a bad grasp of math to begin with.

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Seems like a big waste of time.

Add 7 multiply both sides by 4

Why makes things more complicated than that
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KainWind posted...

What was the point of the boxes when they literally just rewrote the equation afterwards?

It's showing you what you are doing visually.

You divide up a box because that's what the equation shows. X is in fourths, and you can figure out what a fourth of X is easily. Then since you know how much a fourth of X is, you can easily figure out what a whole X is.
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Squall28 posted...

The point of these "bullshit" methods is so people actually understand what they're doing and not just blindly following steps.

What that just showed you visually is exactly what you do with the regular method. People who complain about this probably has a bad grasp of math to begin with.

I guess so. I guess I just find this far more confusing than getting to the meat and potatoes of algebra. I guess really boiling it down step by step with a picture isn't horrible. I feel this implementation is bad though.
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This is what happens when you let liberals rewrite curriculum.
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chetmanly posted...

Seems like a big waste of time.

Add 7 multiply both sides by 4

Why makes things more complicated than that

Because they're learning, not just solving.
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Squall28 posted...

KainWind posted...

What was the point of the boxes when they literally just rewrote the equation afterwards?

It's showing you what you are doing visually.

You divide up a box because that's what the equation shows. X is in fourths, and you can figure out what a fourth of X is easily. Then since you know how much a fourth of X is, you can easily figure out what a whole X is.

And why is that method more effective than isolating a single x?

Isolation takes two steps
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Mizznox posted...

chetmanly posted...

Seems like a big waste of time.

Add 7 multiply both sides by 4

Why makes things more complicated than that

Because they're learning, not just solving.

Learning what? All that method does is say think of this as division instead of multiplication.
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Pepys Monster posted...

This is what happens when you let liberals rewrite curriculum.

For liberals by liberals.

Squall28 posted...

What that just showed you visually is exactly what you do with the regular method. People who complain about this probably has a bad grasp of math to begin with.

I disagree with the idea that you're dividing and then subtracting from one of the divisions. If you need to visualize it, graph it.
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chetmanly posted...

Squall28 posted...

KainWind posted...

What was the point of the boxes when they literally just rewrote the equation afterwards?

It's showing you what you are doing visually.

You divide up a box because that's what the equation shows. X is in fourths, and you can figure out what a fourth of X is easily. Then since you know how much a fourth of X is, you can easily figure out what a whole X is.

And why is that method more effective than isolating a single x?

Isolation takes two steps

What that is doing is teaching a concept. It's not brainlessly following steps. You can learn to follow steps after you actually understand what it is you are doing.

Like how many of you even understand why you would multiply by 4? Just to get x by itself for an easy read? No. You should think and know you have a fourth of X and four of a fourth gives you a whole.
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chetmanly posted...

Mizznox posted...

chetmanly posted...

Seems like a big waste of time.

Add 7 multiply both sides by 4

Why makes things more complicated than that

Because they're learning, not just solving.

Learning what? All that method does is say think of this as division instead of multiplication.

Uh no. That method shows you that multiplication and division undo each other. Even with the standard way, you do the same thing. Multiply by four, so you can combine four fourths to get a whole.

It's just that the regular method glosses over that concept.
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It is so different from how I was taught math, which is my disconnect.

I also assumed that Grade 8 was past the point of just starting out understanding algebraic equations. I am technically a high school trained teacher, so I am not in Grade 8 classes as often.

I will make sure they understand what the equation is asking them to do before I move to isolation. Technically you have to teach to that first anyways. I guess we are just doing it more through visual diagrams instead of writing it out.
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What concept is being taught here? Because the concept of equivalence is one of the most powerful in maths.
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Squall28 posted...

Like how many of you even understand why you would multiply by 4?

I mean, I have no strong feelings here either way, but that's the way I was taught?

you're performing operations in order to get x by itself, yeah. those operations are done in the order of operations. those operations work on x, you reverse engineer them to get x by itself. I guess over time this could deflate into "make x look just like x" or something but it isn't how it was taught, and I'm not sure that this method will actually take in the sense that kids will probably still just end up doing shorthand etc years from now
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Squall28 posted...

Uh no. That method shows you that multiplication and division undo each other.

Something that was already taught so it ain't showing anything new.
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Jeff AKA Snoopy posted...

I am supposed to teach this to my students. I can't not teach them this method cause there are questions involving making these pictures.

Ugh.

I tutor math. I get to see what kind of crap students have to learn these days to solve simple problems. This fits right in with how they teach these kids early on.

The best I can say is these students still understand the way we learned math and with one on one attention, you can get them to work the problem efficiently and surpass the method they were taught. Of course, the majority won't have any tutoring and will have to trudge along with you.
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I think that is my disconnect. They won't be drawing diagrams in Grade 9 to solve for variables. The diagrams are just to aid in understanding what the equation is actually asking you for.

Making it less about numbers and more tactile in their mind. Makes sense for visual learners.
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Balrog0 posted...

Squall28 posted...

Like how many of you even understand why you would multiply by 4?

I mean, I have no strong feelings here either way, but that's the way I was taught?

you're performing operations in order to get x by itself, yeah. those operations are done in the order of operations. those operations work on x, you reverse engineer them to get x by itself. I guess over time this could deflate into "make x look just like x" or something but it isn't how it was taught, and I'm not sure that this method will actually take in the sense that kids will probably still just end up doing shorthand etc years from now

You were taught a method, but not why you use that method. That's the problem.

The concept that is being taught here is the relationship of numbers and how you can manipulate it.

Equivalence and graphing are important to, but it's a different lesson.
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Squall28 posted...

The concept that is being taught here is the relationship of numbers and how you can manipulate it.

Really? Cause that is exactly what equivalence is you know
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what if the equation was y=36X-120, are you supposed to draw 36 squares?

I see it now. It looked like they were grouping x/4 into 8 blocks instead of 4. That's all I was hung up on.
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dave_is_slick posted...

Squall28 posted...

Uh no. That method shows you that multiplication and division undo each other.

Something that was already taught so it ain't showing anything new.

It's being shown in a different context, and how you apply it to algebra. Algebra is essential nothing new either. You pretty much do it when you learn basic arithmetic except you get a blank box instead of a letter.
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polopili posted...

what if the equation was y=36X-120, are you supposed to draw 36 squares?

guess so so we know that x/36 means x divided by 36
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tldr kids apparently dont understand multiplying both sides of an equation

that seems to be the issue here
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As someone studying Astrophysics who has had to do every kind of terrible math imaginable, this is absolute bs and useless
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Squall28 posted...

You were taught a method, but not why you use that method. That's the problem.

I mean I just told you I was taught why to use those things the way we use those things in that method.

Why do you think otherwise? Did most people really just learn through memorization and practice? Like I said, we were taught the order of operations, including their relationship to each other as inverses based on the order in which you consider them, at least by 6th grade when we learned about negative numbers.

Squall28 posted...

The concept that is being taught here is the relationship of numbers and how you can manipulate it.

Like how if you divide something by 4 and then multiply it by 4, you get the same number. Or if you add 4 and subtract 4, you get the same number. These concepts were certainly taught to me, with x being used as a stand in or 'variable' number that has an unknown value but which the operations act on in the same way they do other numbres

what did they do in your school?

Squall28 posted...

Equivalence and graphing are important to, but it's a different lesson.

I'm not sure I really understand what you mean, I haven't said anything about graphing although we did learn those concepts around the same time.

What is it that you're teaching with this other than equivalence? It seems like a way of visually representing how division works on x. That's fine, but I don't understand what it is teaching above and beyond what I just discussed.
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my first thought is they must not expect these students to go to anything past pre-algebra
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like I agree with you that this is how you do math already

its just that it was taught to me without this particular graphical representation, and you seem to be implying that is impossible?
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Squall28 posted...

It's being shown in a different context

But this context isn't needed. It needlessly complicates things.
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That method is an attack against common sense.

I don't see an issue with this. Obviously this method wouldn't fly in college Physics when you're doing a page or more of symbol manipulation per problem... but as a way of developing understanding? Sure, why not?

Back when I first learned Calculus, my teacher made us calculate derivatives the long way for the first few days. It was utterly impractical but the point was to teach us what's happening under the hood.

I think it would be a waste to spend a whole year doing Algebra this way, but you absolutely should understand why something works before you takes shortcuts and use shorthand. Actually, back to Calculus... you see students mess up implicit differentiation all the time because they don't understand why the manipulation is different from the Algebraic rules they already know.
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i disagree 1000%

like if you ask "why did you multiply both sides by 4"

"because x is being divided by 4"

that should be sufficient, why are 4 boxes needed to show that!?
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chetmanly posted...

i disagree 1000%

like if you ask "why did you multiply both sides by 4"

"because x is being divided by 4"

that should be sufficient, why are 4 boxes needed to show that!?

yeah I mean idk if I agree with that necessarily

you can definitely be taught to memorize or whatever and not actually know what that means

I guess my thing is that math is learned by building on prior knowledge just like everything else. By the time you get past long division and start learning fractions and ratios in grade school I feel like you have been taught the concepts that are being re-taught here visually
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Squall28 posted...

It's showing you what you are doing visually.

You divide up a box because that's what the equation shows. X is in fourths, and you can figure out what a fourth of X is easily. Then since you know how much a fourth of X is, you can easily figure out what a whole X is.

Maybe it's different in my mind because moving numbers around is no issue for me, but all that does is create a different variable. You are still doing the exact same thing. It just seems easier to me to say that when you see an equal sign, everything you do to one side must be done to the other. That's not just following steps, it's a pretty basic concept that always applies.

It also seems like if they are going to break it down this much visually, they should at least follow through with it and add the boxes of "x/4" together at the end instead of doing what could have been easily done in the first place.
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Balrog0 posted...

I guess my thing is that math is learned by building on prior knowledge just like everything else. By the time you get past long division and start learning fractions and ratios in grade school I feel like you have been taught the concepts that are being re-taught here visually

agreed. this methodology seems to have some use for helping young kids understand "what is multiplication? what is an equality? how do they interact?"
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Done teaching the lesson. The students didn't mind this for distribution type equations like 4 (x+5) = 32, but didn't really like it when fractions were involved.
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Also the students definitely prefer just isolating the variable. They seem to understand the value in this method though, which I am glad for.
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chetmanly posted...

i disagree 1000%

like if you ask "why did you multiply both sides by 4"

"because x is being divided by 4"

that should be sufficient, why are 4 boxes needed to show that!?

The fact that a picture of a box divided in 4 made people shit their pants here proves different.
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The setup just makes no sense to visualize it like that. The way it's set up looks like you're actually dividing x into four groups, subtracting seven entire groups (not seven from one of the groups) and getting -19 groups. Granted there could be some applications where you'd set it up the other way, but as is, it makes no sense.
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