algebra struggles -- tell me it gets better? and tips??

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My 8th grader is using TT Algebra I, although he "uses" it in that he reads the lesson, we usually do the practice exercises together, and then he does the problems. He will not watch the lectures or examples on CD. (Yes, I realize this defeats the purpose of TT).

So, he's struggling with chapter 4 or 5, simplifying equations. If he sees:

17 - 4(2x + 10)

He wants to turn it into 13 - 2x + 10 and then into 23 - 2x and then he'll still sometimes want to make that = 25. It really throws him when they do a "simplify this expression" without giving him the = side of things. Not that he's 100% stellar on what to do when it is a full equation, either, but.....

I gave him a practice sheet Weds, Thurs & Fri of just "show me what this means" and started with simple 4(x+5) (for him to write (4)(x) + (4)(5)) and moving to things like the first problem I typed.

When I wrote these for him, he did fine. One hundred percent accuracy. That was Thurs & Fri.

Today, same thing but in the book, he went back to missing them every time in the way I described. His excuse?? "Well, that was a long time ago...."

Please tell me there's something other than "we'll just have to do math on weekends, too...." to help this. We had a VERY LONG DAY today with me correcting his math at every.single.problem. because he didn't remember any of it.

The only new concept today was how to shift the negative from a - (parenthetical) and make it a + (-1)(parenthetical). So 5 - (x+3) becomes 5 + (-1)(x) + (-1)(3). that's it. That little bit turned a 20 minute session into an hour long session.

Help??

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Sounds like he might need to back up to pre-algebra. The mistake you cited is an orders of operation issue, and learning orders of operation takes a fair amount of practice.

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We had the same kind of issues with both of my kids: simplifying expressions, multiplying two expressions in parentheses, especially with negative signs involved. They knew the principle, but made many careless mistakes (even though both love math and are good at it)

We solved the problem by consistent practice over several days and weeks. We found this the one topic where the practice problems in our book were not sufficient, so we made up problem sheets for them. Even after we progressed to the next topic, we would give review practice for this.

In the beginning, working with color for the signs helped. Also, insisting on carefully writing down every step is important. They both mastered the skill and have now no problems.

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We had the same kind of issues with both of my kids: simplifying expressions, multiplying two expressions in parentheses, especially with negative signs involved. They knew the principle, but made many careless mistakes (even though both love math and are good at it)

We solved the problem by consistent practice over several days and weeks. We found this the one topic where the practice problems in our book were not sufficient, so we made up problem sheets for them. Even after we progressed to the next topic, we would give review practice for this.

In the beginning, working with color for the signs helped. Also, insisting on carefully writing down every step is important. They both mastered the skill and have now no problems.

Using color for the signs is a good idea, thanks.

I do make him write down every step, which he hates, but it does help.

I'll come up with extra practice problems, too. Good idea.

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It takes a while for these new ideas to sink in.

I think it helps to bring it back to "tiny numbers" and even blocks if necessary at the beginning. The idea is to "see if your way works." So together you'd say, "What if x is 2, what does this problem mean then?" Work the problem out the correct way, from inside of the parens out, and get a result. Then leave that one there & try it "his way."

At the very least, the kid realizes that both methods don't produce the same result. So there is the premise for needing "one way" for all math folks to do a problem like that.

If he's still objecting, then you might try some kinds of blocks. You'd have to think it thru in advance and set it up, "What if you had a 14 in the parens, and you had 4 of those, and you took all that away from 17..."

So in other words, I'd work on "what that equation means" before I'd work on isolating the x on one side of the equation, solving for x, etc.

Julie

Edited by Julie in MN
Trying to be clear?
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I agree with brushing up on the pre-algebra. Order of operations is going to apply to pretty much all his math from now on. It's got to be down pat.

I mark ds's problems wrong when he doesn't show each (reasonable) step. It's non-negotiable. I know my son's problem is that he thinks he's so smart that he doesn't have to write each step. So I Dr. Phil him. "And how's that working for you?!". :tongue_smilie:

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I do make him write down every step, which he hates, but it does help.

My dental hygienist, who was homeschooled, told me that starting with Algebra, her mother made them SESS (Show Every Stinkin' Step). :D

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If he wants to learn from a text and not watch DVDs, I'd switch to a different program. If he used TT for pre-algebra, I'd consider using a different, maybe more involved or advanced?, pre-algebra program and wait until he's mastered operations and other topics before revisiting algebra.

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My dental hygienist, who was homeschooled, told me that starting with Algebra, her mother made them SESS (Show Every Stinkin' Step). :D

HAAAAA! Good one! :D

We said the same to my ds too! It did help as Algebra I progressed. Having done TT since Pre-Algebra (it does go over order of operations in detail -PEMDAS) and assumes the student is well versed by Algebra I. Did the OP do the TT Pre-test (online) to determine placement? It would appear if the student got most of the problems incorrect, then something may be amiss?

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We solved the problem by consistent practice over several days and weeks. We found this the one topic where the practice problems in our book were not sufficient, so we made up problem sheets for them. Even after we progressed to the next topic, we would give review practice for this.

Also, insisting on carefully writing down every step is important. They both mastered the skill and have now no problems.

:iagree:

Having done TT for the last few years since junior high, I would suggest you need to utilize the DVDs for review.

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HAAAAA! Good one! :D

We said the same to my ds too! It did help as Algebra I progressed. Having done TT since Pre-Algebra (it does go over order of operations in detail -PEMDAS) and assumes the student is well versed by Algebra I. Did the OP do the TT Pre-test (online) to determine placement? It would appear if the student got most of the problems incorrect, then something may be amiss?

OP here.

He started with TT 7, then I found a great deal on TT Alg. 1 used and went ahead and bought it. Couldn't find pre-algebra used, decided that the pre-algebra ending of TT 7/beginning of Alg. I was sufficient.......

...yea, kind of realizing that was a mistake at this point.

He does in general have order of operations down, it's just that whole "linked to each other stuff" about first doing what I call unchaining the stuff in the parentheses. He forgets that in a problem like I posted -- 17 + 4(x - 2) -- that the 4 is chained to the parenthetical.

I think also that part of the problem is that TT shows first do this, in this order. (as in simplifying an expression) THEN they go back and say "now, if it's a full equation, undo in the reverse order." So, switching from simplifying expressions back to solving equations, and always back & forth, gets him confused.

So ---- is this the sort of thing that is drilled to death in pre-algebra, and I really do need to back up? Or just take a short break, drill him myself on these particular things, and then move forward?

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:iagree:

Having done TT for the last few years since junior high, I would suggest you need to utilize the DVDs for review.

quick question on that --- I think they are cd-roms, right? will they work in the dvd player or only the computer?

(I guess I should just try it and find out, huh?.....)

And, I agree. Just haven't convinced the boy of it......

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If he wants to learn from a text and not watch DVDs' date=' I'd switch to a different program. If he used TT for pre-algebra, I'd consider using a different, maybe more involved or advanced?, pre-algebra program and wait until he's mastered operations and other topics before revisiting algebra.[/quote']

I would love suggestions if you have some on what to use. I'm not at all married to TT for this child, since he is not wanting to use the computer anyway, but I'm just kind of clueless about what else is out there for upper level maths.

We used singapore up to 5B and moved directly from that to TT 7 for him (did take the placement test for that) and I'm just not familiar with loads of math options.

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It takes a while for these new ideas to sink in.

I think it helps to bring it back to "tiny numbers" and even blocks if necessary at the beginning. The idea is to "see if your way works." So together you'd say, "What if x is 2, what does this problem mean then?" Work the problem out the correct way, from inside of the parens out, and get a result. Then leave that one there & try it "his way."

At the very least, the kid realizes that both methods don't produce the same result. So there is the premise for needing "one way" for all math folks to do a problem like that.

If he's still objecting, then you might try some kinds of blocks. You'd have to think it thru in advance and set it up, "What if you had a 14 in the parens, and you had 4 of those, and you took all that away from 17..."

So in other words, I'd work on "what that equation means" before I'd work on isolating the x on one side of the equation, solving for x, etc.

Julie

thanks, these are good ideas.

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I only scanned responses, but for 8th grade boys struggling in math, they need to coast a year in prealgebra. (Ask me how I know....) All boys forget either their 8th or 9th grade year because of their growth spurts (their brains rewire during that time). I have ds (college now) workbooks in the closet, and asked him once what he did in either 8th or 9th grades..... he said he didn't know. I showed him the workbooks, and he said he had no memory of doing them, but they were in his handwriting! I asked dh the same, he couldn't remember what he did in those years either.

There is a reason middle schools have these boys take shop classes!

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I only scanned responses, but for 8th grade boys struggling in math, they need to coast a year in prealgebra. (Ask me how I know....) All boys forget either their 8th or 9th grade year because of their growth spurts (their brains rewire during that time). I have ds (college now) workbooks in the closet, and asked him once what he did in either 8th or 9th grades..... he said he didn't know. I showed him the workbooks, and he said he had no memory of doing them, but they were in his handwriting! I asked dh the same, he couldn't remember what he did in those years either.

This is one more reason why these skills need to be practiced to the degree that they become automatic. Nobody forgets how to read or how to do simple addition or how to ride a bicycle in 8th grade. The problem is the compartmentalized nature of math education in this country, with content neatly wrapped into one-year packages never to be touched again - for math, this simply does not work.

A student who masters and then actually USES pre-algebra and algebra skills every single year will not lose them.

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I would love suggestions if you have some on what to use. I'm not at all married to TT for this child, since he is not wanting to use the computer anyway, but I'm just kind of clueless about what else is out there for upper level maths.

We used singapore up to 5B and moved directly from that to TT 7 for him (did take the placement test for that) and I'm just not familiar with loads of math options.

It's not for everyone, but we absolutely love Saxon. Their 8/7 course is a solid pre-algebra course with lots of review, mental math, facts practice - fractions, percentages, measurements, etc., and a variety of problems to work each day. The built in review makes it easy to retain what's learned and Saxon adds geometry into their algebra and advanced math texts. You may want to do a search for Saxon here - some love it and others hate it. But for the students it works for - it works very well. :)

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Yup.

TT drills in Pre-Algebra the order of operations to mastery. And they also use terminology in Pre-Algebra that bridges over to Algebra I with problems. It frankly drove me crazy they did that, as I was used to other terminology. But now that we're ending Algebra I, it makes sense.

The TT discs are CD-Roms. (I had a brain fart or synapse relapse as I call it. ;) ) You really do need to use them as the lecture and practice discs help explain to the student key hints that sometimes is not printed in the textbook.

No harm in going to the TT Pre-Algebra. But I would go to the TT website and give him the placement test for sure.

OP here.

He started with TT 7, then I found a great deal on TT Alg. 1 used and went ahead and bought it. Couldn't find pre-algebra used, decided that the pre-algebra ending of TT 7/beginning of Alg. I was sufficient.......

...yea, kind of realizing that was a mistake at this point.

I think also that part of the problem is that TT shows first do this, in this order. (as in simplifying an expression) THEN they go back and say "now, if it's a full equation, undo in the reverse order." So, switching from simplifying expressions back to solving equations, and always back & forth, gets him confused.

So ---- is this the sort of thing that is drilled to death in pre-algebra, and I really do need to back up? Or just take a short break, drill him myself on these particular things, and then move forward?

Edited by tex-mex
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Teach him a cool acronym for the order of operations.. I know the popular one is Please Excuse My Dear Aunt Sally. But if you could come up with one he loves (or have him come up with one) he would be more likely to abide by it.

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Yup.

TT drills in Pre-Algebra the order of operations to mastery. And they also use terminology in Pre-Algebra that bridges over to Algebra I with problems. It frankly drove me crazy they did that, as I was used to other terminology. But now that we're ending Algebra I, it makes sense.

The TT discs are CD-Roms. (I had a brain fart or synapse relapse as I call it. ;) ) You really do need to use them as the lecture and practice discs help explain to the student key hints that sometimes is not printed in the textbook.

No harm in going to the TT Pre-Algebra. But I would go to the TT website and give him the placement test for sure.

Thanks, I'll have a look at the placement test and see if I can find a way to get TT Pre-Algebra here.

It's getting it from the US to Brazil that's going to be a problem.....(grrr). Kicking myself for jumping ahead......

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Teach him a cool acronym for the order of operations.. I know the popular one is Please Excuse My Dear Aunt Sally. But if you could come up with one he loves (or have him come up with one) he would be more likely to abide by it.

The danger with this acronym (or PEMDAS) is that many students get hung up and think that multiplication must be done before division.

Be very careful to stress that multiplication and division are at an equivalent level and that you do whichever appears first from left to right.

I use the explanation of shortcuts for order of operations.

(1) symbols of grouping (parentheses, brackets, fraction bars)

(2) exponents (a shortcut for repeated multiplication)

(3) multiplication/division as they appear from left to right (shortcut for repeated addition/subtraction)

(4) addition/subtraction as they appear from left to right.

If you have something like 6+3*4, you can write in expanded form as

6+4+4+4 and it shows why the order of operations is what it is.

(I see a lot of students who have acronyms memorized but still can't do the problem.)

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The danger with this acronym (or PEMDAS) is that many students get hung up and think that multiplication must be done before division.

Be very careful to stress that multiplication and division are at an equivalent level and that you do whichever appears first from left to right.

I use the explanation of shortcuts for order of operations.

(1) symbols of grouping (parentheses, brackets, fraction bars)

(2) exponents (a shortcut for repeated multiplication)

(3) multiplication/division as they appear from left to right (shortcut for repeated addition/subtraction)

(4) addition/subtraction as they appear from left to right.

If you have something like 6+3*4, you can write in expanded form as

6+4+4+4 and it shows why the order of operations is what it is.

(I see a lot of students who have acronyms memorized but still can't do the problem.)

This has actually come up in a problem going around my facebook the last few days. The problem is 2-2x2+22, and many, many people are correctly doing 2-4+22, then since "addition before subtraction", they are incorrectly trying to add 4 and 22.

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He will not watch the lectures or examples on CD.

He will not?

Tell him he WILL. There should be no choice in the matter. And I'd make him start over wherever he stopped watching the lectures.

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I found that at certain stages in my boys' developing brains (!) I had to sit down with them problem-by-problem until they got the show-me-the-work concept. We got two white boards/markers and would sit side-by-side on the couch working every problem step-by-step together on our own white boards until they got the concept of the necessary and methodical steps that math work involves. This also allowed me to slow down the process to see immediately where they were going wrong - if it was a careless error or order of operations error or a missing math concept, etc. And, even now, occassionally if we hit a rough spot in math - out come the white boards and we work together until the problem is fixed.

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He wasn't reading the text, and he was speeding up the dvds. I walked into his room and his teacher sounded like Mickey Mouse.

Long story, but we jumped back and couple of chapters and started over. If he does it again, we'll start from the beginning with me sitting by his side.:D

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He will not?

Tell him he WILL. There should be no choice in the matter. And I'd make him start over wherever he stopped watching the lectures.

I appreciate the sentiment, truly, but unless you'd like to be the one to come and enforce that.....

It's not so much a matter of defiance, it's more that....the audio/visual of the CD is distracting to him. He learns best with the fewest distractions possible. So, listening to a computer voice explain the problem bothers him. Listening to a computer voice "read" the text to him, slower than he reads himself, bothers him. And watching the problems appear on screen, step by step but without a person there doing it, bothers him.

I thought TT would take the argument and anger out of math, which it did to some extent. The explanations are fine for him when he works through all the practices and have been good for him until I skipped ahead (he didn't watch a single CD during TT 7 either and he did GREAT with that level last year).

I'm learning though that he does not do well with electronic forms of instruction, and that's fine. If it were a matter of defiance only, I'd enforce it, dh would back me up, and the CDs would be watched. But it's a matter of learning style as well, and CD just doesn't work as well for him. Not a passive CD like that. I guess I should have phrased that a bit better in the beginning....

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I found that at certain stages in my boys' developing brains (!) I had to sit down with them problem-by-problem until they got the show-me-the-work concept. We got two white boards/markers and would sit side-by-side on the couch working every problem step-by-step together on our own white boards until they got the concept of the necessary and methodical steps that math work involves. This also allowed me to slow down the process to see immediately where they were going wrong - if it was a careless error or order of operations error or a missing math concept, etc. And, even now, occassionally if we hit a rough spot in math - out come the white boards and we work together until the problem is fixed.

Using the white boards is a brilliant idea.

this is basically what we do right now, except usually it's me working the problem, him watching. Your way is much better and I'll do that starting today.

One question -- did you then just count math lessons as a done/not done situation and only grade the tests? Since you are working with him/correcting as he goes...? I've been trying to keep grades this year (8th grade) so we can all get in the swing of it before high school and I guess I'm hung up on....if I sit there and work his math with him, and in the end he gets all the problems right (because I worked them alongside him), how do I grade that?

Just not give a grade for the daily work?

I'm also going to have him highlight in the original problem what parts belong together so he gets used to the fact that the number on the outside of a parenthetical has to be dealt with as part of the parenthetical, not as part of the whatever else is outside.

Feeling much better prepared to work through all of this with him. Thanks again for all the great ideas in this thread.

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The danger with this acronym (or PEMDAS) is that many students get hung up and think that multiplication must be done before division.

Be very careful to stress that multiplication and division are at an equivalent level and that you do whichever appears first from left to right.

I use the explanation of shortcuts for order of operations.

(1) symbols of grouping (parentheses, brackets, fraction bars)

(2) exponents (a shortcut for repeated multiplication)

(3) multiplication/division as they appear from left to right (shortcut for repeated addition/subtraction)

(4) addition/subtraction as they appear from left to right.

If you have something like 6+3*4, you can write in expanded form as

6+4+4+4 and it shows why the order of operations is what it is.

(I see a lot of students who have acronyms memorized but still can't do the problem.)

This is a good way to explain it, thank you. He does have trouble with that (thinking multiplication comes first). He also struggles with now remembering where to put parentheses, fraction bars, etc. since those were added later on, and then with remembering if he's working forwards or backwards due to the "undo in reverse order" concept.

Thanks for typing out those explanations, I know it will be useful/helpful for him.

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thanks, these are good ideas.

Good, I just want to emphasize that for kids like mine, forcing more memorization of rules isn't what did it.

Having them try to do it "their way" and really absorbing the fact that they will end up with a different answer -- that was the most important thing, that was the thing that made everything else more important than they realized.

Once if they know that order matters, then following an order of operations etc. just naturally followed. And that's where having them start with something concrete and try to put it in a number sentences sometimes came in, to help them see that not only is the order of operations "the rule" that everyone agrees on, but also that it was chosen because it just makes sense.

Julie

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I don"t grade my kids at all so i"m the wrong one to ask about grading> (ignore the typos _ our new puppy licked the keyboard this morning and now it"s typing crazily!) but i think you"ll find that after a few sessions of working together he"ll start developing the skills and won"t need you there as much> also i don"t think daily work should be graded at all as it"s for learning and for practice _ not mastery yet! i hope this keyboard dries out and starts working again!

that"s my @ cents worth!

myra

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I don"t grade my kids at all so i"m the wrong one to ask about grading> (ignore the typos _ our new puppy licked the keyboard this morning and now it"s typing crazily!) but i think you"ll find that after a few sessions of working together he"ll start developing the skills and won"t need you there as much> also i don"t think daily work should be graded at all as it"s for learning and for practice _ not mastery yet! i hope this keyboard dries out and starts working again!

that"s my @ cents worth!

myra

thanks, Myra!

I did the white boards today with him, and backed up to chapter one (he's in chapter 5.....) all the way back to simple equations like x + 32 = 45. We went through I don't know how many, all 4 functions (+, -, x, /) including with decimals and fractions. Got from 1.1 to 1.7 today with him just cruising along on the white board, me beside him doing the same problems on my white board, him on his.

Today's lesson was: SESS (show every stinkin' step, borrowed from this thread!) and making sure he really is totally solid on undoing each function. Whew!

We'll keep doing this as long as he needs until he's back on to new material.

thanks everyone for the help.

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I found that at certain stages in my boys' developing brains (!) I had to sit down with them problem-by-problem until they got the show-me-the-work concept. We got two white boards/markers and would sit side-by-side on the couch working every problem step-by-step together on our own white boards until they got the concept of the necessary and methodical steps that math work involves. This also allowed me to slow down the process to see immediately where they were going wrong - if it was a careless error or order of operations error or a missing math concept, etc. And, even now, occassionally if we hit a rough spot in math - out come the white boards and we work together until the problem is fixed.

:iagree:

There really is something to the brain of young teen boys with higher level math!

We also use a large whiteboard (portable from room to room -- but VERY heavy) that I bring out for what I call, "Review" days. LOL ;) If there is a problem ds is struggling with -- out comes out the whiteboard. We review with the TT discs. Then I choose new problems to review and practice until I know for sure he gets it. What I like is the fact I can see the mistakes as we work together. Make it positive and never be upset with the child/teen. Mistakes do happen -- we are after mastery and understanding before we go on to the next lesson, IMO.

Which is the luxury of hsing versus a regular classroom where the teacher has no time to review for one or two students and has to keep pace with finishing the book by school year's end. We hsers can take our time! HTH

ETA: I'm a former Elementary Schoolteacher and grading for me really helps see trends thru the year -- especially with math.

When ds was younger, I used the following criteria for grading math:

Daily Work = 25%

Drills = 25%

Tests = 50%

---------------

Now that ds is in high school and I do not have to do the (i.e. Saxon Math) type of drill (I loved Saxon, but ds hated it. We switched to TT.) anymore and his math grade is like this:

Tests = 75% (I don't do extra quizzes or semester finals like high school teachers do.)

Daily Work = 25%

---------------

Edited by tex-mex
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Thank goodness my keyboard has dried out so my caps lock will now "unlock", and the pupply is curled up beside me napping! Glad some of my ideas helped you out as I get so many great ideas here, too!

Myra

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