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#1
05-14-2018, 06:03 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
What is the answer to #9 on my daughter's math homework? Third grade, still.

Yep, us again. You may remember me from February.

According to my daughter, every student got a re-do on this math assignment. It's called "Patterns of Geometry".

Check out the assignment here.

Take a look. Realize my wife and my daughter have re-done the work and the checks indicate wrong answers(originally wrong, not the re-do). No matter how much they count that grid in #5, they can't get an answer that produces a good response for #9. We think the answer should be "all of them are divisible by 5", but we can't get it to work out.

The top half with the triangles was a chore, the kind of thing I'd expect in a fun activity pack. The bottom is fine, but we can not work it out.

If anyone is very mathy, feel free to check all the work. It's not the grade(daughter is doing fine normally). It's the principle of not letting this HW defeat us.
#2
05-14-2018, 06:08 PM
 Mithras Guest Join Date: Apr 2008 Posts: 704
The answers are 25, 16, 9, and 4. All square numbers because you're counting squares within a square.
#3
05-14-2018, 06:08 PM
 ElvisL1ves Charter Member Join Date: Jul 2000 Location: The land of the mouse Posts: 47,717
25, 4, and 9 are all square numbers.
#4
05-14-2018, 06:30 PM
 Robot Arm Guest Join Date: Jun 2000 Location: Medford, MA Posts: 23,030
Quote:
 Originally Posted by Mahaloth The top half with the triangles was a chore, the kind of thing I'd expect in a fun activity pack.
What answers did you eventually get?
#5
05-14-2018, 06:35 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by Robot Arm What answers did you eventually get?
The ones written in now on the sheet. Are we wrong?
#6
05-14-2018, 06:40 PM
 Joey P Charter Member Join Date: Jun 1999 Location: Milwaukee, WI Posts: 27,848
Quote:
 Originally Posted by Mahaloth The ones written in now on the sheet. Are we wrong?
All the check marks are incorrect answers. That's why she got a 1/10 and not a 9/10.

ETA, should be 26,16,9,4, which as stated are all perfect squares. I'm not sure if that some how relates back to the beginning or just a happy/forced coincidence.

Last edited by Joey P; 05-14-2018 at 06:43 PM.
#7
05-14-2018, 06:47 PM
 beowulff Member Join Date: May 2001 Location: Scottsdale, more-or-less Posts: 15,910
Quote:
 Originally Posted by Mahaloth The ones written in now on the sheet. Are we wrong?
I count 36 triangles.
#8
05-14-2018, 06:48 PM
 Aspidistra Member Join Date: Feb 2001 Location: Melbourne, Australia Posts: 4,857
Quote:
 Originally Posted by Mahaloth The ones written in now on the sheet. Are we wrong?
Yes, I'm afraid so. They definitely all have to be square numbers (because of the geometry of the thing, in fact).

Also, I believe the number of triangles should be 36 (4x4 for the outer layer, 3x4 for the middle, 2x4 for the inner) and it's possible that the number she's looking for for squares in the picture might be '3', though I'd argue the point if I were marked wrong for 4.

Another extension of the pattern would produce another 20 triangles (5 per corner, since the existing squares go 4-per, then 3-per, then 2-per)

If '24' and '8' were the kid's original answers for 1 and 4, then IMO the teacher should have marked her correct on 5, since she added up right.
__________________
I don't think I'm being unreasonable if I suggest that the number of inferences required to extrapolate the cause of Chinese population growth from your hairdresser's experience puts a burden on fundamental logic fair greater than it can reasonably bear. - RNATB
#9
05-14-2018, 06:48 PM
 griffin1977 Guest Join Date: Feb 2006 Posts: 3,009
Pretty awful ambiguous question IMO. It all boils down to whether you think this:
https://imgur.com/a/p6PKXdQ

Is two rectangles or one. I would say both are valid answers, unless you explicitly define that in the question you are just rewarding making an arbitrary choice.

Teaching that the correct answer that question is "there are two rectangles" is equally wrong IMO. It is just as valid to say that the shape is a single rectangle and two edges.

Last edited by griffin1977; 05-14-2018 at 06:50 PM.
#10
05-14-2018, 06:52 PM
 Tired and Cranky Guest Join Date: Dec 2014 Posts: 1,210
1. 36
2. 4
3. 9
4. 20
5. 56
6. 25
7. 16
8. 9, 4
9. They are all squares.
10. 55

I object to the grading on this. If the answer to 3 depends on the work for the first two, she should get credit for the right answer based on the wrong assumptions.
#11
05-14-2018, 06:59 PM
 MrFloppy Guest Join Date: Sep 2006 Location: Bel Air, MD Posts: 686
36 triangles
4 squares
36/4=9
20 (4 lots of 5)
36+20=56
16 (4x4)
9 (3x3)
4 (2x2)
All square numbers
25+16+9+4+1=55

Good luck.
#12
05-14-2018, 07:04 PM
 Patx2 Guest Join Date: Nov 2016 Posts: 3,584
Quote:
 Originally Posted by beowulff I count 36 triangles.
I also got 36, and a headache.
#13
05-14-2018, 07:04 PM
 Aspidistra Member Join Date: Feb 2001 Location: Melbourne, Australia Posts: 4,857
Quote:
 Originally Posted by Tired and Cranky I object to the grading on this. If the answer to 3 depends on the work for the first two, she should get credit for the right answer based on the wrong assumptions.
yeah, me too, but sadly "she got a 1 and really deserves a 3" doesn't play as well as "she got 4 but really deserves to pass". Also, it looks like she's fine on general arithmetic since she did the adding up correctly, but actually might be struggling in the geometry section.

For instance, seeing that it's symmetrical so that you only have to count a quarter of the triangles in the triangle picture, is a trick that would make her life a lot easier. Also, marking spots on a diagram with your pencil as you're counting up things is a great trick. There are a lot of ways to approach these sorts of problems which would help her out here.

Have they been doing geometry in class for long?
__________________
I don't think I'm being unreasonable if I suggest that the number of inferences required to extrapolate the cause of Chinese population growth from your hairdresser's experience puts a burden on fundamental logic fair greater than it can reasonably bear. - RNATB
#14
05-14-2018, 07:06 PM
 Doug K. Guest Join Date: Jul 1999 Location: Hutchinson, KS Posts: 3,626
I found the worksheet and the answer key online. The answers are what MrFloppy said, except that for 9 their answer is "They are all products of numbers multiplied by themselves.", which of course means the same thing.
#15
05-14-2018, 07:07 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by Aspidistra Have they been doing geometry in class for long?
No, and I suspect this might be in the category of "5th or 4th grade work she brought down." It's her first year teaching 3rd grade and occasionally, we get work we're pretty sure was from 5th grade.

My daughter had a research project that was kind of nuts for her age/experience.
#16
05-14-2018, 07:07 PM
 Patx2 Guest Join Date: Nov 2016 Posts: 3,584
Quote:
 Originally Posted by Tired and Cranky 1. 36 2. 4 3. 9 4. 20 5. 56 6. 25 7. 16 8. 9, 4 9. They are all squares. 10. 55 I object to the grading on this. If the answer to 3 depends on the work for the first two, she should get credit for the right answer based on the wrong assumptions.
My daughter is in high school and these type of questions make her crazy. It’s stressful when one wrong answer screws up your answers to the next several problems especially, as you say, she’s basing her work off of a false assumption. The killer is when she actually shows the original work.
#17
05-14-2018, 07:11 PM
 Sunny Daze Member Join Date: Feb 2014 Location: Bay Area Urban Sprawl Posts: 11,063
Quote:
 Originally Posted by Aspidistra ... and it's possible that the number she's looking for for squares in the picture might be '3', though I'd argue the point if I were marked wrong for 4.
This one tripped me up for a few minutes. They're using the outer line to make the triangles work, but not for the squares.

Mahaloth come back, bring puzzles! This was fun.

ETA: my parents were teachers. I was always told that if most of the class couldn't do something, it wasn't the students, it was the teacher. I'm glad they got a re-do.

Last edited by Sunny Daze; 05-14-2018 at 07:12 PM.
#18
05-14-2018, 07:29 PM
 BigT Guest Join Date: Aug 2008 Location: "Hicksville", Ark. Posts: 34,932
Quote:
 Originally Posted by Doug K. I found the worksheet and the answer key online. The answers are what MrFloppy said, except that for 9 their answer is "They are all products of numbers multiplied by themselves.", which of course means the same thing.
But the kid's answer of 4 squares is clearly marked wrong on the sheet.

And I agree it is the correct answer. As are the ones for the grid--though I would presume that they would be taught exactly how to count squares in such an arrangement. There is a specific way that mathematicians mean. If not defined beforehand, then many different answers are possible. (As a kid, my answer to the number of 2x2 squares would have been either 4 or 6 1/4--i.e. adding up the half squares and no overlaps.)

Last edited by BigT; 05-14-2018 at 07:30 PM.
#19
05-14-2018, 07:36 PM
 jz78817 Member Join Date: Aug 2010 Location: Under Oveur & over Unger Posts: 11,565
question #9 is a piece of shit.

"what do you notice about all these numbers?"

How can there be a wrong answer?

"I didn't notice anything."

are textbooks written by idiots?
#20
05-14-2018, 07:49 PM
 DPRK Guest Join Date: May 2016 Posts: 2,006
Regardless of the competence of textbook authors, recognizing patterns is a legitimate mathematical skill. The book may or may not be rubbish, but we cannot tell based on just the one question.
#21
05-14-2018, 07:55 PM
 pulykamell Charter Member Join Date: May 2000 Location: SW Side, Chicago Posts: 45,183
Quote:
 Originally Posted by BigT But the kid's answer of 4 squares is clearly marked wrong on the sheet.
No, it's confusing. It's the entire question that's marked wrong. The correct answer is 9,4 and the answer is given as 7,4 so the entire thing is just one wrong answer instead of two. I can see how it's confusing.

So she was able to correctly count 16-unit squares. I guess I'd ask how she got only 12 for 4-unit squares and only 7 for 9-unit squares. The way I would count them is just systematically to go:

Code:
```X X . . .
X X . . .
. . . . .
. . . . .
. . . . .

. X X . .
. X X . .
. . . . .
. . . . .
. . . . .

. . X X .
. . X X .
. . . . .
. . . . .
. . . . .

. . . X X
. . . X X
. . . . .
. . . . .
. . . . .```
for four squares; then down a row, repeat for another four; then down a row repeat for another four; and down one more row for four, for a total of 16. Since she got 12, it seems like she perhaps missed a row or column of squares?

For seven 9-unit squares, I'm not entirely sure how 7 would be arrived at, though.

But she got the four 16-unit squares. So what I would check is to see how she's counting up the various x-unit squares within the larger square to get those answers.

Last edited by pulykamell; 05-14-2018 at 07:56 PM.
#22
05-14-2018, 07:55 PM
 CookingWithGas Charter Member Join Date: Mar 1999 Location: Tysons Corner, VA, USA Posts: 12,440
I don't know anything about elementary education theory but I cannot see anything to be gained by this exercise that is the least bit applicable to anything. I can see doing it as a classroom game, but not an assignment for a grade.
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#23
05-14-2018, 08:21 PM
 Mean Mr. Mustard Guest Join Date: Dec 2009 Posts: 10,193
Quote:
 "what do you notice about all these numbers?"
"I notice that they are all ages of people I know."
"I notice that they are all less than one billion."
"I notice that they are all correct."
"I notice that none of them are divisible by 7."

mmm
#24
05-14-2018, 08:29 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by CookingWithGas I don't know anything about elementary education theory but I cannot see anything to be gained by this exercise that is the least bit applicable to anything. I can see doing it as a classroom game, but not an assignment for a grade.
Father here. I am a teacher, too. I use puzzles like these for fun activities when the kids are done with work.
#25
05-15-2018, 01:34 AM
 thelurkinghorror Guest Join Date: Jun 2006 Location: Venial Sin City Posts: 13,207
Ugh, I'm not a regular teacher but I have taught adults. The design is terrible.

- checks should be right answers, not wrong ones.
- how is 2 wrong?
- regardless of the answers on 1 and 2, 3 should be correct because the math is correct. Contingent answers are a dick move.
- 8 deserves half credit
#26
05-15-2018, 06:34 AM
 watchwolf49 Guest Join Date: Dec 2009 Location: State of Jefferson Posts: 8,500
I noticed the eiganvalues are 1 and -1 ... which is redundant but the teacher may not know that ...
#27
05-15-2018, 06:43 AM
 pulykamell Charter Member Join Date: May 2000 Location: SW Side, Chicago Posts: 45,183
Quote:
 Originally Posted by thelurkinghorror Ugh, I'm not a regular teacher but I have taught adults. The design is terrible. - checks should be right answers, not wrong ones.
I grew up with checkmarks being wrong answers through grammar school and most my teachers in high school (80s and early 90s). Perhaps this varies by region. (ETA: Here's a thread on a teacher's board showing there is variation in its meaning.)

Last edited by pulykamell; 05-15-2018 at 06:45 AM.
#28
05-15-2018, 07:10 AM
 CookingWithGas Charter Member Join Date: Mar 1999 Location: Tysons Corner, VA, USA Posts: 12,440
Quote:
 Originally Posted by thelurkinghorror - checks should be right answers, not wrong ones.
You may be about my age. Apparently this is a not-so-recent innovation in scoring. A teacher once told me, "It means they need to 'check' their answer." It also does not come across as negatively as a big-ass X. This allows the student to focus on addressing why it's wrong and learning from it, rather than stressing over the fact that they screwed up.

That's the theory, anyway.
#29
05-15-2018, 07:36 AM
 Isilder Guest Join Date: Mar 2013 Posts: 4,350
Quote:
 Originally Posted by Mithras The answers are 25, 16, 9, and 4. All square numbers because you're counting squares within a square.

Perhaps he didn't arrive at the simplest method for ensuring you get the count right.

Put a 2x2 square at the top left. Now you can move it right one .. So thats a 2nd square, and you can move it right a third time.. And then you can't move it right any more.. So move it down one... Then thats a new row of 2x2 squares, and move down .. until you can't move down any more.

So the number of rows and columns must be the original square with one row off the bottom, and one column off the right side.. so a 4x4 changes to be a 3x3, and its still a square.

When you put the 3x3 and 4x4 on , the original squares sides are reduced by two and three respectively.

Last edited by Isilder; 05-15-2018 at 07:37 AM.
#30
05-15-2018, 11:31 AM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by CookingWithGas You may be about my age. Apparently this is a not-so-recent innovation in scoring. A teacher once told me, "It means they need to 'check' their answer." It also does not come across as negatively as a big-ass X. This allows the student to focus on addressing why it's wrong and learning from it, rather than stressing over the fact that they screwed up. That's the theory, anyway.
I asked my 6th grade class(ELA teacher here). They prefer red and "X". However, I told them I would use purple pens for marking if they go buy them for me. Honestly...they looked pretty excited. I half-expect 20 purple pens coming in tomorrow.
#31
05-15-2018, 11:38 AM
 enalzi Guest Join Date: Apr 2008 Location: Chicago, IL Posts: 7,155
Quote:
 Originally Posted by Mean Mr. Mustard "I notice that they are all ages of people I know." "I notice that they are all less than one billion." "I notice that they are all correct." "I notice that none of them are divisible by 7." mmm
"They've never been in my kitchen."
#32
05-15-2018, 11:41 AM
 John DiFool Guest Join Date: Jun 2006 Location: Jacksonville, FL Posts: 18,108
As a teacher myself, just want to comment on the odd practice of flagging wrong answers with checks; I mark correct answers with checks (wrong ones are circled, or X'ed). I kept wondering why incorrect answers had checks next to them. Just an strange practice-carry on...
#33
05-15-2018, 12:28 PM
 pulykamell Charter Member Join Date: May 2000 Location: SW Side, Chicago Posts: 45,183
Quote:
 Originally Posted by CookingWithGas It also does not come across as negatively as a big-ass X.
I'm not sure about that. If you grew up with checkmarks meaning "wrong," they certainly come across as very negative. Nothing about checkmarks on a test seemed less negative to me than an "X." Some teachers even used green ink to mark papers, because they thought it was "friendlier" or something than red ink, but even with those teachers, green checkmarks were not a welcome sight. (Though, I think there is something to the reaction to the color. Green doesn't feel as aggressive as red to me, but check vs X makes no difference for myself. I might even go so far to say the check mark was more unfriendly looking to me, as they are big and sweeping off to the right. The teachers in college, at least, who used an X -- and there must have been some in high school, but I can't remember -- all made their "x"es fairly small and succinct.)

Last edited by pulykamell; 05-15-2018 at 12:30 PM.
#34
05-15-2018, 12:37 PM
 Yllaria Charter Member Join Date: Nov 2001 Location: Stockton Posts: 10,384
Quote:
 Originally Posted by jz78817 . . . are textbooks written by idiots?
Committees.
#35
05-15-2018, 12:42 PM
 DavidwithanR Guest Join Date: Feb 2018 Posts: 3,691
I think the real problem is that you can only know the answers to this one after you know the mind of its creator. There is missing information that can't come from anywhere except very generous guessing or assumption-making.

The reason those answers are wrong is that the question is wrong.
#36
05-15-2018, 01:11 PM
 Thudlow Boink Charter Member Join Date: May 2000 Location: Lincoln, IL Posts: 25,600
Quote:
 Originally Posted by DavidwithanR I think the real problem is that you can only know the answers to this one after you know the mind of its creator. There is missing information that can't come from anywhere except very generous guessing or assumption-making.
At the bottom, it says "Use with pages 336–337." Presumably those pages provide the necessary context? I agree that it makes a difference whether you've seen these kinds of exercises before; but if you're familiar with the genre, these particular ones aren't all that difficult.
#37
05-15-2018, 01:18 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by enalzi "They've never been in my kitchen."
I tried to make that joke yesterday, but it did not work with the numbers. I...see you just went for it anyway.

Quote:
 Originally Posted by DavidwithanR I think the real problem is that you can only know the answers to this one after you know the mind of its creator. There is missing information that can't come from anywhere except very generous guessing or assumption-making. The reason those answers are wrong is that the question is wrong.
I think it is doable, but hard for a little third grade mind. My daughter is not an "F" student by any means. She ranks herself third in intelligence in the class. Yes, she's figured out where the other kids are in relation to her. Both kids who never get re-dos got re-dos on this one.
#38
05-15-2018, 04:48 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 79,047
pulykamell, that's exactly what I was going to say. Red Xs are intimidating precisely because they mark wrong answers. Any symbol you use instead is going to cause just as much stress.
#39
05-15-2018, 05:05 PM
 BigT Guest Join Date: Aug 2008 Location: "Hicksville", Ark. Posts: 34,932
Quote:
 Originally Posted by pulykamell No, it's confusing.
Yes, but only because I apparently was unclear. I meant in the first set, where it asks how many squares are in the picture. There are 4, but the teacher has marked that answer incorrect. (This is question number 2).

Based on what Mr. Floppy and Doug K said, it looks like the teacher didn't even look at the answer sheet, as it clearly said that "4 squares" was the correct answer.
__________________
sig for testing purposes only

Last edited by BigT; 05-15-2018 at 05:08 PM.
#40
05-15-2018, 05:08 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by BigT So it looks like the teacher didn't even look at the answer sheet if the answer sheet said 4 was the correct answer.
We had erased the original answers and written in new ones. Her check-marks remained.
#41
05-15-2018, 06:12 PM
 pulykamell Charter Member Join Date: May 2000 Location: SW Side, Chicago Posts: 45,183
Quote:
 Originally Posted by BigT Yes, but only because I apparently was unclear. I meant in the first set, where it asks how many squares are in the picture. There are 4, but the teacher has marked that answer incorrect. (This is question number 2).
Oh, duh. Yes, that one should be 4.
#42
05-15-2018, 07:06 PM
 elfkin477 Member Join Date: Apr 2001 Location: NH Posts: 22,373
Wait. Are there 25 or 26 squares? There are 25 little squares but they are all inside a large square too.
#43
05-15-2018, 07:47 PM
 pulykamell Charter Member Join Date: May 2000 Location: SW Side, Chicago Posts: 45,183
Quote:
 Originally Posted by elfkin477 Wait. Are there 25 or 26 squares? There are 25 little squares but they are all inside a large square too.
There are 55 squares. There are 25 "one-unit" (1x1) squares. I suppose you can argue that the whole big square is a "one-unit" square, if you wanted to.
#44
05-15-2018, 08:50 PM
 Wallaby Guest Join Date: Jan 2013 Location: Melbourne, Far South Posts: 785
I find this very hard to take seriously as a 'test'. As has been discussed, the questions are ill-phrased, and the marking seems erratic.

Certainly the 'outside square' in each diagram should be included. The 'outside boundary' is used as a border in many of the squares and triangles allowed, so I see no reason why a square made up entirely of outside boundary borders would be excluded.

The question 'What do you notice about all these numbers' does not make it clear that we are only talking about answers 6,7, and 8. I spent some time struggling with that answer, because the correct answers to #4 and #5 are not squares.

Methinks a teacher has gotten a bit lazy and cribbed from '1000 Amazing Math Puzzles to Waste Hours On!'.
#45
05-16-2018, 07:12 AM
 Colophon Guest Join Date: Sep 2002 Location: Hampshire, England Posts: 13,448
What the hell is this crazy idea of ticking wrong answers? No wonder nobody can learn anything.
#46
05-16-2018, 07:54 AM
 Doug K. Guest Join Date: Jul 1999 Location: Hutchinson, KS Posts: 3,626
What bizarro world do some people live in where checking the wrong answers is considered unusual? That's how it's always been done.
#47
05-16-2018, 08:11 AM
 Jasmine Member Join Date: Jul 1999 Location: Chicagoland Posts: 1,301
Our firewall black listed your kid's homework site! Down with homework! LOL
__________________
"The greatest obstacle to discovery is not ignorance -- it is the illusion of knowledge."
--Daniel J Boorstin
#48
05-16-2018, 12:52 PM
 griffin1977 Guest Join Date: Feb 2006 Posts: 3,009
Quote:
 Originally Posted by Colophon What the hell is this crazy idea of ticking wrong answers? No wonder nobody can learn anything.
Seriously though what is the deal with that? Before this thread (and the previous one) it would never have crossed my mind that check mark* would mean anything else but "correct" (it even signifies that in computer user interfaces).

Is there a particular tradition or nationality where a check mark indicated something is wrong or incorrect?

* - I would call it a tick but I guess that is a Britishism? (I've been in the US for 15 year and still discovering words the American say wrong )
#49
05-16-2018, 01:18 PM
 Mahaloth Charter Member Join Date: Apr 2000 Location: 地球 Posts: 28,800
Quote:
 Originally Posted by griffin1977 Seriously though what is the deal with that? Before this thread (and the previous one) it would never have crossed my mind that check mark* would mean anything else but "correct" (it even signifies that in computer user interfaces). Is there a particular tradition or nationality where a check mark indicated something is wrong or incorrect? * - I would call it a tick but I guess that is a Britishism? (I've been in the US for 15 year and still discovering words the American say wrong )
American here. American teacher here, actually. X for me is always wrong. Check means "OK". I don't really do checks next to right answers, though.
#50
05-16-2018, 02:48 PM
 Doug K. Guest Join Date: Jul 1999 Location: Hutchinson, KS Posts: 3,626
Quote:
 Originally Posted by griffin1977 Seriously though what is the deal with that? Before this thread (and the previous one) it would never have crossed my mind that check mark* would mean anything else but "correct" (it even signifies that in computer user interfaces). Is there a particular tradition or nationality where a check mark indicated something is wrong or incorrect? * - I would call it a tick but I guess that is a Britishism? (I've been in the US for 15 year and still discovering words the American say wrong )
Quote:
 Originally Posted by Mahaloth American here. American teacher here, actually. X for me is always wrong. Check means "OK". I don't really do checks next to right answers, though.
Right answers don't get marked. Wrong answers are usually marked with a checkmark, but could also be an 'X' or a slash through the question number. I've never seen a teacher put check marks next to correct answers. A perfect paper should be "clean" except for the score at the top.

American former student, current teacher's spouse and current para.

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