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Old 05-14-2018, 06:03 PM
Mahaloth Mahaloth is offline
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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.
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Old 05-14-2018, 06:08 PM
Mithras Mithras is offline
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The answers are 25, 16, 9, and 4. All square numbers because you're counting squares within a square.
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Old 05-14-2018, 06:08 PM
ElvisL1ves ElvisL1ves is offline
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25, 4, and 9 are all square numbers.
  #4  
Old 05-14-2018, 06:30 PM
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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?
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Old 05-14-2018, 06:35 PM
Mahaloth Mahaloth is offline
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What answers did you eventually get?
The ones written in now on the sheet. Are we wrong?
  #6  
Old 05-14-2018, 06:40 PM
Joey P Joey P is online now
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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  
Old 05-14-2018, 06:47 PM
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The ones written in now on the sheet. Are we wrong?
I count 36 triangles.
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Old 05-14-2018, 06:48 PM
Aspidistra Aspidistra is online now
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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.
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Old 05-14-2018, 06:48 PM
griffin1977 griffin1977 is offline
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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  
Old 05-14-2018, 06:52 PM
Tired and Cranky Tired and Cranky is offline
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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.
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Old 05-14-2018, 06:59 PM
MrFloppy MrFloppy is offline
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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  
Old 05-14-2018, 07:04 PM
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I count 36 triangles.
I also got 36, and a headache.
  #13  
Old 05-14-2018, 07:04 PM
Aspidistra Aspidistra is online now
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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?
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Old 05-14-2018, 07:06 PM
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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.
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Old 05-14-2018, 07:07 PM
Mahaloth Mahaloth is offline
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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.
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Old 05-14-2018, 07:07 PM
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Originally Posted by Tired and Cranky View Post
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. Its stressful when one wrong answer screws up your answers to the next several problems especially, as you say, shes basing her work off of a false assumption. The killer is when she actually shows the original work.
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Old 05-14-2018, 07:11 PM
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... 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  
Old 05-14-2018, 07:29 PM
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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  
Old 05-14-2018, 07:36 PM
jz78817 jz78817 is online now
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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  
Old 05-14-2018, 07:49 PM
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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  
Old 05-14-2018, 07:55 PM
pulykamell pulykamell is online now
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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  
Old 05-14-2018, 07:55 PM
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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  
Old 05-14-2018, 08:21 PM
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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  
Old 05-14-2018, 08:29 PM
Mahaloth Mahaloth is offline
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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.
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Old 05-15-2018, 01:34 AM
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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  
Old 05-15-2018, 06:34 AM
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I noticed the eiganvalues are 1 and -1 ... which is redundant but the teacher may not know that ...
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Old 05-15-2018, 06:43 AM
pulykamell pulykamell is online now
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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  
Old 05-15-2018, 07:10 AM
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- 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.
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Old 05-15-2018, 07:36 AM
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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  
Old 05-15-2018, 11:31 AM
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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.
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Old 05-15-2018, 11:38 AM
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Originally Posted by Mean Mr. Mustard View Post
"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  
Old 05-15-2018, 11:41 AM
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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...
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Old 05-15-2018, 12:28 PM
pulykamell pulykamell is online now
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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  
Old 05-15-2018, 12:37 PM
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. . . are textbooks written by idiots?
Committees.
  #35  
Old 05-15-2018, 12:42 PM
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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  
Old 05-15-2018, 01:11 PM
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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 336337." 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.
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Old 05-15-2018, 01:18 PM
Mahaloth Mahaloth is offline
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"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 View Post
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.
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Old 05-15-2018, 04:48 PM
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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.
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Old 05-15-2018, 05:05 PM
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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.
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Old 05-15-2018, 05:08 PM
Mahaloth Mahaloth is offline
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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.
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Old 05-15-2018, 06:12 PM
pulykamell pulykamell is online now
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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.
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Old 05-15-2018, 07:06 PM
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Wait. Are there 25 or 26 squares? There are 25 little squares but they are all inside a large square too.
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Old 05-15-2018, 07:47 PM
pulykamell pulykamell is online now
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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.
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Old 05-15-2018, 08:50 PM
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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!'.
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Old 05-16-2018, 07:12 AM
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What the hell is this crazy idea of ticking wrong answers? No wonder nobody can learn anything.
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Old 05-16-2018, 07:54 AM
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What bizarro world do some people live in where checking the wrong answers is considered unusual? That's how it's always been done.
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Old 05-16-2018, 08:11 AM
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Our firewall black listed your kid's homework site! Down with homework! LOL
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Old 05-16-2018, 12:52 PM
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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 )
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Old 05-16-2018, 01:18 PM
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Originally Posted by griffin1977 View Post
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.
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Old 05-16-2018, 02:48 PM
Doug K. Doug K. is offline
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Quote:
Originally Posted by griffin1977 View Post
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 View Post
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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