ATOT, are you smarter than my 3rd grader?

[TecHNooB]

Using division...

row 2 is 2 pets and 2 owners...2/2=1
row 4 is 4 pets and 2 owners...4/2=2
row 6 is 9 pets and 3 owners...9/3=3 or 6 pets and 2 owners...6/2=3

Your own pattern scheme has multiple answers. How is that a pattern.

 

[corwin]

Your own pattern scheme has multiple answers. How is that a pattern.

That's pretty much been the consensus, there is no definitive pattern in the question...that was just showing a possible way to have the "correct" answer be 3 and 3

 

[zinfamous]

That's pretty much been the consensus, there is no definitive pattern in the question...that was just showing a possible way to have the "correct" answer be 3 and 3

If that's the case, then the consensus that believe the question is poorly-worded must have failed simple word problems on a regular basis:

Jane wishes to organize a pet parade. Every row in the parade will have some combination of owners and pets. In the 1st row, Jane puts 1 owner and 1 pet. In the 2nd row, Jane puts 2 owners with 1 pet each. In the 3rd row, Jane puts 1 owner with 2 pets. In the 4th row, Jane puts 2 owners with 2 pets each. In the 5th row, Jane puts 1 owner with 3 pets. If the pattern continues, how many owners and pets will there be in the 6th row

In the rows with multiple owners, it very clearly says that each owner has a complement of pets. 1 pet each = 2 pets; 2 pets each = 4 pets, etc.

Now, It seems to me that there is enough of a pattern to assume that it only goes from 1 to 2 to 1 to 2 owners in each row; so I don't see much of a reason to argue that the 6th row would suddenly jump to 3 owners after a row with 1 owner, based on the wording of the problem.

 

[Squisher]

pics of the teacher?

 

[vshah]

pics of the teacher?

squisher comes through for ATOT

 

[D1gger]

That's pretty much been the consensus, there is no definitive pattern in the question...that was just showing a possible way to have the "correct" answer be 3 and 3

You only came to that conclusion by ignoring rows 1, 3, 5.

 

[Krazy4Real]

The teacher should quit.

 

[corwin]

You only came to that conclusion by ignoring rows 1, 3, 5.

I don't think so...

row 1 is 1 pet and 1 owner...1/1=1
row 2 is 2 pets and 2 owners...2/2=1
row 3 is 2 pets and 1 owner...2/1=2
row 4 is 4 pets and 2 owners...4/2=2
row 5 is 3 pets and 1 owner...3/1=3
row 6 is 9 pets and 3 owners...9/3=3 or 6 pets and 2 owners...6/2=3

Still both options are correct for row 6

 

[SagaLore]

1 1
2 1
1 2
2 2
1 3
---
2 3 <-- The first column is just toggling back and forth between 1 and 2, while the second column increments by one after every second (even) row.

 

[DrPizza]

not hard. you never specified the regions had to be equal in area.

What do you mean "not hard?" You're right I never specified the regions had to be equal in area. I don't care if the regions are equal in area. If you put 6 points on the perimeter of a circle and connect those points by drawing in chords, it's not "hard" to get 32 separate regions - it's *impossible.* Every time you draw a chord, the number of regions increases by 1. Every time two chords cross, the number of regions increases by 1. It takes 2 points to make a chord, and 4 points to create two chords that intersect inside the circle. Therefore, with 6 points, the number of regions = 1 + 6C2 + 6C4 = 1 + 15 + 15 = 31.

Thus, I assign a homework assignment that is impossible to succeed at.

 

[MotionMan]

Thus, I assign a homework assignment that is impossible to succeed at.

How old are your students?

MotionMan

 

[Narse]

1 1
2 1
1 2
2 2
1 3
---
2 3 <-- The first column is just toggling back and forth between 1 and 2, while the second column increments by one after every second (even) row.

This, it is the simplest pattern. Teacher is wrong IMO

 

[DrPizza]

Alternative solution to the OP:

5


Yes, five. Go ahead and search the online encyclopedia of integer sequences 🙂

 

[DrPizza]

How old are your students?

MotionMan

The ones that I assign that homework problem to are generally advanced juniors or seniors in high school. There are a few reasons for that assignment. One is that no teacher has ever given them an impossible task before. Two, I use it to get students to start turning on their thinking, rather than just following specified algorithms for solving problems - up to pre-calculus, it's usually "do it like this . Do these problems like this" With very little room for creativity. It's tough to turn creativity on in older students. Usually, by the time they get to high school, that creativity they had when they were young has been extinguished. Incidentally, when I assign that problem, it's the only problem I assign that night. Further, I tell the students that "if you don't succeed, feel free to give up after about 15 minutes."

Back closer to the topic at hand - I've known very few elementary teachers who were very knowledgeable about science and math. Now, I don't mean to put them down - there's no way in hell that I could handle a couple dozen little kids for that duration. I'd go nuts trying. I did know one elementary teacher who was good at science though - she dual-majored in physics. (Weird dual major; I suspect that by now, she's been shoved into the role of physics teacher in whichever district she's working.)

 

[DaTT]

They way I see it is, as you said earlier, the teacher probably just followed the answer key. But I would imagine that there is a typo in the either the problem, or the solution. Your daughters answer seems to be correct.

 

[Mr. Pedantic]

Alternative solution to the OP:

5


Yes, five. Go ahead and search the online encyclopedia of integer sequences 🙂

This is the dumbest thing about sequences like this; the next number could be any number I bloody well want.

In my experience elementary school teachers don't like to admit they've been bested by a child.

How is it possible to become a primary teacher if you don't admit they can teach you things? Like all other teacher-student relationships, the flow of information goes both ways. Of course, it depends on expertise - if I did a Masters in maths, I wouldn't want to have a maths mistake pointed out by a primary school kid either. But who does a Masters in maths and then teaches 5-11 year olds?

Depends what their interest is. I know someone who likes kids, so she's a kindergarten teacher. She's not overly passionate about things like math or science. Other people teach because they like teaching. I don't really like most people, but I could see myself teaching math and science. My high school chem teacher really seemed to like chemistry and explaining chemistry.

Note that none of this changes the fact that primary school teachers generally don't know shit, and don't need to know shit. Whether they became primary teachers because they sucked at other stuff, or they suck at other stuff because they became primary teachers, doesn't really matter.

 

[JujuFish]

I don't think so...

row 1 is 1 pet and 1 owner...1/1=1
row 2 is 2 pets and 2 owners...2/2=1
row 3 is 2 pets and 1 owner...2/1=2
row 4 is 4 pets and 2 owners...4/2=2
row 5 is 3 pets and 1 owner...3/1=3
row 6 is 9 pets and 3 owners...9/3=3 or 6 pets and 2 owners...6/2=3

Still both options are correct for row 6

You do realize that this isn't an example of 3 owners, don't you? All your division says is that there are 3 pets per owner in the 6th row, something no one has argued in this thread.

 

[eLiu]

row,owners,pets
1,1,1
2,2,1
3,1,2
4,2,2
5,1,3
6,?,?

My first guess is 3,1, but now that I lay it out - 2,3 makes the most logical sense. Teachers answer does not. I'm onboard the teacher is a moron club.

I liked 3,1 as well but could also see 2,3. The 2,3 reasoning has been covered in this thread. For 3,1: we've had 1,1; 2,1; 1,2; 2,2; 3,1 so far. So we had every combination of two 1s (1,1) & every combo using a 2 & a 1 (2,1; 1,2; 2,2). So next up could be every combo using a 3 and a 1 (3,1; 1,3; 3,3, following the pattern set up by the 2 & 1).

I didn't come up w/3,3 on my own but that is valid too. In the 2nd column, we've had "1,2,1,2,1" so far. In the 3rd column, we've had "1,1,2,2,3" so far. In the 3rd column, it seems like the next number could be 3 (then 4,4,5,5,etc). In the first column, it could be something like "1,2,1,2,1,3,1,3,1,3" (teacher's soln) or it could be "1,2,1,2,1,2,1,2,..." (daughter's soln).

Basically a lot of these 'find the pattern' kinds of questions have more than one answer. I'm sure if you tried, you could come up with some goofy 2 or 3 (or more) term recurrence that is satisfied by the numbers we have right now, and then gets something "crazy" (like 4,7) for the next row.

 

[DrPizza]

How is it possible to become a primary teacher if you don't admit they can teach you things? Like all other teacher-student relationships, the flow of information goes both ways. Of course, it depends on expertise - if I did a Masters in maths, I wouldn't want to have a maths mistake pointed out by a primary school kid either. But who does a Masters in maths and then teaches 5-11 year olds?

Just yesterday, I said, "is that calculator buttons I hear?" We were finding the minimum and maximum value of x + 1/x over the interval [.5, 1.5] "You're not using a calculator for 1+1, are you? Or 1/2 + 2?? Are you using the calculator for 2/3 + 3/2?" Meanwhile I added 4 and 9 in my head (while adding 2/3 and 3/2) and wrote 11/6 on the board. I shouldn't have been talking. 🙂

 

[gothamhunter]

I liked 3,1 as well but could also see 2,3. The 2,3 reasoning has been covered in this thread. For 3,1: we've had 1,1; 2,1; 1,2; 2,2; 3,1 so far. So we had every combination of two 1s (1,1) & every combo using a 2 & a 1 (2,1; 1,2; 2,2). So next up could be every combo using a 3 and a 1 (3,1; 1,3; 3,3, following the pattern set up by the 2 & 1).

I didn't come up w/3,3 on my own but that is valid too. In the 2nd column, we've had "1,2,1,2,1" so far. In the 3rd column, we've had "1,1,2,2,3" so far. In the 3rd column, it seems like the next number could be 3 (then 4,4,5,5,etc). In the first column, it could be something like "1,2,1,2,1,3,1,3,1,3" (teacher's soln) or it could be "1,2,1,2,1,2,1,2,..." (daughter's soln).

Basically a lot of these 'find the pattern' kinds of questions have more than one answer. I'm sure if you tried, you could come up with some goofy 2 or 3 (or more) term recurrence that is satisfied by the numbers we have right now, and then gets something "crazy" (like 4,7) for the next row.

Seriously, what the hell? If you look at the full God Damn pattern, 3,1 and 3,3 make no fucking sense.

1,2,1,2,1 - what comes next? A FUCKING 2
1,1,2,2,3 - what comes next? A FUCKING 3

FUCKING 2, 3

/THREAD

GOD DAMN IT

 

[Rhoxed]

could also be 2 owners 4 pets each

it you look, row 2 to 4 doubles - so does 1 to 3, but 5 cancels the double theory and leaves it at +1, but row 2 to 4 is up in the air whether it is doubled or just +1

so imo correct answers would be either
2 owners 3 pets each, or
2 owners 4 pets each.

op/op op/opp/opp opp/oppp/oppp oppp or
op/op op/opp/opp opp/oppp/opppp opppp


wow so i asked my gf.... she made the teachers answer make sense
O,P (Owners,Pets each
1,1
2,1
1,2
2,2
1,3
3,3
1,4
4,4
1,5
5,5

 

[gothamhunter]

could also be 2 owners 4 pets each

it you look, row 2 to 4 doubles - so does 1 to 3, but 5 cancels the double theory and leaves it at +1, but row 2 to 4 is up in the air whether it is doubled or just +1

so imo correct answers would be either
2 owners 3 pets each, or
2 owners 4 pets each.

op/op op/opp/opp opp/oppp/oppp oppp or
op/op op/opp/opp opp/oppp/opppp opppp

THEN IT OBVIOUSLY CANNOT BE 2,4.

caps

 

[corwin]

You do realize that this isn't an example of 3 owners, don't you? All your division says is that there are 3 pets per owner in the 6th row, something no one has argued in this thread.

I'm not sure you can read...

The "simplest" answer IS 2 owners with 3 pets each but it's not the ONLY answer

 

[Rhoxed]

THEN IT OBVIOUSLY CANNOT BE 2,4.

caps

it you look, row 2 to 4 doubles - so does 1 to 3, but 5 cancels the double theory and leaves it at +1, but row 2 to 4 is up in the air whether it is doubled or just +1

miss that part? - this sequence is too open to give a *right* answer.


but as i edited in my last post... the teacher was right... sadly my g/f knew this

 

[iCyborg]

http://blog.tanyakhovanova.com/?p=84

This sums it up nicely for me (and others here claiming there's more than one correct answer). The author has Ph.D. in math and won gold medal at math olympiad in high school...