Third grade division=fail

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Jackslap

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I have a daughter in 3rd grade. Her homework tonight has several questions that I believe to be incomplete or utterly wrong. I would love to see how the great state of CA expects these to be answered, but I cannot find an answer key online, only a home study guide. The homework is Houghton Mifflin 3rd grade chapter 13 lesson 4 "Dividing by 9". I am a perfectly functioning adult who can divide by 9, but I cannot figure out the wording of these questions. The questions surround a kid named Raul and his bookshelf. The information you need is the types of books he has and the amount of each. That information is as follows:

History 72
Art 81
Science 54
Travel 63
Fiction 90
Biography 45
Poetry 27
Cooking 36

Question 1
Raul might put an equal number of each kind of book on 9 shelves. How many types of books will have an even number on each shelf?
My attemtped answer = WTH are they asking?

Question 2
Raul considered combining two of the subjects and placing 9 books on each shelf. It would take 7 shelves to do this. What were the two subjects?
My attempted answer = Cooking and Poetry, but this was confusing as crap because you essentially just have to start adding random subjects together until you get two that equally add up to 63. It wasn't hard for me, but it was for her.

Question 3
How many books would Raul have to buy if he wanted to have 10 books on each shelf, no matter what the subject?
My attempted answer = WTH are they asking? How many shelves are there in this particular scenario? Why would he need to "buy" more books? He has plenty books to fit 10 books on 1 shelf, 2 shelves, 3, etc. He has 468 books total so he could only put up to 10 books per shelf for 46 shelves. How am I to know how many shelves they are wanting for this scenario? 9, 7 as in the previous two questions. In each previous question they have provided the number of shelves they wish for that scenario, but not this question.

Why is the state of CA TRYING to make math frustrating for my 8 year old. A conspiracy perhaps???????
 
Let's see how far we get.

There are 9 shelves.
There are 8 kinds of books.
We need an equal number of each kind of book on each shelf.

If we put just one different book on each shelf, we'll be one shelf short. We have one book of each kind on 8 shelves, but only zero (0) on the ninth shelf.

Start the book types over on the bottom shelf and when you fill the bottom shelf, wrap around to the top. After 8 more books, you should have 2 different books on each of the first 7 shelves, and one book each on shelves 8 and 9.

Do it again. After 8 more books, you'll have 3 different books on the first 6 shelves, and 2 each on 7, 8 and 9

Do it again. After 8 more books, you'll have 4 different books on the first 5 shelves, and 3 each on the last four.

Do it again...etc. Something magic will happen after the 9th attempt.

I must warn you, however, that this is a solution based on the exact wording you have provided. You did not say we had to use ALL the books, or even a large number of them. Since all the book counts are multiples of 9, I suspect I have stretched the limits of the intent.

I'm relatively sure they want you to divide each collection count by nine and put that many books on each of the 9 shelves. For history, 72/9 = 8, so put 8 (an even number) on each shelf. Now do art.

I would have to agree with your assesment of the problem. Get Raul to put his own books on the shelf. :wink:
 
Let me restate the fact that I did indeed give you the absolute amount of info that I was given. You have the exact text and phrasing of the questions. The questions are unrelated in nature, meaning that the outcome of one does not depend on the answer found in the previous. So I am curious about your answer when you say "Let's see how far we get" and then immediately get to "There are 9 shelves...." Which question are you reffering to? 1, 2, or 3?

In question 1 they tell us there are 9 shelves, but the rest of it makes no sense to me. In question 2 they tell us 7 shelves, but the rest makes no sense. But in question 3 they make no reference to any amount of shelves at all. It's almost like they are asking "what divided by what equals 4 (X/X=4)?" A ton of numbers divided by a ton of numbers can equal 4. How do I solve question 3 without knowing the amount of shelves they intend on me using?

Question 3 is exactly the way her paper says it. How many books to buy if he wants 10 on each shelf..............BUT HOW MANY SHELVES???? It could be an infinite number so I'll just say he needs to just keep buying books until he dies, and then that will be the answer to how many books he needed to buy. But once again, why buy any more than he already has. If they intend me to assume they mean 7 or 9 shelves, then he already has enough books to put 10 on each shelf. The question is stupid and is now making me hate math......
 
I sure agree that often (way too often!) teachers screw everything up by trying to make up a cute story
in order to teach something simple; often, more time is required by the students to "understand" WTH
the teacher means than doing the ACTUAL problem. This case is sure a good example!!

I've "put in" what I think is all that was required:

Jackslap said:
History 72
Art 81
Science 54
Travel 63
Fiction 90
Biography 45
Poetry 27
Cooking 36
============
TOTAL 468

INCLUDE the total: why have the poor kids do the addition (they're not learning how to add here!)

Question 1
> Raul might put an equal number of each kind of book on 9 shelves.
> How many types of books will have an even number on each shelf?

If you divide each type by 9, how many times will you get an even result?

Question 2
> Raul considered combining two of the subjects and placing 9 books on each shelf. It would take 7 shelves to do this.
> What were the two subjects?

Find the 2 subjects that add to 63.

Question 3
> How many books would Raul have to buy if he wanted to have 10 books on each shelf, no matter what the subject?

What is MINIMUM number of extra books required in order for total books to be divisible by 10?
Click to expand...
This kind of problem where a "story" has been "devised" then becomes strangely known as a "word problem".
Well, guess that's accurate: the problem is understanding the "words"!!
 
One objective of putting such problems for 3rd grade student would be - to identify "helping" parents. If your daughter could solve this problem - you might be tapped as a prospective volunteer for the next "math-olympics".
 


What am I missing here? Question (1) seems simple enough. All of the given book numbers are multiples of 9.

Divide the book numbers by 9; the quotients are either even or odd. Count the even quotients.

I mean, each shelf contains the following.

8 history books
9 art books
6 science books
7 travel books
10 fiction books
5 biography books
3 poetry books
4 cooking books

The even numbers above are 4, 6, 8, and 10.

Therefore, four types of books have an even number on each shelf.

By the way, there is no such thing as a perfectly-functioning adult.

 
@ mmm4444bot- Touche with the adult remark.

To you and to Khan I say thanks for clearing up number one for me. I see now what you guys mean and what the question is asking. So now my question is, since that was such a simple thing for you guys to come to, how come myself and my wife and my daughter couldn't see it? What was the mental block that we couldn't get over? Why didn't they just ask it more plainly to begin with? Something like, "if all the book totals are divided by 9, how many of those quotients are even numbers?" I just don't see the need to try and confuse kids, they are already intimidated enough with math, they already (a lot of them, I did) feel inferior and not good enough to do math. Why make it confusing instead of rewarding to solve the problems? The journey is so arduous sometimes that when the reward/result is finally acheived the kid just thinks "eh, that was dumb......am I done now, can I go out and play now?"

Question 2 you'll recall I did figure out on my own eventually, but it sure took some roundabout thinking for me to get to that one as well.

Question 3 Khan I still don't understand your explanation. You (like the question) are suggesting that some extra books are needed here. I don't see why extra books are needed if the kid has 468 and an undetermined amount of shelves. When considering your solution are you assuming a certain amount of shelves? Because the question does not specify the shelf count in this scenario.
My understanding of what they are asking is this:

Raul has 468 books, he has a book shelf to put them on. How many books MORE than 468 would he need to buy in order to fit 10 on each shelf? I then cannot solve the question because I don't know how many shelves are on the book shelf in this scenario. End of discussion until I can find out how many shelves they intend on me filling.

Another example of how I understand it. Let's say that the bookshelf only has one shelf. Then Raul wouldn't need to purchase anymore books to put 10 books on 1 shelf. He has plenty to do that with. He'll then have 458 books leftover with no place to put them, but that one shelf will certainly have 10 on it. If the bookshelf has 2 shelves then he can easily fill both of those as well, but he'll have 448 books leftover. And so on in continues until he gets to a 46 shelf bookcase, in which case he no longer has enough books to put 10 on each shelf. After that he'd need to buy extra books to fill the extra shelves, but since the question provides no limit on the shelf count, then the answer is he needs to buy an infinite amount of more books to fill his infinite bookshelf.

I know I'm still failing to understand that question somehow. Where am I going off track with it?
 
Jackslap said:
how come myself and my wife … couldn't see it?

Your neural networks are already "gelled".


What was the mental block that we couldn't get over?

This is a rhetorical question.


Why didn't they just ask … "if all the book totals are divided by 9, how many of those quotients are even numbers?"

That would be tantamount to leading your daughter by the hand. The answer here is unimportant, in my judgment; the mental exertion involved is primary, with this type of exercise, and this exhertion comes from considering the given logical terminology, reasoning about the scenario, and forming a strategy.

Mathematics, and why students are put into positions of puzzling over it, has to do with so much more than arithmetic.

Further, medical science shows that intense mental exertion in young people leads to neural pruning which produces efficiencies in the brain. I mean, exercising the mind causes physical connections in the brain to disconnect from one another and rearrange themselves into new networks with greatly increased associative capabilities.

Doing that can only serve to increase things like insight, spacial aptitude, linear thinking, quantitative analysis, and symbolic reasoning (to name a few). These things are all soon approaching, for your daughter. You want her brain to be as prepared as possible.

To make a long story short, these types of exercises are designed to force your daughter to think -- intensively, if need be.

If her instructors do the majority of her thinking for her by practically handing over the answers, her brain will end up like yours. :wink:

As to the question, "Can I go out and play now?", that's a rhetorical, too, because the appropriate answer is obvious.
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When I saw all the controversy over this question, I decided to find out how I thought a student might approach it. So, I drew a sketch of a 9 shelved bookcase and wrote the type of books across the top. I then started doling out books. For #1, since I needed an equal number of each type on each shelf, it was easy to see that each shelf contained 8 Hist, 9 Art, 6 Science, etc. It wants to know how many types have an even number on each shelf. My answer is 4. There are four types having an even number of books on each shelf, namely, Hist, Science, Fict, and Cooking.

For #2 I assumed we are still dealing with 9 shelves. Nine shelves with 7 books on each shelf means we need 9 X 7 = 63 books. The only two types that add to 63 are Poetry and Cooking. So, that's my answer.

For #3, Assuming we are still dealing with 9 shelves, I had to reread the question. It reads "How many books would Raul have to buy if he wanted to have 10 books on each shelf, no matter what the subject?" My interpretation is that he doesn't "own" the original mentioned books. (they must belong to the school.) So he has to buy 90 books. If he already owns all those books, then he would not have to buy any.

I agree with you. It is confusing. And to think it is going to get worse. After all, when state budgets get tight, the money allocated to education is slashed. Possibly the person(s) responsible for making up these questions went into teaching because they weren't good enough to pursue a more demanding profession that offers a higher salary. As a side note, I feel qualified to make these remarks, having spent 42 years in education from the junior high level through the community college level, in classroom, counseling and administration, about 7/8 of it in the classroom. Further, I was commissioned to write problems for the state of Florida's statewide test. That was followed up by the company supervising the gathering of problems, asking me to do some more for the state of Ohio. The next summer, I was asked to do some more for their archive but I was pooped, so declined. But, none of my problems were this contrived or convoluted. I also agree with a person above who says the reason for these types of problems is to make the student think. In my opinion, the purpose of education is to teach us how to learn (and to think in so doing), not to get the answer on the answer key.
 
Forgot to check this post for a few days, sorry.

mmmmbot guy/gal, I had a response typed out regarding your last non helpful post. But my wife laughed at it, called you a troll and told me not to respond to you because you are obviously waiting for it.

To Loren, I say thanks for the time you may have put into your thoughts but you still have assumed as many others have that the questions refers to 9 shelves. That was never specified in the instructions, the previous questions, or the wording of the problem itslef. In fact, on the page itself there are other questions which refer to the bookshelf as having a different number of shelves, more or less than nine. So it is not possible to assume that 9 shelves was implied for this question based on that fact. I just don't see how this made it past some proofreading by the state. The question is incomplete. Might as well be asking 2+X= What? Infinite possibilities. Thanks for sharing your experience about writing questions for the state and your thoughts about the quality of individual who may have written such a nonsensical question. I'd love to create an image of the page for you so you could see it. Perhaps that will be a possibility after Christmas break is over and she gets the graded paper back.
 
SO SO we have a badly worded problem.
We adults(?) arguing won't help anything.
 
Jackslap said:
@ mmm4444bot- Touche with the adult remark.


Question 3 Khan I still don't understand your explanation.

I believe you have me mistaken for somebody else. My statement was:

One objective of putting such problems for 3rd grade student would be - to identify "helping" parents. If your daughter could solve this problem - you might be tapped as a prospective volunteer for the next "math-olympics".
Click to expand...

By the way, Mark (mmm444bot) is a highly respected contributor to this forum. I suggest you practice reading carefully .....
Click to expand...
 
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