8 votes

Any teachers in the house?

We home school our 10 year old, however, due to financial restraints, have been forced to use a Charter School online school and it's curriculum. Common Core started this year and we've been affected. FYI, we do plan to switch next year to Dr. Paul's curriculum which begins at 6th grade. At any rate, she is required to submit a monthly math work sample based on a problem submitted by the school. She has been on Fall break this past week and here is the monthly problem she found this morning:

There are 2 parts to this math question for a total of 15 points. In order to get full credit you need to answer both parts. (Show your work!!!!)

At school in Ms. Davidson's 5th grade class, 18/28 of the class was wearing shorts. 4/5 of the class was girls.

1. What fraction of all the students was girls who was wearing shorts? (10 points)

2. Explain in 3-5 sentences how you solved your answer. (5 points)


After completing her daily Kumon work, Simultaneous Linear Equations with 3 and 4 Variables, she headed upstairs to work this problem. About 15 minutes later, she came downstairs crying.

I have already sent a message to her teacher that she will not be completing this problem and if future math sample problems are as ridiculous as this one, she will not be completing those either. She has been a straight A, honor roll student since first grade.

I was so ticked this morning when I originally wrote the post, which was only questioning the grammatical correctness of the narrative, but then deleted it.

Anyway, I was just looking for some comfort. There are so many things wrong with this problem, I was just seeking conformation from an educator.

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Perhaps I can't give you an answer you will like. I can offer some suggestions and indicate what I would do.

I would first ask my daughter: "Why are you crying?" That, to me, would be an important thing to figure out.

If the answer has something to do with not being able to figure the problem out, then I would say something like: "Don't worry. I'm sure we can figure something out."

What does it mean that 18/28 of the class was wearing shorts? (Wait for answer.) If she can't answer, then there is a place to start. It means that if there are 28 students in the class, then 18 of them are wearing shorts. If there are 56 students in the class, then 36 of them are wearing shorts. If there are 84 students in the class, then how many of them are wearing shorts?

84 students would be a big class wouldn't it. We wouldn't expect there to be that many students, but maybe it's possible.

Notice that the numbers could get smaller too: There could be 14 students in the class. Then how many would be wearing shorts? (9)

But we couldn't have 7 students. Why? (That would mean there were 4 and a half students wearing shorts, and half students tend to make the classroom too bloody.)

So it looks like 14 is about as low as it could go. (Explain why if possible giving a discussion of common factors and reducing fractions.)

But now, what does it mean that 4/5 are girls? Well, if you think about it, that means the number of students must be divisible by 5. (It would have to be a number like 5, 10, 15, 20,...) And that means (since there are no factors of 5 in 14) that the smallest possible number of students in the class is 5 times 14 or 70 students. That's also a big class, but maybe there are some classes that big somewhere.

So let's say there are 70 students. Then how many are wearing shorts. That would be (9/14)(70) = 45. How many girls? (4/5)(70) = 56.

4/5 are girls? Why so many girls? Anyway.

We still don't know how many girls are wearing shorts do we? We've satisfied all conditions that are given in the problem and we know we can have 45 students wearing shorts and 56 girls in a class of 70 students.

I guess, we could have the 45 kids in shorts include any number of girls from 31 (that would be if all 14 boys are wearing shorts) to 45 (no boys wearing shorts). (That is assuming we had 70 students. Of course, we don't really know that we don't have more---like 140---students.)

This is kind of a silly problem isn't it? But it can be understood without too much trouble can't it?

Also, whoever wrote this problem does not know how to express himself in correct English. Here's why...

Anyway, that's the way it would go in my house. I can say that as a result, all of my children would be able to take such a problem and give the solution/discussion I've given above. The youngest is 11 which is a bit older than yours. I can imagine that at 9, she might have gotten frustrated and not been able to get all of it, but she was pretty good with fractions by 9.

I wouldn't be too quick to write off word problems or feel that young children can't think about such things. It takes some patience. There are a lot of exceedingly stupid people in the world, and presumably some are not worth wasting time on. Nevertheless, it is sometimes a good exercise to try to understand what people are saying and if what they are saying makes any sense. I guess usually it doesn't. But that's also something worth learning.

There are too many loose ends here

in the way the problem is stated to think that one could come up with a correct answer. However, not to defend the teacher, but... what *might* clear things up some is the TOPIC of the unit in which this problem appeared. That is, the CONTEXT. It could be solved in a few different ways - as a probability, as an estimation, or (as an engineer below explained) as a range of answers for each of, theoretically, an infinite number of class sizes in multiples of 140 (so as to prevent an answer that would involve a partial human being).

IF it is part of a unit where it would be understood what is expected (because the class had learned how to solve such a question in a particular way and had practiced with other similar problems), that would be one thing. If not, it's bad teaching, a poorly-designed math problem, and not fair to the student. P.S. There is no excuse for the poor grammar that only made a confusing situation worse.

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.
~ John Muir

Hi Mdefarge...

Thank you for your reply. This fifth grade class has just started learning basic fractions. Nothing other than the basic fraction equation of 28 x 0.80 has been taught to these kids.

Get outta here! That's ridiculous!

I'm so sorry, Kinsjon. Oh, man. I'm laughing, but it's really not funny. It's pathetic. I feel so badly for your daughter. Here she's just starting to learn basic fractions, and... adults - including teachers, engineers, and others with some sort of math background - are confused by the problem. All I can say is, it's really not even a matter of Core Curriculum. It's public school and teacher training. I just hope that you were able to reassure your daughter that it's "not her."

Seriously, it warrants bringing it up at a school board meeting. I'd make a couple dozen copies of that problem - just as you had it here - to give to board members and other interested parties in attendance, asking a) how the school district could have invested in curriculum materials in line with Core Curriculum standards that could be so unprofessionally planned - inappropriate in terms of the content (an undecipherable problem with the data provided) and modeling improper basic English grammar; and b) how the district had prepared its teachers to be teaching the curriculum. I'd say that you weren't blaming the teacher but whoever approved the curriculum and expected teachers to not use their better judgment but just follow it. Grrr. Good luck.

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.
~ John Muir

Hey mdefarge...

Couldn't have said it better myself.

Just let me clarify one more time. Emily is an amazing child and awesome student. She has attended Kumon for math since first grade and has received awards for her achievements. She currently ranks 864 out 43,334 age appropriate Kumon students nationwide. We use the public school curriculum out of necessity and it does provide us structure at home. Over the past 4 years at Kumon she has completed over 100,000 analytical equations starting with addition and moving forward to where she is now. I doubt she has done 500 in school. She is now working linear equations with multiple variables. Here is an example from Khan academy:


The school math is something we simply go through the motions as she's way beyond what is being taught. It is so inferior and pathetic and you really hit the nail on the head. I posted the common core example to illicit comments and discussion. Emily's only source of frustration in school is story problems in math. But, when the day comes where her little mind understands logic, she'll have the tools to work the problems. Right now our focus is and has been giving her a solid foundation of the basics of mathematics.

I feel so sorry for kids, and their parents, who attend public school.

While I'm at it, Emily is also a wonderful little musician and I've posted her video's her before, but I'll post her channel again....yes, we're very proud of her.


As I stated, we've moved on from this, but I want to Thank all of you who imputed and participated in the discussion. I did get what I came her for with this issue. Thanks again.

I won’t address the answer to

I won’t address the answer to the math problem, but rather why I believe the problem is worded the way it is. I am finishing up my Masters in Secondary Education at Texas A & M this semester and have taught at a private Christian school in the past. I only plan on teaching as a backup plan since I have a job right now. My wife taught for six years in the same private school and she now stays at home and homeschools our three boys.

In public education today and in Charter Schools there is a move across schools nationwide whether using common core or not to try and get students to think more, rather than just answer a question. From my perspective as a libertarian, and a former candidate for office, if we are going to have public schools, then teaching kids how to think critically about everything they are given is a positive.

Instead of indoctrinating them into the governments version of the truth. If we can teach kids how to think, not what to think, how to find the right answer or figure out an answer does not exist then we wouldn't be in the mess we are in today as a society.

This type of theory comes from Dewey and most liberal educators worship everything he taught. (I have tried to understand his work to get something out of it to help educate people, but I believe he missed the mark in many ways.) The theory makes sense and works on paper and it does work if it is done correctly. The problem is you cannot give a student a problem and say figure it out and explain your answer. Students have been taught for years to answer the problem and that the problems only have one correct answer. For a student or a parent to have to change this thinking process should not be taken lightly by the school. Also the school sounds like some of the online classes I took in college. It was almost a joke and a lot of what was assigned was only to justify to others that something was being done. In this case, true education gets thrown out the window and the school is in it for the money.

A lot of ground/preparation must be done by the teacher. The teacher needs to model and teach the students how to think through problems. The teacher should be having them practice this theory and slowly work with them so they understand it. They should practice how to critically think, question and find answers. This is what we in the liberty movement are trying to get people to do…critically think and question everything they are being bombarded with and not accept any information they are given as truth until they can prove it as such. I know how to properly use this theory in the class room and have not had a problem with it.

For many teachers who try and teach this way, they don’t understand the theory or how to teach it. This creates a lot of confusion, especially among students and parents that have not had to do this in the past. If the students are not taught through the process it is rather meaningless to use it and really calls into question what criteria the teacher is using to decide if the students are thinking through the processes correctly. They teacher may not have any criteria. It may just be for show and any answer is a right answer.

At the other end, the teacher may not be using Dewey’s theory but rather post-modernist theories to try and teach that there is no truth. I personally believe that we can know the truth and that truth does exist. Many educators though don’t believe that truth exists. I have debated countless teachers in my Masters classes about this. What was funny was the fact that the professors and I are the only ones that believed in truth while the public school teachers were arguing against the ability to arrive at, understand or know truth.

If the teacher is like this, understand that they are teaching a belief system. They believe that the Constitution is not for today, it is antiquated, and should be violated. The teacher either believes in truth or does not believe in truth. That is a belief system that will dictate how they will teach your child to think about the world. If the teacher believes in truth, she is probably not doing a good job of teaching your daughter the processes of critically thinking that the teacher is using in the classroom. If the teacher does not believe in truth, assignments like these are meant to try and prove a point that truth does not exist and that we really cannot know anything. In this case, it is not meant to question what is presented to find truth, but to question the concept of truth itself, so that the student believes that everything is arbitrary and cannot truly be known or understood.

I would talk with the teacher either by phone or email and try and find out what models of teaching and learning theories they are using. If they use certain educational terms, google them and find out what they are all about. Try to find a creative way to ask them if they believe in truth or not. This will help you better understand the mindset of the teacher. Since your child is being taught right now by them the best you can do is find out how the teacher thinks and what the teacher is expecting from problems like these and help your child get through it until you can homeschool again.

Thanks J,

Please keep in mind, these are 10 year old kids.

The problem from my perspective is the fact the the math curriculum is 90% reliant on using story problems to teach math and has been since first grade. Based on scientific evidence, the human brain does not comprehend abstract thought processes, logic, etc. until around the age of 9 or 10. I've never understood how elementary school teachers can expect these young children to solve story problems when these kids only receive 10% of math instruction doing analytical equations. I am all for critical thinking skills, but at this age, the focus should be on developing a solid understanding of the analytical foundation of basic math, not logic and reasoning skills. I did enjoy reading your post. Thanks. And again, we homeschool her and have for over 3 years, she receives no instruction from a "teacher", other than myself.

You're right about the

age appropriateness of mastering basic skills vs. analytical work. There is an order to best fostering intellectual development just as there is with physical development - where you need to crawl before you walk.

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.
~ John Muir

Today's teacher ed is a farce

Sorry, but I had to laugh at your suggestion to "try and find out what models of teaching and learning theories they are using." I don't mean I was laughing at you. To an intelligent person, it would be a valid question. I was laughing at the thought of this mother asking such a question and receiving a cogent reply.

When we try to pick out anything by itself, we find it hitched to everything else in the Universe.
~ John Muir

I heard

I heard a rumor that Einstein, Isaac Newton, Galileo, Nickola Tesla, and a bunch of others didn't do well in the public school setting.
Forget the math problem...as long as your daughter is "collaborating" with her peers, well there you have it, that's all that counts in today's schools.
I'd send the teacher an e-mail saying the problem is not solvable with whole numbers...and ask "What happened to the apples and oranges questions?" Know what I mean?

To everyone who posted below

To everyone who posted below that there are fractional girls in the class:

That is not necessarily true. There is no reason to assume that there are 28 students in the class.

I was a teacher for 13 years

And I'm sorry I clicked on this thread.
Your daughter doesn't have a teacher.
She has an a-s-s-h-o-l-e giving her problems that probably have several different possibilities for correct answers.

We don't know if this a-s-s-h-o-l-e intends for the student to take

(18/28 of the class was wearing shorts.) to mean 9/14, .6428571 or 9 out of 14 or even 18 out of 28 students are wearing shorts.

(4/5 of the class was girls.) So if 4/5 of the class are girls that would mean 80% or 11.2 of the students are girls wearing shorts.

Now we don't know how many students are in the process of undergoing gender change so I would say there is not enough information to come to the correct conclusion.

In all probability the teacher was so busy getting ready for the next grievance meeting that he/she may have just missed a typo in the question.

Hey Cuda,

Well, thankfully I waited a few hours before mailing her a response or I may have said exactly as you.

To clarify, the online school is independent study based and Em does not participate in any of the available online classes. We tried them in second grade and found them to be geared towards struggling students. Em has no issues with school and as I stated she is light years ahead in math, currently doing 10th grade algebra.

Her "teacher" is really nothing more than a facilitator and we speak with her/him 4 times a year, at report card time to have a conference.

This math problem is the second monthly work sample of the year and it is based on common core standards. I don't believe the teacher created the problem, however I did express my disappointment that as a teacher, she sent it out.

And, for the record, my daughter has the very best teacher she could possibly ever hope to have.

OK. So stop bragging on Em's teacher.

Did you ever get the facilitator to explain?

Lol, um

no never received a response. We've moved on.

See that would just fire me

See that would just fire me up so bad I would mount an administrative assault on that facilitator until they were fired.

Is this what everybody were

Is this what everybody were telling about Common Core?

That 2+2=5 as long as the student can explain how they did it ... LOL

Math is an exact science. All science is rooted in the foundation of mathematics, and there can be trick or out-of-box questions, but questions with random answers shouldn't be part of math.

Yup, perfect comment.

Yes, this is what common core people were talking about and one of the reasons I posted it.


Anyone who calls themselves a teacher for the most part and graduated from college in the last 20 years or so is not really a teacher imo. Discipline is the agenda and not learning from my experiences.

I am still figuring out a term for it but it is still a work in progress. ;)

...wuz? or were?

p.s. hope you did not p.o. the 'teacher' too much. You know what many are like...ie. control freaks imo.


I hope her English grammar is not affected by this exercise.

It's you're job as parent to explain that this math problem has a range of answers and should be solved as such. Teach her to think out of the box and consider all extremes as the problem is worded. I would argue that you could not have fractional girls wearing shorts, but maybe half shorts considering some of the recent fashions.

It wasn't, in fact it was she who informed me that it was

improper English.

Solutions to the problem.

1) The null solution as there were no students in the class, as the teacher was possibly on paid suspension under a union contract for whatever reason.

Assuming no fractional gender identification issues, there would have been at least 140 students in the class, violating No Child Left Behind. Although, some undergraduate classes at state universities commonly have 200 to 300 students, so I assume this to be a college level class.

2) Minimum girls wearing shorts: 62/140.
S= 18/28*140 = 90 wearing shorts
B= Boys in class 1/5*140 = 28
G= Girls in class 140-28 = 112
Since G>S, then all girls can not be wearing shorts, so up to 28 boys
Min = (90-28)/140 = 62 or 44.29%

3) Maximum girls wearing shorts: 90/140
Since G>S, then no boys wear shorts, but not all girls
Max = (90)/140 = 90 or 64.29%

4) An infinite series of ranges implied by solutions #2 and #3, where the previous minimum and maximum are multiplied by integers.

Answers 1 and 4 might be confusing and should not not be expected of a fifth grader, but they come from my engineering math class "Non-Linear, second order differential equations"

I wish they had challenged me like this in fifth grade; I might have advanced more than I have.

Great answers

Except that minimum possible class-strength should be 70 instead of 140.

Thank you

for the correction.

Answer to part 2

Now, explain how a ten year old came up with this answer. ;)

All in all this is quite a rediculous problem.

Joel Salatin is part of a national organization of home schools.

There are thousands, it would be a good place the compare experiences.

Joel and Lew Rockwell were discussing it. Let us know if it's any good.

Free includes debt-free!

I am a high school math

I am a high school math teacher and you are right, it is a poorly designed and worded problem. If there are 28 students in the class and 4/5 of them are girls, then there are 22.4 girls. I don't know how you can have 4/5 of a girl so there is the first problem. There is no reason to assume that girls and boys wear shorts at the same rate but if they did there would be about.14.39 girls wearing shorts. I would tell your daughter point out that there is no way to give a precise answer but to give about 14/28 as an estimate,but point out that it is an estimate and also point out all the flaws in the problem. If the people are too stupid to give her credit, you really have no control over that other than to drop their program.

22.4 girls would leave 2/5 of

22.4 girls would leave 2/5 of a girl, not 4/5.


Liberty = Responsibility

your are right, I meant to

your are right, I meant to type 4/10

Thanks amc.

You are correct, there are 22.4 girls and 5.6 boys. As the problem fails to state how many boys are wearing shorts, the answer can't be definitive. Assuming, the idea is to round each to 22 and 6, there are anywhere from 12/28 to 18/28 girls wearing shorts.

The issues I had, for one was the grammar in the problem. I'm fairly certain "was" is improper use of the English language and find it ironic that improper grammar would be sent to my daughter by a teacher. Also how does one explain in 3-5 sentences how you solved your "answer"?

The main issue is, as has been seen in common core video's posted here before, that the answer really isn't important. What they want is the sentences explaining how she reached her answer, right or wrong. As far as I'm concerned, there is no educational value whatsoever in this problem, only confusion.