They are two closely aligned, yet separate issues.

I probably would have rounded down to 25 and 100.

I agree it is a horribly worded math question. The student gave the correct answer.

If you would have rounded it down it wouldn't be correct.
103 should be rounded down to a 100.
100-30=70.
75 should be rounded up to 80.
70 does not equal 80.
Therefore the answer isn't reasonable if you know how to correctly round up or down (even though it's correct).

3 is less than 5. 103 therefore is rounded down to 100.

10's, 100's, 1,000's, 1/10's, 1/100's, etc. if the problems says to round to the nearest 30 you round to the nearest 30.

wouldn't you?

Since both numbers were only off 25x by 3?

Is that allowed?

Round half towards zero
0, 1, 2, 3, 4, 5 rounds down to 0
6, 7, 8, 9 rounds up to 10


Round half away from zero
0, 1, 2, 3, 4 rounds down to 0
5, 6, 7, 8, 9 rounds up to 10

75

you round to the nearest 10 not 5

People have given several reasons why, I don't know what the real reason is, I just know that is the rule.

Who am I to argue?

Are we educating children to provide correct solutions to problems or do we just want reflexive obedience?

I'm not a teacher so I won't be training them not to think.

which is always done in terms of powers of ten. We want kids to get used to rounding off to the nearest tens, hundreds, thousands, etc.

8 is more than 5. Therefore 28 is rounded up to 30.

And what is the &quot 2-7)" in reference to?

You can see the student highlighted and marked the two parts. 7 is the points. It doesn't say if it is 7 points for each part or 7 points total.

So at worst, the student lost 1 out of 7 points possible for not estimating correctly.

School was a long time ago

Probably part of homework assigned, or covered in class.

I would guess that Chapter 2 Section 7 was a section on estimating

Estimating skills are important, and when I first permitted students to use calculators in my class we focused a lot on whether the number on the LCD was reasonable.

I would have phrased this: Carole calculated that she read 75 more pages on Tuesday than on Monday. Is this a reasonable answer? if so, use estimation to explain why.

(I might even have said, Carole calculated that she read 131 more pages on Tuesday than on Monday. Is this a reasonable answer?)

103 - 28

Round each to the nearest multiple of 10: 100 - 30 = 70. 70 is close to 75, so 75 is a reasonable answer. (If you look at the second way I worded the question, which is what the student would get if s/he added, instead of subtracted, it is clear that 131 is not close to 70, so 131 is not a reasonable answer.)

Especially if you are using calculators, mentally estimating a correct answer is a good way to do a gut check to make sure you didn't have fat fingers on the calculator. It won't work if you don't know what operation to use, but otherwise it is a good way to make sure you're in the ballpark (reasonable).

I also use it when I'm shopping and have to pay in cash (I go to one store that doesn't accept credit cards - so I have to make sure I have enough cash on hand). I'm rarely more than $2 off out of $60 - $100. I just round everything to the nearest $1 and keep a running total in my mind.

all the numbers? Well, 75 is supposed to rounded up to 80. Is 70 the same as 80 these days?
And what do you mean by 75 is close to 70? What wouldn't be considered close?

You are checking to see if the answer is reasonable (i.e. in the ballpark). You don't round the answer - you compare the answer you got (theoretically the exact answer - but that is why you are checking) to the rounded answer and make sure the calculated answer is in the ballpark.

For an integer subtraction problem, using rounding to the nearest 10 as a way of estimating, close means plus or minus 9 to the estimate. Using the problem here, as long as the calculated answer is between 61 and 79, the answer is in the ballpark (reasonable). Since the calculated answer is 75, which is between 61 and 79, it is reasonable. (I.e. you probably didn't have a fat finger problem on your calculator.)

I doubt the student was taught the exact bounds - most people have a good sense for which answers are close - and at least in the early stages, most teachers will choose problems that give an exact answer in the same decile, which is typically what most people naturally think of as close.

As an aside, there are also other ways of checking for reasonableness. Unless I had specified a particular way of estimating, I would have given credit for different ways of estimating. Truncating, for example, is another (generally less accurate) way. I would also give credit for only rounding the second number, which still reduces the problem to an easier subtraction problem: 103 - 30 = 73, as an estimate.

of the word.

Suggesting that the correct answer is not reasonable seems designed to trick the child.

I think your suggested substitution is MUCH better.

This question, as worded, would have driven my two kids crazy (including the PhD engineer).

My youngest is currently going through estimation in math. The questions seem ridiculous to me because they're so simple I can find the correct answer in my head. But I realize when things get more complicated the importance of estimation.

His work however clearly asks for an answer by using estimation. That is what is missing from the example given above.

a comparison to the calculated answer to verify that the calculation was carried out correctly.

I can't tell you how many times when I was teaching math that a student shoved a calculator in my face to show me that s/he was right and I was wrong - with no comprehension that what was on the calculator was caused by (1) fat fingers or (2) a misunderstanding about which operations should be done, in what order.

Estimation gives you the skills to verify that what shows on the calculator LCD (or what you calculated by hand as an exact answer) is a reasonable answer. If you get a similar number by estimation, it provides at least a basic check that the calculated answer is likely right.

Doesn't allow students to Use calculators until 6th grade. They believe that kids need to learn the basic principles before learning to use a machine.

Last edited Sat Oct 24, 2015, 05:30 PM - Edit history (1)

I used to be absolutely opposed, at any grade level. I allowed my physics students to use slide rules (I know, I'm dating myself) only if they could explain to me the math behind using them to multiply & divide.

I also taught the second lowest high school math class. I "lovingly" referred to the two lowest classes as "1+1 = 2," and, "Now that you know 1+1 = 2, what can you do with it." They really weren't much more sophisticated at that - and the class demographics were students who had failed 9th grade at least once. They tended to be (1) a small group of students who really didn't have the mental capability to do more advanced math and (2) a much larger group of students who could meet behavioral expectations a sufficient quantity of time to earn enough points to pass. Their age ranged from 15 through 21.

At the time, the school policy was absolutely no calculators. I quickly figured out most of these students would never learn the basic arithmetic skills - since they hand't learned them in the prior decade (or more) of math - and I lobbied to permit calculator use. We negotiated the equity aspects (not everyone could afford to buy a calculator for class - so we bought a class set that students were permitted to check out), and the school comparables (everyone takes the exact same final exam - so my students were required to take the test without calculators). No one was particularly happy about it, but ultimately the school allowed me to experiment.

What I found, that was apparent from the very first final exam, was that once I relieved them of the struggle with arithmetic their ability to understand the problem solving aspects of the course dramatically improved. They no longer got the wrong answer because they picked the wrong operation, and out-performed their peers on the final exam because during the semester they actually learned "Now that you know {insert random arithmetic calculation} what do you do with it"?

So - I do think it is important to learn arithmetic. But I think it is much more important to learn how to use it. And if the first is a barrier to the second, the first has to be sacrificed.

Given that 6th grade is the start of algebra now, for some students, that may be a bit late to be quite so rigid about prohibiting calculator use. They are way beyond learning basic arithmetic skills by then.

As you note.

I do not know if our school has similar policies. I know there are two students with Downs syndrome who are in regular classes and are keeping up with their peer group.

We also have a couple with behavioral issues that allowance may be made for them. Luckily we do not subscribe to zero tolerance which really seems to help whether a behavior issue is chronic or acute.

causing is pushing special education students to keep up with general education peers. If special education students can keep up with general education peers that is great but I think these new education policies push too hard. Special education students already have a process where they get an individual education plan where the teachers and parents come up with educational goals to help the students reach their potential while at the same time allowing them the time and space they need given their disability. The individual education plan has pretty much been overridden by new standards and the power has been taken out of the hands of the teachers and parents and put into the hand of federal bureaucrats who have never met these children.

Of our special needs students is in 5th grade this year. This is also the first year we have a student resource specialist on staff. I am thinking those two things are not a coincidence.

Some of the things they use look similar to common core but I don't think the school fully uses it.

math comprehension. They told me that their policy was that ALL 6th grade students have to take 6th grade math/algebra. He came home crying a lot that year. He would ask to skip school and it was beginning to affect his self esteem. I would tell him everyday how smart he was. I would tell him he thinks outside the box, is creative, inventive, determined. I would tell him that school just doesn't know how to teach kids who think differently. They passed him all the way through middle school math, all three years, even though he did not understand the material. Luckily, we moved to a different school district that took the time to test him and went back and reinforced addition/subtraction, multiplication/division before they tried to teach him algebra. He is now in 11th grade and is now learning algebra. He is still struggling with the concept of having letters in math problems, but he is certainly more ready for it now then he was in 6th grade.

If they don't understand that no where near all 6th grade students would be ready for algebra, then they are idiots.

When I was in my 40's and taking calculus, and absolutely loving it, I talked to several of the math teachers at the junior college I was attending about this. I told them that back when I was in high school and came up against calculus, I started very nearly failing the math. Couldn't understand it at all. And now, thirty years on, I'm loving and understanding calculus. Why was that? To a person they all said, "Oh, Sheila. What most people don't understand is that math is developmental," and they'd go on to say that even a lot of fairly bright kids simply weren't ready for calculus at age 17 or 18, but would be in just a couple more years. They said they'd seen it all too often, kids being pushed just a bit too hard and fast in math in the local high schools and getting burned out.

I often tell that story to kids in high school and assure them that it's okay not to take every single math class their school offers, especially if they are struggling, but that a year or two into college they may well be ready.

Your son is a very good example of that, and in addition he's probably someone who is going to come up against a real limit to how much math he's going to be able to learn ever. Nothing wrong with that. It's not a reflection on him as a human being, just the reality of his own abilities.

we can just push learning earlier and earlier. I feel like my children are being treated like guinea pigs, some weird science experiment to see how early we can push these concepts. I wish the people who created these curricula would get a degree in child psychology or neurobiology first.

(he is REALLY smart) had trouble learning to read. When he was in first grade I was made crazy because the kids who caught on to reading easily were being rewarded, and he was having a very hard time. Meanwhile, he was ahead of everyone else in math, but wasn't rewarded, couldn't advance.

At the beginning of second grade he still couldn't read. He was placed into "special reading" which was basically reading tutoring, and (thank god) phonics, not the stupid sight reading crap. Don't get me started. Anyway, half way through second grade he was finally reading.

The public school he was then attending also did this nonsense (in my opinion) of timed math tests. The kids had to finish 50 problems in some absurdly short length of time. My son could NEVER finish the fifty problems, but he also never missed a single one of those he did. Arrggh! Luckily, he completed second grade and in third grade at that very same school, didn't have to put up with such nonsense.

Fast forward twenty-five years or so. This son is finally completing his bachelor's degree in physics. Turns out he's slightly autistic, has Asperger's syndrome, which got in the way of formal schooling. But he's compensated, is doing very well now, and as I said at the top, is applying to some of the best programs in the country for astrophysics, including the University of Arizona. Plus, he's doing research into galaxy evolution. How cool is that?

The important point is how very individual kids are, and how badly our schools, even our good ones, do with dealing with those differences.

Hardly exceptions!

The district had a policy of no academic retention until students hit 9th grade, so there were tons of social promotions. It was an urban school district with well over 90% of the students on public assistance - which required school attendance for at least older kids so they didn't drop out in order to continue the assistance, they just hung around largely creating trouble until they completed the school-year in which they turned 22 and there was no longer any financial motive to stay in school.

It was a really hard place to be (both for the students, and for those of us trying to make a difference).

His mother and father were alcoholics and his father abused his mother. He did terrible in school until they transferred him to an alternative high school. That was a god send for him. In the alternative school the class size was small enough and the curriculum was flexible enough that he had the attention and resources he needed to graduate.

Then, I let my son who was probably in about third grade at the time, fool around with a simple four function calculator. What a revelation! He did things with it, played with numbers and operations in a way he never would have with pencil and paper. He was, of course, still required by the school to learn the basics all along.

These days he's getting a degree in physics and is in the process of applying to grad schools for astrophysics.

As you learned, the calculators are an amazing tool and need to be put to use properly.

If the student had written that 75 is reasonable because 105-30=75 I would not have deducted anything. But simply subtracting the actual numbers misses the point of "estimating".

I agree more than I disagree. We estimate when information is incomplete which is not the case here.

I think examples asking kids to identify variables/quantities that would be needed to even be able to make an estimate would be more educational and scientific. Granted, that may be beyond the grade level illustrated here.

I sure don't.

I didn't read the question carefully enough and assumed that what was being asked for was an estimate.

it was an estimate.

In the world of mathematics, as in the standard dictionary, the word "reasonable" and "estimate" mean two different things.

If they didn't want to purposely trick a child, they could have asked if an number far out of range was "reasonable." Wording the question to suggest that the CORRECT answer was not reasonable is deliberately misleading.

Is it a reasonable answer?
The student is correct. Yes

It does not say show estimate.

No reason to deduct a point.

or section of the test.

in this particular question. The word "reasonable" and "estimate" mean two different things, in mathematics and everywhere else.

The estimation thing makes sense pretty easily if the proper context exists, but I can't tell why points are being lost in the multiplication by addition answers. Any teachers able to explain what's happening there?

Edit: Oh, the "array" thing looks like they maybe are establishing a standard for rows vs. columns like in matrix math and 2d arrays in programming. So first number = rows, second = columns.

And the 5 x 3, I'm guessing they're being taught a certain way of visualizing like 5 x 3 translates to 5 groups of 3 hense 3 + 3 + 3 + 3 + 3

The product of two numbers is not order dependent in the real number group, which is the setting by default.

Your definition is only a convention of the English language; and I’m not even sure that it’s an accepted convention in every English speaking countries. Others countries have other conventions.

I'm just passing along what they said. If you read my posts you would have found that I am of the rather controversial opinion that 5x3 = 3x5.

Or I missed the person with a PhD in algebra.

I'm a physicist and I've worked in research laboratories but it doesn’t make me an expert in physic.
At best I could be an expert in my field, and even this doesn’t exempt me from being challenged or dispense me to demonstrate my claims.

And I agree with you that 5x3=3x5.

As was pointed out to people multiple times:

http://www.democraticunderground.com/?com=view_post&forum=1002&pid=7277210

http://www.democraticunderground.com/?com=view_post&forum=1002&pid=7277743

I'm just an engineer. I stopped after differential equations.

thread. "It's because multiplication is defined that way" (actually, it's often defined closer to what the student wrote), "It's because it's testing on matrix multiplication" (no, those questions make no sense if you act like they're talking about matrices), "It's a test on the order of operations" (Eh, there's only one operator), "It's important to teach kids that not all multiplication is commutative" (you do this by teaching them that multiplication that is commutative isn't commutative?).

I imagine one of the main reasons why people hate math and find it confusing is because there are a lot of people who don't understand it but still love to lecture others about it.

In engineering (and other areas of applied mathematics) we often do things that are just "wrong" from a pure math pov. We just don't care. Our profs were always careful to point out where they were flouting convention but sometimes it's the only way to make a problem solvable.

I'm always curious about things like this.

so tomorrow I could have some more explicit examples but off the top of my head, things like trig expressions that cancel out or can be ignored for verry small angles. Also the ways we would manipulate differentials (dx, dy, etc.), moving them around equations like they were variables. Things like that. Math PhD s would be aghast.

My understanding with the issue of moving around differentials is that, though they're not fractions, thinking of them like fractions can help people remember what to do in certain situations (separation of variables). Most of the time I seem to see something like "these aren't fractions, it's wrong to say these are fractions, but think of them kind of like fractions while we do this one specific thing."

Did a search and found this; the explanations seem to make sense (from my limited understanding of these things).

But yes, that's pretty much what I was talking about.

And you've really sum up that thread.

I see no basis for forming an opinion here.

Losing a point seems fair. Just the question out of context obviously makes little sense.

It doesn't matter what the instructions might have said at the top of the page. The "correct" answer, 75, would always be a "reasonable" choice. A fair question would have asked if a clearly unreasonable estimate, such as 100, would be reasonable.

This test question seems to have been written deliberately to trick the student -- which test questions are not supposed to do.

I'd be punching school admins in the face over this shit.

they are stupid you definitely think about punching somebody. It took all the strength I had to sit there and tell my kid no you can't skip school. You have to go and do the work and try your best. I also made sure he knew that it was not his fault and that he is smart, thinks outside the box, and has creativity, determination, and grit which they don't test for but can be a much better indicator at later success in life than test scores. I also told him that the school simply didn't know how to education kids who learn differently than everybody else. My son has one and two thirds more years in the K-12 school system and I can guarantee when he is done we are going to throw one hell of a party to celebrate that he is out of the loony bin.

100-25 which is 75. And in my reckoning just as good an approximation as what the test wanted.

Don't put the CORRECT answer and then ask a smart kid if it's a "good estimate," FGS. (I swear I'd have written "Good? It's a GREAT estimate! In fact, it's right on the money!" I was a smart-aleck.)

College Ed depts. are turning out morons who are indoctrinated into believing they are teaching students to think by their, the teachers', using methods directly opposed to that goal.

Admins make their bonuses by thinking up more and more topics for "In-Service" and more and more new "methods" for teachers to use, the inevitable culmination of which was seen this week in NY, with a principal tossing out teachers' desks and filing cabinets (since returned):

http://www.slate.com/blogs/schooled/2015/10/20/bronx_principal_bans_desks_from_spuyten_duyvil_school_citing_21st_century.html

This is getting ridiculous.
I'm glad I got my primary and secondary education in the '60s and '70s, when we didn't have this kind of shit screwing with kids' minds.

Question doesn't even provide instructions that the student is supposed to "estimate."

Pull up the wambulance.

Here's the point of the OP >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>and here's you.

The instructions might have said that you were supposed to round to the nearest multiple of 10 and then use those numbers to estimate.

100-30 is 70. So if they wanted students to understand how to round up or down, then 75 in not in fact a reasonable answer (even though it's a correct answer).
I don't know how they are teaching poor kids these days.

it allows you to avoid glaring errors

lets say you are looking at your checkbook and you see much less or more money than you think you have.

estimates allow you the cruise thru quickly to see if you have an obvious mistake.

you use it all the time...

If they put down the right answer instead of the estimate how will the teacher know they have learned the lesson??
Please direct your outrage at real issues like the distribution of funds in a city that allows one school to go without
critical learning tools and another schools get so much money they have swimming pools, basketball courts, and stadiums etc.

Learning critical life lessons is not something to attack.

Just sayin'

if you estimate within $100 of your chosen showcase, you win both Showcases.

If you can "roughly calculate" the answer is 75 just by doing the math problem in your head then you have come to an excellent estimate.

but don't recall having to deal with it in word problems like this. It should be worded to estimate rather than whether something is a reasonable answer.

customers think an "estimate" is a rock solid price.

It's better to get as close to possible and figure in everything that MIGHT incur cost, since if you raise your ESTIMATE, they'll scream holy murder and not want to pay ANY upcharges.

So yeah, go figure.

Perhaps the teacher skipped her lesson on rounding off first? If the teacher had made clear that the student was to round off the numbers (28 to 30 and 103 to 100) first, then the student would have gotten a entirely different answer. It would have been; no because 100-30=70.

was in fourth grade, he took a test on model drawing word problems. He got more points on one question where he got the wrong answer but put the "who" of the word problem (the name of the person) in the right place on the model drawing than he got for a question that he had the right answer but didn't put the "who" of the problem in the right place. I am a college professor. I asked his teacher what she thought students would do if I used a rubric that gave more points for a wrong answer than for a correct answer. She said good point.

The question doesn't ask for an estimate, and if it did, that would be nonsensical. The question already tells you how many pages were read - why would you need to estimate how many pages were read? I'm wondering if this is even real? Maybe the top of the test says "These are all rough estimates" or something?

That's like saying, "I have 30 cents in one hand, and 45 cents in the other hand. Is '75 cents' a good answer for the total amount of money I have? Sorry - that's wrong, I do have 75 cents, but you needed to estimate the amount I had.'

Wat?

Same thing happened to me on an estimate question. Convinced me, even as a kid, that I would never subject my children to public schools.

I note that Section &quot 2-7)" is mentioned in the question.

In the actual textbook, section 2-7 could well have had estimating as the topic an, therefore, the ability to estimate is what was being tested.

Having said that, most students when taking a test would probably have not remembered what section 2-7 contained...

...still, this is a very poorly worded question of the type that I remember editing when I worked as a temp with these types of K-6 math materials...what this really is is a poor editing job on the part of those who edited this (apparent) math workbook...and the techer for being so wedded to the materials not to evaluate it as such.

and actually...since this is a question with a 2 part answer, I would give the student credit for the portion of the answer that he got correct and maybe deduct for the improper method used.

Not to say that this didn't happen, or it can't happen, or that worse has not already happened and has been happening all along.

But this thread is full of replies based on a Facebook post of part of a scanned page. Who says it's authentic? Can anyone even name the school or the state in which it supposedly happened?

This is the origin of the blog post and thus of this thread:
https://www.facebook.com/photo.php?fbid=10153229525218602&set=a.10150385964368602.352654.584143601&type=3&permPage=1