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News flash: Massachusetts kids can't do simple math

This morning's Boston Globe had a story about the MCAS (Massachusetts Comprehensive Assessment System test. They quoted what was, going by the number of kids who got it wrong, the hardest question on the 10th grade math test.

Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?

A) 27,000
B) 20,000
C) 16,000
D) 18,000.

Now, I freely admit I have a head for math. I can do arithmetic and algebra in my head faster (sometimes a LOT faster) than a lot of people can with a calculator. And it surprises me sometimes when others can't, or seem surprised that I can. But this was NOT that tough a problem. I broke it down and had the answer in about 30-40 seconds, just in my head. But over half the tenth-graders in the Bay State blew it -- and they had access to pencil, paper, and a calculator.

If we need more evidence that the public school system is failing our children, here it is.

(Solution in the extended section)

OK, we have 1/3 of X plus 1/4 of X equals X-11,250. First, make the fractions compatible (simplifying the denominator) by converting them to twelfths -- 1/3 = 4/12, and 1/4 = 3/12.

That changes it to 4/12 X + 3/12 X = X - 11,250, which means that 7/12 = X - 11,250. And since X, in twelfths, is 12/12, we have 7/12 X = 12/12 X -11,250. Subtract 7/12 X from both sides, and we get that 0 = 5/12 X - 11,250. Then add 11,250 to both sides and you get 11,250 = 5/12 X.

Divide 11,250 by 5, and you find out that X = 2,250 (my shortcut here is instead of dividing it by five, I multiply it by 2 and then divide by ten. That gives me the answer 22,500, and then I just move the decimal place one place to the left and get 2,250. It's faster for me.)

So, we now know that 1/12 of X is 2,250. So to get the final value of X, we multiply 2,250 by 12. But that can be tricky, so let's do it in pieces.

You get 12 by multiplying 2 x 2 x 3. So let's do this in steps. First, double 2,250 and get 4,500 -- nice and simple. Then double it again and get 9,000 -- also nice and simple. Finally, triple it, and you get the final answer -- 27,000, or A.

It took me about five times as long to type this as it actually took me to think it through. Over half these kids, far better equipped and having had much more recent teaching on the subject, couldn't do that.

Comments (47)

Uh,....nerd?... (Below threshold)


They had calculators and st... (Below threshold)

They had calculators and still couldn't figure that out? Wow. That is really bad. Math here in Norway has been going down the shute as well.

Eeek - that is pretty bad.<... (Below threshold)

Eeek - that is pretty bad.
I am a math moron, haven't had a class in over a decade, was always bad with fractions - yet even I managed to figure it out in about 1 minute in my head - although not in the proper way.
They're given 4 answers - if you can't figure it out the proper way - you most certainly could figure it out working backwards - like I did.
(I know, I know - not proper math - but I did get the correct response)

Jay, the reason Massachuset... (Below threshold)

Jay, the reason Massachusetts students can't do math has already been given, and on this site. I'm surprised you don't remember this story that Kevin wrote about in January. It pretty much explains why math isn't the priority when teaching math, it is the respect of human differences!!!!

The story you wrote about here and Kevin's is the reason why this Massachusetts resident will no longer be living in Massachusetts when his daughter is old enough to attend school!

I didn't click on your exte... (Below threshold)

I didn't click on your extended section, so I did it an even easier way on my cell phone's calculator. You know 1/3 and 1/4 of the people are, so you just need to find where the rest are (1- .333333333 - .25 = .416666667). So 11250/.416666667=26999.9999784 which I then made the great mental leap to be answer A. Two quick calculations (the percentage you are trying to find out about and then the answer).

This should take about fift... (Below threshold)

This should take about fifteen seconds. You don't need to calculate anything. Just from reading the quesion you know that 11250 is less than 50% of the total (i.e., 1/3 + 1/4 = about 58%, so 11250 is about 42%). So, 27,000 is the only possible answer, because it's the only answer that is more than 2X 11250.

Ooooooo... I quiver at the ... (Below threshold)

Ooooooo... I quiver at the geekiness of it all. ::swoon!!::

I so heart nerds.

Even in the worst case scen... (Below threshold)
Bill K:

Even in the worst case scenario the student should be able to check his work and know when he/she got the wrong answer. At most it would take them four guesses.

1/4 of 18000 = 4500
1/3 of 18000 = 6000
+ 11, 250:

oops, too much.


1/4 of 16000 = 4000
1/3 of 16000 = 5,333

+ 11,250

oops, too much

and so on.

If it makes everyone feel b... (Below threshold)

If it makes everyone feel better, I couldn't figure it out either. It's been a while since I had to sit down and do a math problem.

You should see me when I'm doing my taxes. It looks like a UN meeting that has the intent of solving genocide in Sudan.

In other words, it's not pretty.

It's interesting to see how... (Below threshold)
Richard Bradley:

It's interesting to see how different people approach the problem. My take was that 7/12 of the people were in the grandstands or bleachers, leaving the 11,250 people as equal to 5/12 of the total attendees. To get the answer, one only has to solve the equaltion 5/12 X = 11,250. Multiply by 12 to get rid of the denominator and divide that result by 5 to get X equals 27,000.

33% of X = grandstand seats... (Below threshold)

33% of X = grandstand seats
25% of X = bleacher seats

therefore, 58% were in these seats-
that leaves 42% of X = 11,250.

Since it's multiple choice, you don't even have to get an exact answer, just know that the other three could not be correct.

Jewels, I solved the proble... (Below threshold)
j. blair:

Jewels, I solved the problem using simple calculus. I timed how long it took the audience to do the "the wave" in the various sections of seating. Then, I differentiated the rate of wave change over the respective seating areas. That allowed me to determine the wave rate ratios which I used to calculate the total population.

My solution was similar to ... (Below threshold)

My solution was similar to notanotherjohn's. 1/3 + 1/4 = 7/12. The remaining 5/12 represents the 11,250. All you have to do is solve the ratio 5/12 = 11,250/x or 5x = 135000 or x = 27000.

So many ways to skin a cat, and still they couldn't do it...

I'm with Michael on this.</... (Below threshold)

I'm with Michael on this.

A few seconds to determine that:

5/12 x total = 11,250

means that the total must be more than double 11,250 which must be more than 20,000.

So the answer had to be A w/o doing any more math.

I solved it the same as Ric... (Below threshold)

I solved it the same as Richard Bradley.

You should see me when I'm doing my taxes. It looks like a UN meeting that has the intent of solving genocide in Sudan.

You sit around doing nothing while watching "Schindler's List" and laughing your arse off? Funny way to do taxes.

I refused to answer this qu... (Below threshold)

I refused to answer this question because there was a slight possiblity that the teams playing had questionable team names that might offend Native Americans.

That - and I had no clue how to begin to get the answer.

I used the Bill K method. ... (Below threshold)
Lew Clark:

I used the Bill K method. Since we had choices, it was easier to take 1/4 and 1/3 of each possibility and see which answer left 11,250. And since I started with (a), wa la.
Although my first guess was "The number of people in Florida who actually did vote for Al Gore in 2000", but all the answers were too high.

700 solutions to a math que... (Below threshold)

700 solutions to a math question :)

Here's mine
(which is similar, but not identical to some others)

1/3 + 1/4 is more than half.
You don't need to figure out _how_much_ more than half, just recognize that it is _more_ than half. (Which is a duh).

So the only actual multiplication, _estimate_ doubling the remainder. That's 22000 some odd.

You know it has to be _more_ than that number - and only one of the answers fits. That means STOP.

The only 'real math' performed in this method is 2x11. My six year old just solved this question. (well, she turned 2x11 into 11+11, but hey ;)

all this means is that they... (Below threshold)

all this means is that they haven't gotten to algebraic word problems yet?

I was at a local school fes... (Below threshold)

I was at a local school festival/event a few years ago and witnessed a 10 year old trying to buy a couple of items at one of the booths. One item was $1 and the other was $2. The child held up a $5 bill and asked “Is this enough”….

I'm a pretty dismal failure... (Below threshold)

I'm a pretty dismal failure at math, not to mention completely out of practice, and I got it in less than a minute. Whew! I didn't even have to count on my fingers. Thanks, Jay Tea! This is the first geek thread I've been in on. I demand more elementary math problems!

for me 38 seconds.. DAMN we... (Below threshold)

for me 38 seconds.. DAMN we are good, and trust me people.. what he once told me about number crunching is more then a mere nerd, we are talking .. NERDVANA

Just think how many would h... (Below threshold)
lee allaben:

Just think how many would have missed the correct answer if it wasn't multiple choice!

When I was an underg... (Below threshold)

When I was an undergrad I had a teacher who told us if we wanted to pass his class we had to remember the five stages of compilation (lexical, syntactic, semantic, optimization, linking) and one sentence about what each of them were. He said that this five-part question would be on the midterm and final and answering it correctly on both would get you a C even if you got everything else wrong. He reviewed the question before each midterm and each final every year.

He had a girl take his class twice and fail it twice. She missed that question 4 times despite his pleas, to her personally on several occasions, to remember those five things. How do you teach someone like that?

I also did it Michael's way... (Below threshold)

I also did it Michael's way, as it quickly became apparent there was no need to solve for a value in light of the ones provided.

Wow, kids are pretty dumb huh?

This isn't really news though - I've more or less realized it since 7th grade when I had a chance to take the college entrance SAT and beat nearly 70% of high school seniors (I'd toot my horn, but, really, given the state of education, that's not saying much).

How do you teach someone... (Below threshold)

How do you teach someone like that?

In special ed.

I'm with lee allaben. I wou... (Below threshold)

I'm with lee allaben. I would love to have seen a mathematical proof or essay question. That would have been simultaneously hilarious and sad. Do they even ask those anymore in High School, or is everything Scan-tron and Fill-in-the-Blank?

I just did what Michael did... (Below threshold)

I just did what Michael did, it's sort of a quick and dirty first try at it. 1/3 and 1/4 is more than 50% what's 11,250 x 2? 22,000+.

Hmm, must be 27,000. Now if the multiple choice answers were 25,725, 26,500, 26,725 and 27,000, I'd have to actually write it out.

27,000 overpriced tickets t... (Below threshold)

27,000 overpriced tickets to see 'roided-up baseball players. That's the real tragedy here.

You all seem to be missing ... (Below threshold)

You all seem to be missing the point of this post, which is that if our species is producing kids this dumb, it's impossible that an Intelligent Designer had anything to do with our evolution.

Short way to do it is just ... (Below threshold)
Cardinals Nation:

Short way to do it is just figure that 33% and 25% is more than half. Multiply 11,250 by 2 and see which answers fall out.

Or you could use a calculator.

Or you could just sue the school district and the test makers for subjecting you to such an esteem-lower experience.

Here's a tougher one:... (Below threshold)
Just John:

Here's a tougher one:

How much money would the Department of Education have to pay to Armstrong Williams to ensure that children in Massachusetts can do math?

Feel free to use a calculator.

I hate math but even I can ... (Below threshold)

I hate math but even I can figure that one out. That's simple basic math that I have to use every damn day at work. Some of these kids are gonna be screwed when they try to get and hold jobs.

just use the ratio method, ... (Below threshold)

just use the ratio method, and solve for x.

15535.71+11250=26785.71 or 27000 (a)

RE: tyler's post (August 25... (Below threshold)

RE: tyler's post (August 25, 2005 02:02 PM)

...Some of these kids are gonna be screwed when they try to get and hold jobs.

Perhaps. But I have a scary (or hopeful) anecdote that might put this in perspective. I worked with a resident with a B.S. in Chemistry who could not draw the structure of methane. Trust me (if you're unfamiliar with organic chemistry) when I say that is shocking. However, this resident was very good with patients and wholly functional tending to delicate lives and publishing papers. These kids aren't necessarily doomed, but it sure doesn't look good on the resumé.

Two of the provided answers... (Below threshold)

Two of the provided answers are not evenly divisible by 3. That
is, you can't take 1/3 of 20,000 or 16,000 and come up with a
meaningful number of people. So, two answers are eliminated immediately.

This makes Michael's approach provide an even more obvious answer.

If you can't do that withou... (Below threshold)

If you can't do that without a calculator by 10th grade... somewhere along the line, the education system has failed.

The reason that this questi... (Below threshold)

The reason that this question is difficult for the average student to answer is that kids don't like baseball. It's an Anglo-Saxon tilted trick question designed merely to extend the hegemony of the WHITE MAN.

If, however, the question were framed in a more respectful way, it might be worded thusly:

Yo, holmes. I gots one-third a my dope over at Leroy's; cuz, you know, I gots to have my personal stash safe, you dig. And my bitch, she stole one-quarter of my dope and leff my ass lass night cuz she an OPP. I can only come up with $11,250 for that kilo today. Yo, so how much do I need to come up with in total to keep you from poppin a cap in my ass?

lol cute rightnumberone, cu... (Below threshold)

lol cute rightnumberone, cute

RE: rightnumberone's post (... (Below threshold)

RE: rightnumberone's post (August 25, 2005 04:26 PM)

Man! Ebonics be raisin' dat ugly head ag'in. We all be doomed... doomed!

Easy to eliminate 16,000 an... (Below threshold)

Easy to eliminate 16,000 and 20,000, because if 1/3 is multiplied by either of these, it would leave a remainder that ends with 667 or 333 (and you're searching for 11,250).

Now you're down to two possibles, 18,000 and 27,000. The small one doesn't work as stated above (1/3 + 1/4 is greater than 1/2) so it has to be 27,000.

It is surprising to me that... (Below threshold)

It is surprising to me that you are surprised by this result.

The method that the kids are taught would approach the question like this:

Of the European-American people in attendance at a recent baseball game, one-third enjoyed their cultural hegemony from the grandstand, while one-fourth had their consciousness raised by sitting with their no-longer-minority co-hummons having temporary access to bleacher tickets, and the remaining 11,250 people in attendance flaunted in front of all others their greedy use of global resources that all other people around the world could not even dream of. Given this scenario, how should we feel about the game of baseball, and how many minority managers are currently in the game?

Once you put it in the language they understand, it's perfect. Then again, the Ebonics version works for me, too.

This thread is an example o... (Below threshold)
Just Me:

This thread is an example of why I hate math. You guys can't even use the same method.

Btw my method was the one that didn't really do any math, I just looked at the numbers and eliminated the ones that were too small. Didn't even have to pull out a calculator or scratch pad for that one.

I would much rather write a billion essays than take a math test.

btw my 11 year old could figure the answer out.

I started to use Michael's ... (Below threshold)

I started to use Michael's method, but then stopped because I didn't really care. I wonder if that's why so many kids got it wrong?

Also, interesting to see who did the math methods and who used the estimating methods. Its not a left brain/right brain thing. Nor a guy/girl thing.

And Michael, it must have taken a lot of self restraint to hold the obvious "intelligent design" quip back for so long. But, you see, a truly intelligent designer would design a lot of flaws into the system so as to provide amusement for the more intelligent and less flawed ones (and hopefully eventually humility for even them).

Which is why younger studen... (Below threshold)

Which is why younger students should not be allowed the use of calculators while learning math. Or at least until they can demonstrate on paper that they have mastered the basics, demonstrating that they only need to use a calculator for its sole function: saving time.

This high school should print a disclaimer on the back of their diplomas:

"Warning: posession of this document does not guarantee the bearer useful knowledge, basic employability, or any of the benefits of actual educational achievement, whether stated or implied."

and before you giggle at th... (Below threshold)

and before you giggle at the misspelling of the word "possession", all I can say is: was it irony, or was it typ]o?

This thread is an exampl... (Below threshold)

This thread is an example of why I hate math. You guys can't even use the same method.

And that's the beauty of math: if the numbers are right and you're doing the right things to them, how you apply those numbers and operations doesn't really matter.

For me the problem was essentially solved as soon as I recognized that the common denominator was twelfths. Which was at the third comma of the first sentence.






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