# Are you smarter than an 8th grader? (math) **URL:** \ **Category:** Factual Questions\ **Created:** [January 22, 2009, 11:52am UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433 "2009-01-22T11:52:52Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Salem](https://avatars.discourse-cdn.com/v4/letter/s/8c91f0/32.png) [@Salem](https://boards.straightdope.com/u/Salem)\ **Post date:** [January 22, 2009, 11:52am UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/1 "2009-01-22T11:52:52Z")
We received these questions and published them in our paper. We published the answers as were given to us by the test maker. We’ve since had a reader question the answers. I was an 8th grader a hundred or so years ago and always hated these kinds of problems, so I’m not the person to make a definitive call. For this I turn to my fellow dopers and ask… 1. Ms. Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of 50 units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles? a. 76 b. 120 c. 128 d. 132 e. 136 2. For how many positive integer values of n are both n/3 and 3n three-digit whole numbers? a. 12 b. 21 c. 27 d. 33 e. 34 Answers (that we were given as correct) will follow after I see some responses. (Didn’t think I was going to let you cheat did you?) ---
**Author:** ![puppygod](https://avatars.discourse-cdn.com/v4/letter/p/ce7236/32.png) [@puppygod](https://boards.straightdope.com/u/puppygod)\ **Post date:** [January 22, 2009, 12:06pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/2 "2009-01-22T12:06:15Z")
Easy. 1. d 2. e So, what’s to win? ---
**Author:** ![Desert\_Nomad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/desert_nomad/32/177_2.png) [@Desert\_Nomad](https://boards.straightdope.com/u/Desert_Nomad)\ **Post date:** [January 22, 2009, 12:06pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/3 "2009-01-22T12:06:45Z")
[spoiler]2a. Max area is 12x13 = perimeter of 50, area of 156 sq units 2b. Min area is 24x1 = perimeter of 50, area of 24 sq units 2 is D… 132 sq units For n/3 to be a 3 digit number range is 300 to 2997 For n\*3 to be a 3 digit number range is 34 to 333 Overlap range is 300 to 333 but the only ones that divide to a whole number are: 300,303,306,309,312,315,318,321,324,327,330,333 Thus 3 is A (12)[/spoiler] ---
**Author:** ![puppygod](https://avatars.discourse-cdn.com/v4/letter/p/ce7236/32.png) [@puppygod](https://boards.straightdope.com/u/puppygod)\ **Post date:** [January 22, 2009, 12:09pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/4 "2009-01-22T12:09:21Z")
Damn you, **Desert Nomad**. You are right in 3., and I was wrong. This is what I get for trying to be first and doing hasty calculation in head without checking results. ---
**Author:** ![Tapioca\_Dextrin](https://avatars.discourse-cdn.com/v4/letter/t/3d9bf3/32.png) [@Tapioca\_Dextrin](https://boards.straightdope.com/u/Tapioca_Dextrin)\ **Post date:** [January 22, 2009, 12:13pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/5 "2009-01-22T12:13:12Z")
I guess spoilers might be a good idea 1 There is no question 1 2 d (doing it my head - smallest is 24x1 rectangle, biggest is 12x13 156-24=132) 3 a (had to get out a piece of paper 'cause I’m getting old - lowest is 100/300/900 biggest is 111/333/999) ---
**Author:** ![dlh210](https://avatars.discourse-cdn.com/v4/letter/d/9fc348/32.png) [@dlh210](https://boards.straightdope.com/u/dlh210)\ **Post date:** [January 22, 2009, 12:21pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/6 "2009-01-22T12:21:28Z")
2. is d 3. is 12 ---
**Author:** ![Salem](https://avatars.discourse-cdn.com/v4/letter/s/8c91f0/32.png) [@Salem](https://boards.straightdope.com/u/Salem)\ **Post date:** [January 22, 2009, 1:30pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/7 "2009-01-22T13:30:51Z")
Ok, thanks very much. Most of you ARE smarter than 8th graders - even if you have a hard time discerning the letter answer required from the actual numerical answer… 🙂 It’s funny - I see these types of problems and my eyes just glaze over. I typically am one of those weird people who actually likes taking quizzes/tests. I looked forward to the “fill in the ovals” in school. But, there’s just something about this type of math problem. But after reading your responses and seeing the logic of how you worked it out - yes, they were easy. Thanks for taking the trouble to think out loud. Now, the issue - - I’ve tracked down that the writer mistyped the first answer - should have been “d” as noted above, but she became momentarily dyslexic and typed “b”. My fault (as editor) for not doublechecking first. Second answer is listed in the test answer booklet, garnered directly from the teacher administering the test, as “c”. This is clearly incorrect and should have been “a”. Apparently in the answer booklet itself (which I didn’t have prior to publication, but the writer did) is also a verbal explanation of how to arrive at the correct solution and within that paragraph, they conclude the answer is 12. Unfortunately, that does not correspond to the answer ‘c’. So, now the question is, how were the kids graded? We’re checking into that with the teacher. This is from a standardized test, too, so the implications go beyond this particular classroom. Hopefully there’s an easy explanation and it won’t effect the rest of the entire math-test-taking world… ---
**Author:** ![Santo\_Rugger](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Santo\_Rugger](https://boards.straightdope.com/u/Santo_Rugger)\ **Post date:** [January 22, 2009, 2:37pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/8 "2009-01-22T14:37:22Z")
Easy. It’s what those guys said! 😛 ---
**Author:** ![BellRungBookShut-CandleSnuffed](https://avatars.discourse-cdn.com/v4/letter/b/bcef8e/32.png) [@BellRungBookShut-CandleSnuffed](https://boards.straightdope.com/u/BellRungBookShut-CandleSnuffed)\ **Post date:** [January 22, 2009, 3:24pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/9 "2009-01-22T15:24:26Z")
I found the first one easier than the second. I was trying to remember how to graph inequalities, and then how to interpret the intersections of two inequalities graphed together. Then I gave up. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [January 22, 2009, 3:24pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/10 "2009-01-22T15:24:56Z")
> [@Salem](#): > > it won’t effect the rest … Affect. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [January 22, 2009, 4:23pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/11 "2009-01-22T16:23:14Z")
Math geek here, did it without external calculating aids other than a text scratchpad. Work is in spoilers 1: smallest area - 1 by 24 - 24 largest area - 12 by 13 - 6 + 20 + 30 + 100 = 156 difference - 132 D 2: smallest n - 300 largest n - 333 inclusive difference - 34 E ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [January 22, 2009, 4:36pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/12 "2009-01-22T16:36:36Z")
:smack::smack: ---
**Author:** ![DanBlather](https://avatars.discourse-cdn.com/v4/letter/d/f4b2a3/32.png) [@DanBlather](https://boards.straightdope.com/u/DanBlather)\ **Post date:** [January 22, 2009, 6:59pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/13 "2009-01-22T18:59:31Z")
> [@chrisk](#): > > :smack::smack: Me too. Guess we both failed the reading comprehension part. I hated both of those questions. They are too “mathy” and not at all the sort of thing one would do in real life. If I was a kid I’d be bored in a class that taught those sorts of questions. At the very least have something like “you have 50 feet of fringe. What is the largest and smallest quilt you could make from 1 foot squares.” ---
**Author:** ![Sublight](https://avatars.discourse-cdn.com/v4/letter/s/439d5e/32.png) [@Sublight](https://boards.straightdope.com/u/Sublight)\ **Post date:** [January 23, 2009, 11:23am UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/14 "2009-01-23T11:23:30Z")
#3 basically reduces to “for what x are x and 9x both 3-digit numbers?” 100 x 9 = 900 111 x 9 = 999 ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [January 23, 2009, 11:36am UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/15 "2009-01-23T11:36:16Z")
> [@DanBlather](#): > > Me too. Guess we both failed the reading comprehension part. > > I hated both of those questions. They are too “mathy” and not at all the sort of thing one would do in real life. If I was a kid I’d be bored in a class that taught those sorts of questions. At the very least have something like “you have 50 feet of fringe. What is the largest and smallest quilt you could make from 1 foot squares.” I got 33 too. And I’m a teacher :o I agree with your idea of making questions more real life. How about: 1. You are a drug dealer and have 50 feet of fencing. What is the largest area you can surround to grow your product in? :eek: ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [January 23, 2009, 1:51pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/16 "2009-01-23T13:51:11Z")
> [@Sublight](#): > > #3 basically reduces to “for what x are x and 9x both 3-digit numbers?” Except it doesn’t, as demonstrated by the correct answers in spoiler boxes. Question 3 is a particularly nasty question, and it really tests the reader’s reading comprehension and logical reasoning more than it does any particular learned math skill. ---
**Author:** ![Ximenean](https://avatars.discourse-cdn.com/v4/letter/x/aca169/32.png) [@Ximenean](https://boards.straightdope.com/u/Ximenean)\ **Post date:** [January 23, 2009, 2:21pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/17 "2009-01-23T14:21:07Z")
> [@RickJay](#): > > Except it doesn’t, as demonstrated by the correct answers in spoiler boxes. > > Question 3 is a particularly nasty question, and it really tests the reader’s reading comprehension and logical reasoning more than it does any particular learned math skill. Unless you’re quibbling that it should be “for how many values of x are x and 9x both 3-digit numbers”, or that it doesn’t explicitly say that the numbers must be positive, I don’t see what is wrong with **Sublight** ’s assertion. Set n = 3x and substitute into the original question, it’s equivalent. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 23, 2009, 3:20pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/18 "2009-01-23T15:20:57Z")
> [@DanBlather](#): > > I hated both of those questions. They are too “mathy” and not at all the sort of thing one would do in real life. If I was a kid I’d be bored in a class that taught those sorts of questions. At the very least have something like “you have 50 feet of fringe. What is the largest and smallest quilt you could make from 1 foot squares.” And I enjoyed the questions. Which I guess is what separates the pure mathematicians from the applied mathematicians. The pure mathematicians know that 2 + 3 = 5. The applied mathematicians know that $2 + $3 = $5. [QUOTE=Salem] This is from a standardized test, too, so the implications go beyond this particular classroom. Hopefully there’s an easy explanation and it won’t effect the rest of the entire math-test-taking world… [/QUOTE] Yikes; I find this a bit scary. There’s no way anyone should give a standardized/multiple-choice test unless they’re absolutely sure that each question has exactly oe correct answer and that that’s the answer given in the answer key. ---
**Author:** ![John\_DiFool](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_difool/32/19543_2.png) [@John\_DiFool](https://boards.straightdope.com/u/John_DiFool)\ **Post date:** [January 23, 2009, 4:59pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/19 "2009-01-23T16:59:47Z")
These types of questions would be fair game for the SAT (for which I tutor)-I’d probably peg them at a 3 or 4 difficulty (out of 5). Those who chose the wrong answer for #3 did what many of my students do-didn’t read the question carefully enough (the word “integer” is the first thing you look for in such questions). ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [January 23, 2009, 6:15pm UTC](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433/20 "2009-01-23T18:15:44Z")
The first one was easy, the second one I had to read carefully to realize that N was not meant to be the three digit number, but both {X, Y} where X = (n/3) and Y = (3n). [Next page](https://boards.straightdope.com/t/are-you-smarter-than-an-8th-grader-math/482433.md?page=2)