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School-ish stuff - The Phantom Librarian
Spewing out too many words since November 2003
School-ish stuff
I forgot how to do cross-multiplication.

We were between tutors at the library and a kid came up needing someone to explain (verbally) what his teacher needed on a math assignment (converting feet to miles and so on). I knew how to do the conversions and could explain it, but he was supposed to do it by cross multiplying, and I've utterly forgotten how to do that.

And on the academic line, during my translation question, the issue of a comm for people who want to learn Latin came up. Anyone with a good idea on a pedagogy for learning a foreing language on an LJ comm?
21 comments or Leave a comment
alphabet26 From: alphabet26 Date: February 7th, 2006 04:57 am (UTC) (Link)
Well, if it's more complicated than:
1/8 x 3/5
and you multiply the 1 and the 5 and the 3 and the 8, then I have, too.

If it's not, then go me!
fernwithy From: fernwithy Date: February 7th, 2006 05:02 am (UTC) (Link)
It was 10,000 ft.=_____miles, and he was supposed to express it as cross-multiplied fractions. I know it's 10000/5720 (or whatever the foot-to-mile is; the chart was on the top of the paper), but I couldn't figure where it all went fractionally. I could do it like 5720:1 :: 10000:x, or 5720/1=10000/x, but I forget how to cross multiply the thing to figure for X.
alphabet26 From: alphabet26 Date: February 7th, 2006 05:19 am (UTC) (Link)
Oh, I see...yeah, misunderstood what you were needing to do.

(And I only know the mile thing because I lived by the Mile High City, and if you didn't know that...)
dudley_doright From: dudley_doright Date: February 7th, 2006 05:54 am (UTC) (Link)
sam/ainsley is my favorite ever =D
alphabet26 From: alphabet26 Date: February 7th, 2006 06:09 am (UTC) (Link)
I love Sam and Ainsley and it's my hope that we see them, together, now that the show is ending. I can't imagine that it will truly happen, but I'm allowed a fantasy, darn it all.

Hi, Fern!
waterofthemoon From: waterofthemoon Date: February 7th, 2006 06:56 am (UTC) (Link)
You had it set up right... so you have:

5720    10000
----- = ------
  1         x

then multiply across the diagonals, so you have:

5720x = 10000

and then divide it out so you get x by itself:

x = 10000/5720, or 1.748

Except Google says that's not the right answer (it's actually 1.893 miles), so I think the 5720 part is off. But that's how you would do it, as far as I remember from years of compulsory math classes.
waterofthemoon From: waterofthemoon Date: February 7th, 2006 07:15 am (UTC) (Link)
I got overly curious and finally managed to look it up - it's 5280 feet to the mile, and plugging that number in makes the equation come out all right. Thanks for this little brain exercise, anyway. :)
dudley_doright From: dudley_doright Date: February 7th, 2006 05:09 am (UTC) (Link)
actually if you multiply the 1 and the 5 and then the 3 and the 8, you'd get 1/8 % 3/5

kindly pretend the % is a division sign =)
dudley_doright From: dudley_doright Date: February 7th, 2006 05:03 am (UTC) (Link)
...do you still want to know cross-multiplication?

It sounds like what he's talking about is the thing where you have say..1.7 miles and then you basically multiply by 1. since you're multiplying by one, the value doesn't change.

1.7 miles * 5280 ft * 12 in
-----------1 mile----1 ft

1.7 miles * 5280 ft * 12 in = 107,712 in
-----------1 mile----1 foot

unless he's talking about cross-multiplying vectors in space in which case that's entirely different.

Of course, cross multiplication is now unnecessary because you can go to google and type "1.7 miles in inches" or for that matter "6 cubits and a span in light years" and get an answer.

Goliath was in fact 3.1413 times 10^-16 light years high.
dudley_doright From: dudley_doright Date: February 7th, 2006 05:04 am (UTC) (Link)
I should like it to be known that I spent a while formatting this so the fractions would line up in the preview, even though they look completely screwed up on the actual page
cambryn From: cambryn Date: February 7th, 2006 06:07 am (UTC) (Link)
As far as learning the foreign language goes-
I believe it would be best to run it much like you would the class room.
Getting a Latin I book would be helpful, as it has simple sentences, and helps you to learn the cases.

I believe that the books I learned form, and are very widely used, were published by Cambridge publishing, but I'm not sure.
You could cover one - three chapters each month, depending on how advanced and complicated they are. Sharing a Latin 'quote of the day' is always fun, as is learning some of the history and mythology. :)
From: (Anonymous) Date: February 7th, 2006 08:32 am (UTC) (Link)
Good morning. I can't help with miles and feet and so because I was born into the decimal metric sistem, but we have been doing a lot of cross multiplying since the change of our national coin to euros. The general explanation is as follows:

You know that ONE amount of something (miles, pesetas, stones, pounds, celsius degrees...) is
equivalent to AN EXACT AMOUNT of the unit you want to convert into. I'm using 1 as the first amount because it is easier, but it works with any equivalence:

1----> "A"

for instance, with pesetas and euros:

1 euro-------> 166,386 ptas.

Then, you have a second amount of the first unit that you want to convert into the second unit. The result you're looking for is called "X":

"B"-----> "X"

50 euros------> "X"

Then you have:


Then, you isolate the "X" . X = (B x A)/1

1--> 166,386
50-> X------------> x= 50 x 166,386/in this case, divided by one, but as said, works with any equivalence. And also, the "X" can be any of the four elements (you can be looking for any of them). The trick is to have very clear WHERE EACH ONE IS PLACED (which means understanding equivalences).

Sorry, the ", " means decimal, not thousands.

I hope it is clear. You see, I'm a teacher at the university and I HAVE HAD TO EXPLAIN THIS TO FIRST YEAR STUDENTS SEVERAL TIMES !!!!! Have you ever heard about the PISA REPORT? (This country is queuing in education...sob..sob...sob

About latin, I'm intrigued about how easy it is for you English speaking people. My mother tongue comes from latin and so, the tremendous amount of verbal tenses we use come form latin verbs conjugations, as well as the roots of a huge amount of words, so I figure it is easier. Nevertheless, when I was at school it was compulsory only one year, and that was what I took. I can, more or less, understand a building plaque (never read a book) and of course I'm unable of translating into latin. At present it is even possible that there isn't even one compulsory year...But I often recognize it was one of the most useful things I learned at school. It has been very useful for studing other foreign languages, as well as understanding the original meaning of a lot of sentences and words we use.

Have a nice day

snorkackcatcher From: snorkackcatcher Date: February 7th, 2006 05:48 pm (UTC) (Link)
You see, I'm a teacher at the university and I HAVE HAD TO EXPLAIN THIS TO FIRST YEAR STUDENTS SEVERAL TIMES !!!!!

Not mathematics students, I hope. :)

This is such basic algebra that after a little while, students hopefully get so used to it, it becomes virtually instinctive. I remember having to explain it to someone who was doing GCSE (UK) and actually having to stop and think what the theory behind it was!
fernwithy From: fernwithy Date: February 7th, 2006 06:44 pm (UTC) (Link)
Yeah, the problem with the problem set was less figuring out what to do as it was doing the expression. I could do the answers in my head, but I could figure out where they were all supposed to go in the "show your work" part of the program. The kid didn't understand it at all, so I think I at least got the principle across to him, but he was sure that the answer was supposed to be phrased as a fraction, and I totally drew a blank on what the teacher wanted. (That, added to paranoia after learning that a young friend was supposed to do her arithmetic left to right rather than right to left and her mother had gotten a wrist-slap for trying to explain the old way, kept me from saying, "Oh, just answer it.")
From: underaloggia Date: February 7th, 2006 02:15 pm (UTC) (Link)
The standard college textbook for Latin is Wheelock, currently in its Nth edition--it's a Textbook, with a capital T, but it's thorough. You'd probably want to get hold of a basic grammar (like Allen and Greenough) to go with it. I would suggest setting a specific time in which to cover a chapter (2 weeks? a month? depending on how fast you want to go), and then encourage people to share tips, answers, help, etc. on the comm. You'd probably also want to get someone who knows Latin to mod it, so that if the group as a whole ran into broader questions, you'd have an Authority to ask, and so that he/she could recommend outside readings and/or websites. Not sure I'm volunteering: I'm a medievalist, and after many years I'd characterize my Latin as intuitive ("hm, given the rest of the sentence, that word should function as an ablative, so I'm going to call it an ablative whether it actually is or not...") but maybe I need the practice? Anyway, that's what I'd suggest on a logistical level.

sannalim From: sannalim Date: February 7th, 2006 03:44 pm (UTC) (Link)
I used Wheelocks when I took Latin as a fun class during my senior year of undergrad, five years ago. I've kind of wanted to go through the book again and learn the Latin more thoroughly--and having a community to study with and help keep me on-track would be great.
fernwithy From: fernwithy Date: February 7th, 2006 03:50 pm (UTC) (Link)
I just put our library's copy of Wheelock on hold. I guess there's no way around everyone working with the same book.
hermia7 From: hermia7 Date: February 7th, 2006 08:55 pm (UTC) (Link)
I'll reiterate here what I said in the other thread, since i doubt many interested parties saw it—Wheelock's 6th edition is $19 on Amazon, and if we wanted to use it with the accompanying workbook, the pair is $31. Not *too* bad, especially compared to continuing ed classes!

hermia7 From: hermia7 Date: February 7th, 2006 08:58 pm (UTC) (Link)
Hmm, an addendum. It seems Grote's companion to Wheelock is the self-taught latin learner's tool of choice, but it's much more expensive:

Any Latin students out there who have experience with the various companions and workbooks?
terrathree From: terrathree Date: February 7th, 2006 10:22 pm (UTC) (Link)
I'd recommend Grote's companion for this kind of mostly-self-study setup. Quite simply, I'm teaching one of my Latin classes from Wheelock this year (high school, honors class, mostly sophomores), and Grote's is my reference book for when I'm in doubt about how to teach a particular topic out of Wheelock. It's good for extra practice and helping you to make connections between a new grammar topic and whatever related topics came up several chapters ago.
terrathree From: terrathree Date: February 7th, 2006 10:35 pm (UTC) (Link)
I wouldn't mind helping out with the community. (Yes, silly me, I don't do enough teaching during the day at school...*G*) I'm really not sure how I would recommend pacing the work...I think the usual routine on the Latinstudy mailing lists, though, is that a chapter is assigned, everyone works out their translations and posts them, and then the group can compare everyone's results and discuss any variations to figure out what it should be. At least, that's the pattern for the advanced groups that are translating whole texts of Latin. For Wheelock, each chapter has a grammar explanation (and on the whole these are very lucid and readable), then a list of new vocabulary words, then sentences to translate for practice, then (in most chapters) some sentences adapted or, in many cases, quoted without change from authentic Latin authors for more practice. Most chapters also have a paragraph-length reading, also adapted from an authentic author; sometimes there's a short poem after that; a section on Etymology pointing out important English derivatives of words in the vocabulary and practice sentences; and my favorite, each chapter ends with "Latina est Gaudium - et Utilis!", or "Latin is Fun - and Useful!" which points out fun, and useful, random facts about things in the lesson, e.g. pseudo-Latin quotes like "Semper ubi sub ubi" or strange derivatives, or conversational Latin phrases...it really is fun stuff. Anyhow, given that chapter setup, you could give a week or two for the chapter, during which everyone reads the grammar, etymology, Latina est Gaudium, etc. and then translates the practice sentences and posts their work. After everyone's posted, you could discuss any points where people differed.

Incidentally, if Wheelock is chosen for the community's text, you'll find its website at http://www.wheelockslatin.com/ very helpful. Audio files for pronunciation, links to web sites with practice and review games, etc. And I keep a list at http://www.hse.k12.in.us/staff/rbush/latin_ii_h_practice.htm of review games from Quia.com et al. for Wheelock.
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