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Posted:
Jul 5, 2006 8:35 AM


Received: from TheWorld.com (pcls4.std.com [192.74.137.84]) by europe.std.com (8.12.8p1/8.12.8) with ESMTP id k64JkAkC018875 for <numeracy@europe.std.com>; Tue, 4 Jul 2006 15:46:11 0400 (EDT) Received: from oxygen.iphouse.net (oxygen.iphouse.net [216.250.190.150]) by TheWorld.com (8.12.8p1/8.12.8) with ESMTP id k64JYYFK027121 for <numeracy@europe.std.com>; Tue, 4 Jul 2006 15:34:34 0400 Received: from webmail.iphouse.com (localhost [127.0.0.1]) by oxygen.iphouse.net (Postfix) with ESMTP id 9FAB81F1ADD; Tue, 4 Jul 2006 14:34:33 0500 (CDT) Received: from 200.165.129.224 (SquirrelMail authenticated user milo@prons.net); by webmail.iphouse.com with HTTP; Tue, 4 Jul 2006 14:34:33 0500 (CDT) MessageID: <61812.200.165.129.224.1152041673.squirrel@webmail.iphouse.com> InReplyTo: <004001c69e35$0113d4d0$1ed4de40@marknrachel> References: <11058218.1151401422464.JavaMail.jakarta@nitrogen.mathforum.org> <44A1594D020000BF00001C03@NCS2.RDALE.K12.MN.US> <6.2.1.2.2.20060627214457.036e23f0@pop.iphouse.com> <004001c69e35$0113d4d0$1ed4de40@marknrachel> Date: Tue, 4 Jul 2006 14:34:33 0500 (CDT) Subject: Re: Fractions and Statistics From: milo@prons.net To: numeracy@europe.std.com UserAgent: SquirrelMail/1.4.4 [CVS] XMailer: SquirrelMail/1.4.4 [CVS] MIMEVersion: 1.0 ContentType: text/plain;charset=iso88591 ContentTransferEncoding: 8bit XPriority: 3 (Normal) Importance: Normal XSpamStatus: No, score=1.0 required=10.0 tests=NO_REAL_NAME autolearn=no version=3.1.0 XSpamCheckerVersion: SpamAssassin 3.1.0 (20050913) on pcls4.std.com XVirusScanned: ClamAV 0.88/1584/Tue Jul 4 10:18:29 2006 on pcls4.std.com XVirusStatus: Clean
I liked your word problem 1. Jane is 1/2 as old as Tom; Mary is 2/3 as old as Tom. How old is Jane compared to Mary? These comparisons are simple ratios so the inversion is straightforward. 2. ´Mary is 2/3 as old as Tom` becomes ´Tom is 1.5 times as old as Mary.` Either way, the answer is, ´Jane is 3/4 as old as Mary.´
The problem becomes more difficult using percentage change. 3. Jane is 50% younger than Tom; Tom is 50% older than Mary. Does this mean that Jane is the same age as Mary? No.
Again, wording makes a difference. =================================================== > Interesting discussion about fractions; let me tell you what my students > have taught me. > > What they say is "It's not about fractions; it's notation". Those aren't > their exact words, but whether doing operations with fractions, or using > them in equations, or word problems, or any time they appear, students > have > trained me to explain carefully what the problem means. For example (a > simple one), when you have 1/2 divided by 2/3, this can be expressed many > ways. What I found is that typically the first thing they do is search for > the rule. I've learned to ask them to put down their pencils and pens and > stare at the problem and converse with themselves  "what's the problem > asking me to do?" In essence, know what the notation (think about how many > ways this problem can be written, directly and indirectly) is specifying; > what is the relationship; can you visualize the problem; can you maybe > draw > a picture? Then, pick up your tools and go to work. The notation: (I don't > have the capacity to produce all the characters, but ... onehalf divided > by > twothirds; 1/2 / 2/3; one stick is 1/2 foot long, a second one is 2/3 of > a > foot long; if you lay them end to end, what length have you? Jane is 1/2 > as > old as Tom; Mary is 2/3 as old as Tom. How old is Jane compared to Mary? > and > on and on. > > The point isn't fractions (or equations or integers or ...); it's notation > and understanding what it's asking you to do ... mark >  Original Message  > From: "Milo Schield" <milo@prons.net> > To: <numeracy@europe.std.com> > Sent: Tuesday, June 27, 2006 11:03 PM > Subject: Fractions and Statistics > > >> The concepts of fractions, decimals and percents are important >> in statistics where they can reflect conditional probabilities. >> >> Consider these phrases: >> 1. The percentage of men who are smokers >> 2. The percentage of men among smokers >> This is the difference between P(SmokerMan) and P(ManSmoker) >> where the vertical bar means "given that." >> >> Consider these two statements: >> 3. Widows are more likely among suicides than widowers. >> 4. Widows are more likely to commit suicide than widowers. >> The first compares P(WidowSuicide) with P(WidowerSuicide). >> The second compares P(SuicideWidow) with P(SuicideWidower). >> >> In both cases, small differences in syntax can reflect big differences >> in >> semantics. This focus on ordinary English to express these algebraic >> relationships is the basis for statistical literacy. And since students >> will encounter these ordinary English statements in the everyday news, >> they must understand these differences if they are to be numerate. >> >> Milo Schield >> www.StatLit.org >> >>  >> To unsubscribe from the Numeracy mail list send email to >> majordomo@world.std.com. >> In the body of the message type "unsubscribe numeracy your_address" >> >> If you have any questions email edl@world.std.com >> > >  > To unsubscribe from the Numeracy mail list send email to > majordomo@world.std.com. > In the body of the message type "unsubscribe numeracy your_address" > > If you have any questions email edl@world.std.com > >
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