Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
(no subject)
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@pro-ns.net);
by webmail.iphouse.com with HTTP;
Tue, 4 Jul 2006 14:34:33 -0500 (CDT)
Message-ID: <61812.200.165.129.224.1152041673.squirrel@webmail.iphouse.com>
In-Reply-To: <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@pro-ns.net
To: numeracy@europe.std.com
User-Agent: SquirrelMail/1.4.4 [CVS]
X-Mailer: SquirrelMail/1.4.4 [CVS]
MIME-Version: 1.0
Content-Type: text/plain;charset=iso-8859-1
Content-Transfer-Encoding: 8bit
X-Priority: 3 (Normal)
Importance: Normal
X-Spam-Status: No, score=1.0 required=10.0 tests=NO_REAL_NAME autolearn=no
version=3.1.0
X-Spam-Checker-Version: SpamAssassin 3.1.0 (2005-09-13) on pcls4.std.com
X-Virus-Scanned: ClamAV 0.88/1584/Tue Jul 4 10:18:29 2006 on pcls4.std.com
X-Virus-Status: 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 ... one-half divided
> by
> two-thirds; 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@pro-ns.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(Smoker|Man) and P(Man|Smoker)
>> 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(Widow|Suicide) with P(Widower|Suicide).
>> The second compares P(Suicide|Widow) with P(Suicide|Widower).
>>
>> 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 e-mail to
>> -majordomo@world.std.com.
>> -In the body of the message type "unsubscribe numeracy your_address"
>>
>> -If you have any questions e-mail edl@world.std.com
>>
>
> -----------------------------------------------------------------------
> -To unsubscribe from the Numeracy mail list send e-mail to
> -majordomo@world.std.com.
> -In the body of the message type "unsubscribe numeracy your_address"
>
> -If you have any questions e-mail edl@world.std.com
>
>
-----------------------------------------------------------------------
-To unsubscribe from the Numeracy mail list send e-mail to
-majordomo@world.std.com.
-In the body of the message type "unsubscribe numeracy your_address"
-If you have any questions e-mail edl@world.std.com
|
|
|
|
