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Esther D Leonelli

Posts: 391
Registered: 12/4/04
(no subject)
Posted: Jul 5, 2006 8:35 AM
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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
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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
>>
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>
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