Re: 'plug & chug' problems - scaling

[Larry Woolf <larry.woolf@GAT.COM>]

-----Original Message-----
From: John S. Denker
Sent: Thursday, July 25, 2002 10:50 AM
Subject: Re: 'plug & chug' problems

Joseph Bellina wrote:
> Interesting comment, in particular the call for proportional reasoning.
> How many people actually attend to that...how many textbooks work on it
> explicitly?  I suspect few.

Probably few.  But there are counterexamples. I
was most certainly taught proportionality, scaling laws,
and qualitative reasoning in general.

To address Joseph's other question:  I have no clue where to
find a textbook discussion of this.  I've just flipped through
the indices in my (rather spotty) collection of textbooks and
have come up with nothing very useful.  David Goodstein _States of
Matter_ has a dozen pages on "scaling laws" at the end, but it's
neither elementary nor up-to-date (it's pre-renormalizaton-group).

snip

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Scaling is apparently discussed in a wide variety of texts:

http://www.enc.org/resources/search/1,1232,search,00.shtm?OFFSET=0&limit=15&;
searchstatus=1&source=search&ip=141.248.78.245&searchtype=simple&WORD=scalin
g&resource=R0&grade=G0&COST=9999&Submit=Submit+search

For example:
Comparing and scaling: ratio, proportion, and percent
ENC#: ENC-021258
Series: Connected mathematics.
Publisher: Prentice Hall
Date: 2002
Ordering Information


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Grades:
7
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Abstract:
This student text with teacher guide, one of the eight CONNECTED MATHEMATICS
PROJECT (CMP) units available for grade 7, features six investigations that
involve comparisons and reasoning with rates, ratios, and proportions. The
CMP series, supported by the National Science Foundation, presents a
complete middle school mathematics curriculum. It emphasizes connections
among the core ideas of mathematics, between mathematics and other subjects,
and among classroom activities and student interests. Each CMP unit, with
investigations supporting problem-centered teaching, breaks instruction into
three phases: launch, explore, and summarize. The developers believe that
this instructional model encourages students to use higher-level thinking
and problem-solving skills and to make sense of mathematics and its uses.
CMP was developed with the belief that calculators should always be
available and that students should decide when to use them.

In a sample investigation fromComparing and Scaling, students estimate the
size of a crowd in a simulated photograph by counting the number of people
in a small area and scaling up. They also gather and analyze data with the
capture-tag-recapture method for counting populations using a simulation
with 100 white beans. These two methods apply reasoning with ratios and
proportions and address questions about population density. The teacher
guide features a section to help teachers use this unit to review basic
facts and maintain students' number skills. Also found are lesson plans,
blackline masters, and suggestions for using embedded assessment, journals,
portfolios, and testing materials. (Author/JRS)

Contents:
[Teacher's guide:]
Unit introduction
 Overview
 Mathematical and problem solving goals
 Summary of investigations
 Connections to other units
 Materials
 Technology
 Pacing chart
 Comparing and scaling vocabulary
 Assessment summary
Introducing your students to Comparing and scaling
Mathematical highlights
Using this teacher's edition
Investigation 1. Making comparisons
 Student pages
 Teaching the investigation
Investigation 2. Comparing by finding percents
 Student pages
 Teaching the investigation
Investigation 3. Comparing by using ratios
 Student pages
 Teaching the investigation
Investigation 4. Comparing by finding rates
 Student pages
 Teaching the investigation
Investigation 5. Estimating populations and population densities
 Student pages
 Teaching the investigation
Investigation 6. Choosing strategies
 Student pages
 Teaching the investigation
Assigning the unit project
Looking back and looking ahead: unit reflections
Assessment resources
Blackline masters
Additional practice
Descriptive glossary
Index

[Student edition:]
Mathematical highlights
Investigation 1. Making comparisons
 Writing ads
 Targeting an audience
 Getting the message across
 Applications, connections, extensions
 Mathematical reflections
Investigation 2. Comparing by finding percents
 Comparing leisure activities
 Comparing your class to the nation
 Applications, connections, extensions
 Mathematical reflections
Investigation 3. Comparing by using ratios
 Mixing juice
 Helping the cook
 Sharing pizza
 Applications, connections, extensions
 Mathematical reflections
Investigation 4. Comparing by finding rates
 Comparing fuel economy
 Using unit rates
 Solving problems with rates
 Buying beads
 Applications, connections, extensions
 Mathematical reflections
Investigation 5. Estimating populations and population densities
 Estimating the size of a crowd
 Estimating a deer population
 Finding population densities
 Comparing the Dakotas
 Predicting traffic jams
 Applications, connections, extensions
 Mathematical reflections
Investigation 6. Choosing strategies
 Scaling up or down
 Using rules of thumb
 Selecting delegates
 Applications, connections, extensions
 Mathematical reflections
The unit project
Looking back and looking ahead: unit reflections
Glossary
Index

Specifications:
1 teacher's guide (166 pages : illustrations ; 28 cm.)
1 student edition (90 pages : illustrations ; 26 cm.)




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