Math 105 Guidelines for Team Homework
Overview
Successful teams meet at least twice during the week. Before the first meeting, try to get as far as you can individually
on each of the problems in the set. The major amount of the work should be accomplished at the first meeting.
Each person on the team should come to the first meeting having worked hard on each problem--with some questions to
ask others in the group.
Before the second meeting, the Scribe should write a rough draft of the homework. During this meeting, the team
should help to refine the draft so that the finished problems will be
polished and an acceptable final product for the group.
When the homework is due, one set of the solutions (typed is preferable) should be submitted at the
beginning of the class period. Your instructor may have specific guidelines he or she requires for your class, so if you have questions regarding solution submissions, please direct such questions to your instructor. The solutions should be written by the Scribe, and accompanied by a cover sheet
written by the Reporter. Both the solutions and the cover sheet should be neat, legible, and with attention
to correct English. No late or partial solution sets will be accepted.
The reporter's cover sheet should list each person's role and include: (1) Dates, times, and location of your meetings;
(2) Each member's participation (you may give names or not, as you choose); (3) Comments on how the group worked together;
(4) Comments you may want to include regarding the course or assignment in general.
Scribes should write up the solutions as if other students were the audience. Pretend you are explaning your thinking
to another student who had to miss class. Start each solution with a paraphrasing of the problem (e.g. "We are to find...").
Define your variables and functions precisely (with units where appropriate), and write the algebra and precalculus in complete
(mathematical) sentences. Include neat, clearly labeled graphs whenever you possibly can, even if the problem does not specifically
ask for them. Finally, think back on the main idea of the problem and state a summary of your conclusions.
See below for some formatting suggestions, and also see the excellent tutorial on writing team homework, available at http://instruct.math.lsa.umich.edu/support/teamhomework/.
Format
The homework you hand in should be neat, organized, and legible. Every
solution should contain a version of the problem statement from the book.
Your version can be a summary, as long as you have included all
mathematically important pieces and captured
the general flavor of the problem.
For example, Section 3.3 #40 (p. 130, 3rd edition), which reads:
Three scientists, working independently of each other,
arrive at the following formulas to model the spread of
a species of mussel in a system of fresh water lakes:
f1(x)=3(1.2)x,
f2(x)=3(1.21)x,
f3(x)=3.01(1.2)x,
where fn(x), n=1,2,3, is the number of individual mussels (in 1000s) predicted by
model number n to be living in the
lake system after x months have
elapsed.
(a) Graph these three functions for x
between 0 and 60, inclusive, y between
0 and 40,000, inclusive.
(b) The graphs of these three models do not seem all that different
from each other. But do the three functions make significantly
different predictions about the future mussel population? To answer
this, graph the difference function,
f2(x)-f1(x),
of the population sizes predicted by models 1 and 2,
as well as the difference functions,
f3(x)-f2(x)
and
f3(x)-f1(x).
(Use the same window as in part (a).)
(c) Based on your graphs in part (b), discuss the assertion
that all three models are in good agreement as far as long-range
predictions of mussel populations are concerned. What conclusions
can you draw about exponential functions in general?
One acceptable way to
summarize the problem for your homework write-up is:
Three scientists find models for the spread of mussels in a lake system. The models they found are:
f1(x)=3(1.2)x,
f2(x)=3(1.21)x,
f3(x)=3.01(1.2)x,
where each fn(x)
gives the population of mussels (in 1000s), predicted by
model n, living in the lake system
x months after the beginning of the project.
(a) The graphs of the three functions for x
between 0 and 60, inclusive, y between
0 and 40,000, inclusive, are show below.
[ Show the graphs, labeling the axes and important features.]
(b) Graphs showing the differences, f2(x)-f1(x),
f3(x)-f2(x),
and
f3(x)-f1(x) are given below, using the same window as in part (a).
[ Show the graphs, labeling the axes and important features.]
(c) We are asked whether the models are in good agreement about long-range
predictions of mussel populations. By looking at the graphs in part (b), we found [ your team's well-written observations here...].
From our observations, our team came to the supposition that in general exponential functions [your team's well-written conclusions here...].
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