Curr: Math Problems (Middle/High Sch)

Michael Williamson (
Mon, 18 Aug 1995 09:37:13

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From: Michael Williamson <williams@WHALE.SIMMONS.EDU>
Subject: Curr: Math Problems (Middle/High Sch)
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SERC Written Component - Whales (Metric)        Williamson
SERC Mathematics Exercises
Math Component
SERC Program
J. Michael Williamson
Associate Professor - Wheelock College
Associate Director - Mingan Island Cetacean Study
20 Moynihan Rd.            Wheelock College
S. Hamilton, MA 01982      200 Riverway
                           Boston, MA 02215
508/468-4699               617/734-5200, x256
fax: 508/468-0073          617/566-7369
Math Problems
{Download a data entry from the WhaleNet bulletin board for
some of the problems}
1.1 Use the chart to plot the fixes of the cruise.  Draw a
line on the charrt to show the course.  Use an effective
wide of the transect of two miles to either side of the
research vessel.  Draw, with dotted lines, lines
parallel to the research cruise and at a distance of two
Calculate the study area of the research cruise.
% How many miles did the cruise travel?
% Estimate how many square miles was studied.
% How many sightings of each species of whale did we
% How many whales per square mile did we see?
1.2 Use the data table to estime the amount of time that
was effectively spent on the research cruise.
% How many sightings per hour of each species did we
1.3  Using the data that you calculated in 1.1 and 1.2,
how might these ratios be useful in data analysis?
1.4  Create two different displays using the data in 1.1
and 1.2, showing the differences in sighitng frequency
for each of the species of whales.
% Which is easiest to understand?
% What are the advantages of each disply?
2.1  Growth of a Blue Whale.  At the moment of birth a
blue whale calf averages 7 meters long and weighs 3
metric tons.  For the first six months of its life its
average weight gain per day is 100 kilograms.
(assume that every month has 30 days)
What is the estimated weight at the end of:
1 month (30 days)?
2 months (60 days)?
3 months (90 days)?
4 months (120 days)?
5 months (150 days)?
6 months (180  days)?
2.2 Create a display using the data in 2.1 to show the
growth (in weight) of a blue whale calf over time from
birth to six months of age.
2.3  At 100 kilogramss per day, what is the percent
weight gain in a day of the whale's total weight at the age of:
1 day ?
1 month ?
2 months ?
3 months ?
4 months ?
5 months ?
6 months ?
2.4 Create a display using the data in 2.2 to show the
growth (in weight) of a blue whale calf in relation to
the time it grows.
2.5 How does the growth rate change as the calf grows?
Why does the growth rate change if the weight gain
remains the same?
2.5b Create a display using the data in 2.3 to show the
growth (in weight) of a blue whale calf in relation to
the time it grows.
3.1 If a blue whale eats food equivalent to 4% of its body
weight each day how much would a whale eat if it
20 metric tons?
45 metric tons?
50 metric tons?
70 metric tons?
80 metric tons?
100 metric tons?
3.2 How much would a group of three whales eat in a day
if one weighted 70 tons, the second weighed 47 tons, and
the third weighed 67 tons?
How much would they eat in a:
3.3 If a herring weighs an average of  _____ grams
each, how many  herring would the three whales eat in a: