ERIE COMMUNITY COLLEGE
TITLE III
Numeric Skills Assignment
Interdisciplinary Course Materials
Biology
Course:
MT001
Course Outline Topic:
Evaluating percents
Using proportions to solve problems
Reading a graph
Project Title:
The Smokestacks
Project description:
Given case studies, students will use a
‘PredictionNomogram’ to obtain predicted normal values
of a patient’s Forced Vital Capacity (FVC). They will then
evaluate the patient’s actual FVC using a given vitalograph
recording and find percentages comparing the actual
readings to the predicted readings. Students will also use
proportions to evaluate various facts concerning the
dangers of smoking cigarettes.
Author:
Sherri Kobis – North Campus Mathematics Department
Curriculum Expert:
Thomas Franco – North Campus Biology Department
Semester Created:
Spring 2009
A.
Essential Questions
What effects will illness caused from smoking or other factors have on a person’s
breathing? What effects will long term smoking have on a person’s finances and
time?
B.
Introduction
If a person is having difficulty breathing, one thing a doctor may do is perform a
pulmonary function test. This would be a test to check the person’s lungs and
air usage. One test that the doctor could perform would be a test of the person’s
forced vital capacity.
A person’s Forced Vital Capacity (FVC) is the total amount of air that can be
forcibly blown out after taking in a full breath. It is usually released in a period of
6-7 seconds and is measured in liters. Forced Expiratory Volume (FEV) is the
amount of air expelled during specific time intervals of the FVC. FEV1, FEV2,
FEV3, (etc.) is the amount of air exhaled during the first, second, third (etc.)
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second, respectively, of the FVC (measured as a percentage). 75-85% is normal
for FEV1. That is, 75-85% of the forced expiratory volume (FEV) is normally
released during the first second of exhalation.
You can obtain an expected normal value of a person’s forced vital capacity by
using a Prediction Nomogram. To use the Prediction Nomogram (below), you
would find the person’s height on the left and their age on the right. Connect the
height and weight with a straight edge. The expected normal values for that
person’s FVC and FEV1 is found where the straight edge crosses those lines.
Example: To be sure that you understand how to use the prediction nomogram,
use a straight edge to find the predicted normal FVC and FEV1 values for a
male who is 50 years old and 5’10” tall. To do this, you must first change 5’10”
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to all inches. Consider that one foot contains 12 inches. Multiply 5 feet times 12
inches to get 60 inches. Then add the 10 additional inches to obtain 70 inches.
Therefore, 5’10” is the same as 70”. On the prediction nomogram, connect 70”
with 50 years of age using a straight edge. You should see that the straight edge
crosses the FVC line nearest to 4.9 L and the FEV1 line nearest to 3.8 L. So, the
person’s predicted normal FVC value is 4.9 L and predicted FEV1 value is 3.8 L.
A vitalograph recording can be used to find a patient’s actual Forced Vital
Capacity (FVC). The doctor can use a vitalograph recording to determine the
patient’s Forced Expiratory Volume (FEV) during the first, second, third, (etc.)
second. These results can then be compared to the predicted normal values taken
from a prediction nomogram to help determine if the person is ill and/or in need
of respiratory treatment.
C.
Basic Directions
You will first be given case studies for Mr. John Smokestack and his wife, Mary
Smokestack. You will use the prediction nomograms to find their predicted
normal forced vital capacity values given their age and height. You will then read
the doctor’s vitalograph recording to determine their actual forced vital capacity
values. You will use these values to determine if they are able to release the
expected 75-85% of the entire FVC in the first second of exhalation (FEV1).
You will then be given various smoking facts and asked to use proportions to
answer questions.
D.
Things to Learn Before Starting the Project
You must be able to evaluate percents and use proportions to solve problems.
You must also be able to read a graph.
E.
The Project Assignment
Complete all questions in the space provided on this paper. All work must be
shown and completed neatly and in an organized manner.
Part I – Case Studies
First Case Study - Mr. John Smokestack
Mr. John Smokestack arrived at the doctor’s office with a chief complaint of
shortness of breath when climbing stairs. He states that he has a “cold that he
can’t shake”. Significant medical history includes smoking 2.5 packs of cigarettes
per day for 40 years. Mr. Smokestack is 5’8” tall and is 60 years old.
a.
Use the prediction nomogram for males (in the introduction) to obtain his
predicted normal values.
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Predicted Forced Vital Capacity (FVC) = _________ L
Predicted Forced Expiratory Volume in 1 second (FEV1) = _________ L
b.
The doctor performed a vitalograph test on Mr. Smokestack. The actual
vitalograph recording is below.
Using his vitalograph recording, find the FEV1 (the reading on the graph
at one second), FEV3 (the reading on the graph at 3 seconds), and FVC
(the highest air volume exhalation on the graph) to the nearest tenth.
Actual FEV1 = __________ L
Actual FEV3 = __________ L
c.
Actual FVC = __________ L
To make the test results easier to understand, the doctor gives the results
as a percentage of the normal predicted values.
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1. What percent of his predicted FVC did Mr. Smokestack achieve during
his vitalograph test? Round your answer to the nearest hundredth
percent. (Normal value is greater than 80%)
2. What percent of his predicted FEV1 did Mr. Smokestack achieve
during his vitalograph test? Round your answer to the nearest
hundredth percent.
3. Mr. Smokestack should have the ability to exhale 75-85% of his entire
FVC in the first second of exhalation (FEV1). What percentage of the
actual FVC did he exhale during the first second of his vitalograph test
(actual FEV1)? Round your answer to the nearest hundredth percent.
Second Case Study – Mrs. Mary Smokestack
Mrs. Mary Smokestack arrived at the doctor’s office with complaints of always
being tired and never having any energy. She was diagnosed by her doctor with a
sinus infection a few weeks ago and, after taking her prescribed antibiotics, is still
not seeing any relief from the infection. Significant medical history includes
smoking 1.5 packs of cigarettes per day for 20 years. Mrs. Smokestack is 5’1”
tall and is 55 years old.
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a.
Use the prediction nomogram for females (above) to obtain her predicted normal
values.
Predicted Forced Vital Capacity (FVC) = _________ L
Predicted Forced Expiratory Volume in 1 second (FEV1) = _________ L
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b.
The doctor performed a vitalograph test on Mrs. Smokestack. The actual
vitalograph recording is below.
Using her vitalograph recording, find the FEV1 (the reading on the graph
at one second), FEV3 (the reading on the graph at 3 seconds), and FVC
(the highest air volume exhalation on the graph) to the nearest tenth.
Actual FEV1 = __________ L
Actual FEV3 = __________ L
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c.
Actual FVC = __________ L
To make the test results easier to understand, the doctor gives the results
as a percentage of the normal predicted values.
1. What percent of her predicted FVC did Mrs. Smokestack achieve
during her vitalograph test? Round your answer to the nearest
hundredth percent. (Normal value is greater than 80%)
2. What percent of her predicted FEV1 did Mrs. Smokestack achieve
during her vitalograph test? Round your answer to the nearest
hundredth percent.
3. Mrs. Smokestack should have the ability to exhale 75-85% of her entire
FVC in the first second of exhalation (FEV1). What percentage of the
actual FVC did she exhale during the first second of her vitalograph
test (actual FEV1)? Round your answer to the nearest hundredth
percent.
Part II – Questions
Set up a proportion to solve each of the questions below. Solve the proportion to find
the answer. You must show all work on this sheet.
1.
Mr. Smokestack smokes 2.5 packs of cigarettes each day. If there are 20
cigarettes in one pack, how many cigarettes does he smoke each day?
Multiply this answer by 365 days to see how many cigarettes Mr.
Smokestack smokes in a year!
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2.
It takes approximately 7 minutes to smoke 1 cigarette (this includes
walking outside, smoking the cigarette, chatting with fellow smokers, and
returning to your job or activity). At 50 cigarettes per day, approximately
how many minutes are spent smoking per day?
Divide this answer by 60 minutes to determine approximately how many
hours of Mr. Smokestack’s day is spent on smoking.
3.
Assuming the cost of 1 pack of cigarettes is approximately $5.00 and Mr.
Smokestack smokes 2.5 packs per day, how much does he spend on
cigarettes each day?
Multiply this answer by 365 days to determine how much money Mr.
Smokestack spends on cigarettes in a year. (What a waste of money! Not
to mention the irreversible damage he has done to his lungs!)
F.
Student Resources
MT001 or MT006 Textbook
G.
Faculty Resources
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H.
Grading Rubric
Suggested point values given with each answer below for a total of 50 points
Part I – Case Studies
First Case Study - Mr. John Smokestack
a.
Predicted Forced Vital Capacity (FVC) = 4.3 L
Predicted Forced Expiratory Volume in 1 second (FEV1) = 3.2 L
(+2)
(+2)
b.
Actual FEV1 = 1.0 L
Actual FEV3 = 1.7 L
Actual FVC = 1.8 L
(+1)
(+1)
(+1)
c.
1. 41.86%
(+4)
2. 31.25%
(+4)
3. 55.56%
(+4)
Second Case Study – Mrs. Mary Smokestack
a.
Predicted Forced Vital Capacity (FVC) = 2.9 L
(+2)
Predicted Forced Expiratory Volume in 1 second (FEV1) = 2.4 L (+2)
b.
Actual FEV1 = 1.4 L
Actual FEV3 = 2.1 L
Actual FVC = 2.5 L
(+1)
(+1)
(+1)
c.
1. 92.59%
(+4)
2. 66.67%
(+4)
3. 56%
(+4)
Part II - Questions.
1.
2.
3.
50/day, 18,250/year
350 minutes/day, approximately 5.8 hours/day
$12.50/day, $4562.50/year
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(+4)
(+4)
(+4)