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Math-in-CTE Lesson Plan Template
Lesson Title: Infection Control & Safety
Lesson # 5
Author(s):
Gabriele Coslop
Phone Number(s):
(856) 692-8490
E-mail Address(es):
[email protected]
(609) 427-6196
[email protected]
Stefanie Villano-Boyd
Occupational Area: Dental
CTE Concept(s): Growth of bacteria.
Math Concepts: Exponential Functions
Lesson Objective:
Students will be able to demonstrate a working knowledge of math concepts regarding exponential functions and
and its application to the growth of bacteria in the dental/medical field.
Supplies Needed:
calculator
THE "7 ELEMENTS"
TEACHER NOTES
(and answer key)
1. Introduce the CTE lesson.
Ask: What is the best way to fight transmission of infection?
The students will probably mention things like hand washing, hand
sanitizers, personal protective wear (gloves, mask, eye wear, etc.)…
Today we are going to talk about the importance of hand washing in
order to break the chain of infection in the workplace.
Ask: What is the percentage of the population who wash their hands
after they use the restroom?
Only 40% of the population wash their hands after they use the
bathroom.
Ask: Lets break it down further, what percentage of high school female Only 58% of High School females wash their hands after using the
and male students wash their hands after using the restroom?
restroom, and only 48% of High School boys wash their hands after
using the restroom.
The spread of bacteria is not only restricted to individuals who do not
wash their hands after using the bathroom, only 30% of the population
wash their hands after coughing or sneezing.
Because of this, the spread of bacteria is rapid and its growth is
exponential.
2. Assess students’ math awareness as it relates to the CTE
lesson.
In the laboratory, a growing bacterial population doubles at regular
intervals. Growth is by a geometric progression: 1, 2, 4, 8, etc. or 20,
21, 22, 23.........2n (where n = the number of generations). This is called
exponential growth. In reality, exponential growth is a only part of the
bacterial life cycle, and not representive of the normal pattern of growth of
bacteria in nature.
Ask: What do you think the typical bacterial growth curve looks like?
Have students pick their brains on what they think the typical growth
curve looks like. Tell students there are different stages of a
bacteria’s growth- there is the lag stage, the exponential stage,
stationary stage, and the death stage. This information may help
them produce the proper curve.
Ask: Why is 2n an exponential function?
Students should be able to say that as the value of n increases, the
resultant is a greater number each time and the value doubles in
size each time.
Ex: 1, 2, 4, 8, 16, 32, 64,…
Let’s consider this problem: Suppose your neighbor says that he will
give a penny on the first day you water his flowers. If you continue this
work for thirty consecutive days, he will double the previous day’s pay.
How much money could you possibly earn after 30 days of consecutive
work?
Students will luckily be amazed by this number. Explain to them that
exponential functions drastically increase because of the exponent in
the equation-the larger the exponent, the more drastic the change.
2^30 = 1,073,741,824 pennies = $10,737,418.24
How is this possible?
Students should have the knowledge to fill in the blanks:
The formula for bacterial growth is represented by the equation
G=growth
G = a(1 + r) ^ t. The ^ symbol, also known as the carot button, means a=number of bacteria at the beginning of the time interval
raised to. Therefore, the t is exponent of the (1 + r).
r=rate
Ask: What do you think the G, a, r, and t represent in the function?
t=time (in minutes)
Students should be able to explain that it is a formula used to
calculate interest that is compounded over a period of time.
Ask: What is compound interest?
Remind students that the formula for compound interest is:
A=P(1 + r) ^ n
Where
P is the principal (the initial amount you borrow or deposit)
r is the annual rate of interest (percentage)
n is the number of years the amount is deposited or borrowed for.
A is the amount of money accumulated after n years, including
interest.
This formula directly correlates to the growth formula where
Growth = Amount
a=P
r=r
t=n
3. Work through the math example embedded in the CTE lesson.
Let’s say that we had a patient who is sitting in a dental chair and
coughs into his hands and then proceeds to touch the armrest of the
dental chair. The initial bacteria amount is 2500 colonies, the rate of G=?
growth is 2.8%. How many bacterial colonies will be present after 15
a=2500
minutes?
r=2.8% = 2.8/100=0.028
t=15 mins
G = a(1+r)^t
G=2500(1+0.028)^15
G=2500(1.028)^15
G=2500(1.5132) = about 3,783 bacterial colonies
So originally, the initial amount of bacterial colonies was 2500 and
after fifteen minutes, the amount of colonies grew to 3,783.
Okay, how many colonies will be present after 30 minutes?
G=?
a=2500
r=2.8% = 2.8/100=0.028
t=30 mins
G = a(1+r)^t
G=2500(1+0.028)^30
G=2500(1.028)^30
G=2500(2.2898) = about 5,724 bacterial colonies
G=?
How many colonies will be present after 45 minutes?
a=2500
r=2.8% = 2.8/100=0.028
t=45 mins
G = a(1+r)^t
G=2500(1+0.028)^45
G=2500(1.028)^45
G=2500(3.4649) = about 8,662 bacterial colonies
4. Work through related, contextual math-in-CTE examples.
1.) A dental hygienist does not use the proper sterilization process G=?
to clean a certain dental instrument. Currently, there are 1,256
bacteria colonies present on the instrument. If the rate of a=1,256
growth is 3.5%, how many colonies will be present after 15
r=3.5% = 3.5/100=0.035
minutes?
t=15 mins
G = a(1+r)^t
G=1,256(1+0.035)^15
G=1,256(1.035)^15
G=1,256(1.6753) = about 2,104 bacterial colonies
a.) How many colonies will be present after 30 minutes?
a.)
G=?
a=1,256
r=3.5% = 3.5/100=0.035
t=30 mins
G = a(1+r)^t
G=1,256(1+0.035)^30
G=1,256(1.035)^30
G=1,256(2.8068) = about 3,525 bacterial colonies
2.) Johnny is waiting for the hygienist to develop his x-rays. He
decides to explore the room around him while he waits and
begins playing around with the oral evacuator. At the time,
Johnny has about 6,300 bacterial colonies on his hands. Thirty
minutes later, the hygienist uses the same oral evacuator in
Johnny’s mouth. If the growth rate of the bacteria is 4.6%, how
many bacterial colonies are present at the time it is placed in
Johnny’s mouth?
2.) G=?
a=6,300
r=4.6% = 4.6/100=0.046
t=30 mins
G = a(1+r)^t
G=6,300(1+0.046)^30
G=6,300(1.046)^30
G=6,300(3.8543) = about 24,282 bacterial colonies
3.) Dr. Rebecca, sneezes into the sleeve of her shirt. The growth rate is 3.) G=49,000
3.2%. After 25 minutes, the bacterium on her shirt grows to 49,000
colonies. What was the initial amount of bacteria on Rebecca’s shirt a=?
from her sneeze?
r=3.2% = 3.2/100=0.032
t=25 mins
G = a(1+r)^t
49,000=a(1+0.032)^25
49,000=a(1.032)^25
49,000=a(2.198)
49,000/2.198=a
a = 22,293 bacterial colonies
5. Work through traditional math examples.
At age 27, Jill deposited $4,000 into an IRA, where it
earns 2.875% interest compounded yearly. What will it be
3.)
worth when she retires at sixty-five?
3.) P = 4000
r = 2.875% = 2.875/100 = 0.02875
65-27 = 38 years
So, n = 38
A = P(1 + r) ^ n
A = 4000(1+0.02875)^38
A=4000(1.02875)^38
A=4000(2.9361)
A= $11,744.49
4.) P = 5,000
r = 5% = 5%/100 = 0.05
4.) What is the value after 8 years of $5,000 invested at
5% annual interest compounded yearly?
n=8
A = P(1 + r)^n
A = 5,000(1 + 0.05)^8
A = 5,000(1.05)^8
A=5,000(1.4775)
A=$7,387.28
6. Students demonstrate their understanding.
Ask: What have you learned about the growth of bacteria? Why is it so Listen to the students discussion and answer any questions that they
important that we maintain a clean and disinfected workplace?
may have.
Ask: If you were an office manager, how would you instill the
importance of infection control regarding bacteria growth to a new
Students complete the attached worksheets independently or with a
employee?
partner.
7. Formal assessment.
Students have completed the worksheet and we review it together as a Quiz will be given a day after the review of the worksheets and will
class.
contain a mix of the material learned.
NOTES: