Download The Effects of Variables on Microbial Growth in Wastewater

The Effects of Variables on Microbial Growth in
Wastewater Treatment
A TECHMATH MODULE
TEACHERS
Tonya Little & Sudeepa Pathak
STUDENTS
Victor Shepherd, Shaivya Pathak, Tyler Moore, Emily Tadlock
SCHOOL
WILLIAMSTON HIGH SCHOOL
BUSINESS Greenville Wastewater Treatment Plant
BUSINESS REPRESENTATIVE Jason Manning
July 2008
TABLE OF CONTENTS
PREFACE
P.
3
ABSTRACT
P.
4
THE BUSINESS PARTNER
P.
5
MODULE LESSONS
P.
6
LESSON ONE: FIELD TRIP WASTEWATER TREATMENT
P.
7
LESSON TWO: “MEETING THE EMPLOYEES”
P.
20
LESSON THREE: THE MATHEMATICS OF POPULATIONS
P.
48
LESSON FOUR: EXPERIMENTAL DESIGN, MICROBIAL
P.
60
P.
96
PLANT
GROWTH WITH A BENCH-TOP BIOREACTOR
LESSON FIVE: ANALYZING THE DATA: MATHEMATICAL
MODELING OF GROWTH CURVES OF MICROBES
PREFACE
Problem
Ecological education and the creation of an environmentally literate society has been identified as one of
the most pressing needs for development and survival on our planet. This module provides the instructor
an opportunity to teach in a realistic, inquiry setting rather than using lecture. Learning takes place in a
context similar to empirical ecological and environmental research which is based upon field-experiments,
long-term experiments and the scientific or mathematical method.
Further, there is an increasing reliance on long-term field experiments in the development and testing of
modern ecological theory. Thus a dichotomy between teaching and research exists despite the long-held
belief among educators that students learn through inquiry and the scientific method as practiced by
practitioners of the discipline. We suggest that the incorporation of long-term experiments laced with
mathematical analysis into the curricula will greatly benefit secondary students taking biology and math
courses. The students will attain a better appreciation for how relevant scientific research and its
mathematical analysis are undertaken.
ABSTRACT
The purpose of this module to introduce secondary students taking biology and / or algebra related
mathematics courses to the concept of long-term experimental field research through the establishment
of a series of long-term experimental study plots.
Wastewater treatment in wastewater facilities can be done by physical, chemical or biological methods.
Physical and chemical methods are fairly straightforward including; filtering, gravity settling and chemical
reactions. Biological methods use a wide variety of processes and a host of different microorganisms.
These reactions are carried out in large tanks and lagoons (See Figure 1). Bench top bioreactors can be
used to model the activity of microorganisms. In order to accurately stimulate microbial activity the
conditions of the natural environment must be simulated. Variables such as temperature, oxygen and
nutrient availability have to be controlled. If the vessel is deprived of any of these limiting factors, growth
and metabolic activity of the microorganisms is greatly affected.
Figure 1. Greenville Utilities Commission Wastewater Treatment Facility
Teachers are highly encouraged to arrange a tour of a nearby wastewater treatment plant. Students are
able to make a stronger connection between microbial niches and wastewater treatment, if they see the
process in action. This will establish background knowledge for Lessons 2 and 4. This module provides
the opportunity for first and second year high school students to do microscopic sampling of their
communities and also conduct a short term linear study pattern among food available and growth of the
organisms. Upper level high school students can use sophisticated sampling techniques of
microorganisms and the effects of several variables such as nutrients and/or chemicals within the
communities for quantitative studies
This module will provide students the opportunity to gain knowledge in the following areas:





Understand the biology and mathematic modeling involved in fermentation theory.
Develop technical skills in use of a special apparatus.
Preparation of nutrient media.
Technical writing skills (graphing data and report writing).
Time management with a long-term experiment.
THE BUSINESS PARTNER
Greenville Utilities Company’s (GUC’s) Wastewater Treatment Plant is operated by professionals,
dedicated to protecting the environment from water pollution. The ultimate goal of wastewater
treatment is to protect the environment not only for GUC customers, but for their neighboring
communities as well. Each city and town along the Tar-Pamlico River Basin of North Carolina is affected
by the quality of water discharged from their plants. The care GUC takes now will make a difference for
the generations to come.
This activity was completed with the invaluable assistance of Jason Manning (pictured above). Mr.
Manning is a wastewater treatment chemist with GUC. His knowledge as a chemist and former
classroom teacher were very beneficial in our endeavor to compose a challenging module that was
reflective of the knowledge and skills utilized in the wastewater treatment plant.
MODULE LESSONS
Lesson I: Field Trip Wastewater Treatment Plant
Lesson 2: “Meeting the Employees”, an Introduction to the Microorganisms Used
in Waste Treatment Facilities
Lesson 3: The Mathematics of Populations
Lesson 4: Experimental Design, Microbial Growth with a Bench-top Bioreactor
Lesson 5: Analyzing the Data- Mathematical Modeling of Growth Curves of
Microbes
Lesson I: Field Trip Wastewater Treatment Plant
TIME: 2 class days
Day 1: 50 – 90 minutes, In Class
Day 2: 90 minutes, Field Trip
Note to Teachers: If a field trip to a local wastewater treatment facility is not possible, the
following options will suffice.
A. Secure a speaker from a local wastewater treatment facility, to conduct an in-class
virtual field trip.
B. Secure a speaker from a local, state or federal environmental agency, the local utility
company, or an environmental consulting firm to discuss each person’s responsibility
in protecting our surface waters.
C. Have students use the Internet to investigate the jobs and processes at a wastewater
treatment facility.
D. Have students take a virtual tour of a wastewater treatment facility using the Internet.
On line virtual tours can be found at
a. http://www.wsd.dst.il.us/vtour.shtml
b. http://www.tampagov.net/dept_wastewater/information_resources/Advanced_
Wastewater_Treatment_Plant/Virtual_Tour/index.asp?sitemenuhide=n
MATERIALS:

Notes and photographs from visit to a local wastewater treatment plant or photographs or
posters of water and wastewater treatment plants

List of steps involved in water and wastewater treatment plants

Local map

Student sheets
OBJECTIVES
The student will do the following:
1. Identify the reasons for purifying water for communities.
2. Describe the water treatment processes that occur at a water filtration and treatment plant.
3. Describe the wastewater treatment processes that occur at a municipal wastewater
treatment facility.
4. Compare the municipal system’s water purification system to the ways water is purified in
nature.
7
BACKGROUND INFORMATION
Rivers and lakes are sources of water for municipal areas. Water samples are collected from these
water sources often look cloudy. Samples can look clear and still contain invisible sources of
pollution. Rivers and lakes must be monitored for contamination and other sources of pollution.
Water that enters the municipal water supply has to be cleaned before it can be used and must
also be cleaned after it is used. Pre-cleaning and post-cleaning takes place at a wastewater
treatment facility.
Municipal water systems are responsible for cleaning the water before it is used. The water
treatment system includes standardized steps for the treatment of the water before it is allowed to
enter the homes and businesses of individual citizens.
The following steps are included in some water treatment filtration systems:
1. Screening removes large objects from the water.
2. Pre-chlorination adds chlorine to kill disease-causing organisms.
3. Flocculation removes suspended particles by trapping them in a jelly-like suspension formed
from added particles.
4. Settling allows trapped particles and solids to settle to the bottom.
5. Sand filtration allows sand to act as a natural filter, removing nearly all suspended material.
6. Post-chlorination adjusts the chlorine to maintain long-term action to kill disease-causing
organisms.
7. Other treatments, such as flocculation, fluoridation, pH adjustment, and further aeration can
be optional steps.
The following steps are included in a wastewater treatment system:
1. Preliminary Treatment: Screening is when large objects are removed.
2. Primary Treatment: Primary settling happens when floating grease and scum are skimmed
and heavier organic solids settle out.
3. Secondary Treatment: Aeration tanks add air and allow bacteria to digest organic
substances.
4. Final settling is when bacteria settle out of the wastewater and are removed to a solids
treatment process for stabilization. The stabilized solids, called biosolids, are then
suitable for disposal on cropland, in landfills, or other beneficial uses, such as compost.
5. Disinfection: chlorination or ultraviolet irradiation is used to kill harmful bacteria.
6. Optional treatments my include controlling water pH by using carbon dioxide to form
carbonic aid. Carbonic acid can neutralize alkaline compounds.
8
PROCEDURE
I.
Setting the Stage
a. Locate the water treatment facility in your area on a local map.
b. Discuss the water supply that provides water for the water treatment plant.
c. Compare the number of students in the class that use water from a water treatment
plant with the number who have private wells.
II. Activities
a. List the steps involved in the water purification of a municipal water supply and
explain what happens at each step.
b. Ask the students to flowchart the activities involved in each step on Student
Worksheet #2.
c. Have students speculate what might happen if a step was not included.
d. List the steps involved in the treatment of wastewater at a wastewater treatment
plant.
e. Have the students flowchart the activities involved in each of these steps.
f.
Have students speculate what might happen if a step was not included.
g. Visit a local wastewater treatment plant, have a speaker come into the classroom
to discuss this process, or have students research wastewater treatment plants on
the Internet.
h. Have students compare their flowchart and descriptions to the processes they
actual see in the on site visit, hear about through the guest lecturer, or research on
the Internet.
III. Follow Up
a. Ask students to research the optional steps used by water treatment facilities in
local and surrounding communities. Discuss which optional steps can be
detrimental to people or to the environment.
b. Discuss the possible hazards of using well water rather than water from a water
treatment facility.
IV. Extensions
a. Design posters reflecting each person’s responsibility in protecting our water
supplies. These posters can be displayed around the school.
b. Develop a clean water monitoring group to collect data from local rivers and
streams.
9
Appendix One
Lesson One
Student Sheet #1
Terms
10
STUDENT SHEET #1
Wastewater Treatment
Terms
carcinogen: cancer-causing agent.
chlorination: water disinfection by chlorine gas or hypochlorite.
flocculation: the process of forming aggregated or compound
masses of particles, such as a cloud or a precipitate.
purification: the process of making pure, free from anything that
debases, pollutes, or contaminates.
settling: the process of a substance, such as heavy organic
solids or sediment, sinking.
sewage contamination: the introduction of untreated sewage
into a body of water.
wastewater: water that has been used for domestic or industrial
purposes.
11
Appendix Two
Lesson One
Student Sheet #2
Steps in Wastewater Treatment
12
STUDENT SHEET #2
Wastewater Treatment
The following steps are included in a wastewater treatment system:
Step 1 – Preliminary Treatment:
1. Screening – large objects are removed; smaller objects are ground into even smaller pieces, and
sand and dirt are allowed to settle out.
Step 2 – Primary Treatment:
2. Primary settling – floating grease and scum are skimmed and solids settle out.
Step 3 – SecondaryTreatment:
3. Aeration – aeration tanks add air and allow bacteria to digest organic substances.
4. Final settling – sludge continues to settle out, and it is aerated, chlorinated, and dried for
incineration are for dumping in landfills.
5. Disinfection/chlorination – additional chlorine is added to kill disease-causing organisms. Other
disinfection processes include ultraviolet irradiation.
6. Optional treatments – water pH can be controlled by using carbon dioxide to form carbonic acid.
Carbonic acid can neutralize alkaline compounds. Heavy metal ions and phosphate ions can also
be removed by precipitation.
13
Appendix Three
Lesson One
Student Sheet #2
&
Answer Key
Flowchart Steps in Wastewater Treatment
14
STUDENT SHEET #3
FLOWCHART WATER PURIFICATION
15
STUDENT SHEET #3
FLOWCHART WATER PURIFICATION
ANSWER KEY
Screening removes large objects from the
water.
Pre-chlorination adds chlorine to kill
disease-causing organisms.
Flocculation removes suspended particles
by trapping them in a jelly-like suspension
formed from added particles.
Settling allows trapped particles and
solids to settle to the bottom.
Sand filtration allows sand to act as a
natural filter, removing nearly all
suspended material.
Post-chlorination adjusts the chlorine to
maintain long-term action to kill diseasecausing organisms.
Other treatments, such as flocculation,
fluoridation, pH adjustment, and further
aeration can be optional steps.
16
Appendix Four
Lesson One
Student Sheet #4
Flowchart Steps in Wastewater Treatment
17
STUDENT SHEET #3
FLOWCHART WASTEWATER TREATMENT
18
STUDENT SHEET #3
FLOWCHART WASTEWATER TREATMENT
KEY
Preliminary
Treatment
Primary
Treatment
Secondary
Treatment
Settling
Disinfection
19
Lesson 2: “Meeting the Employees”, an Introduction to the Microorganisms Used in Waste
Treatment Facilities
Purpose: To introduce the students to microorganisms involved in wastewater treatment.
1. Allow one class period to discuss classification of bacteria, identification of bacteria, and the
importance of bacteria.
2. Lecture/Discussion: Microorganisms and their Growth Characteristics.(See Appendix 1: The
Microbiology of Activated Sludge)
3. Allow one lab period for students to observe the organisms in the "pure" cultures so that they
become familiar with the appearance of each type. (Alternative options may include viewing
images on the Internet or accessing the PowerPoint of Wastewater Treatment Microorganisms)
4. Students will complete “Microbe Trading Cards”, identifying characteristics of the organisms.
These will be used for future reference in identifying the microorganisms.
Timeline: Two ninety minute periods on a 4x4 block schedule.
North Carolina Standard Course of Study for Biology
Competency Goal 1: The learner will develop abilities necessary to do and understand scientific
inquiry.
1.01 Identify biological questions and problems that can be answered through scientific investigations.
1.02 Design and conduct scientific investigations to answer biological questions.
Competency Goal 5: The learner will develop an understanding of the ecological relationships
among organisms.
5.01 Investigate and analyze the interrelationships among organisms, populations, communities, and
ecosystems.
National Science Education Standards:
CONTENT STANDARD A: As a result of activities in grades 9-12, all students should develop
 Abilities necessary to do scientific inquiry
 Understandings about scientific inquiry
CONTENT STANDARD C: As a result of their activities in grades 9-12, all students should develop
understanding of
 Interdependence of organisms
 Matter, energy, and organization in living systems
 Behavior of organisms
Materials (per team of four):
 “Microbe Trading Cards” templates
 Medium size culture dishes - 6
 Boiled pond or spring water
 Droppers - 6
 Cooked wheat grain
 Stereomicroscope
 Microscope (compound light)
 Glass Slides
 Cover slips






Paramecium culture
Mixed rotifer culture
Euglena culture
Amoeba culture
Tardigrade culture
Bacteria culture
20
Teacher notes:
 If possible, obtain a sample collection from a local wastewater treatment facility to
demonstrate microorganisms actually used in industry.
 To help identify microorganisms from a local wastewater treatment facility or if access to
culture and/or industry samples is not available, “Interactive Microscope” at
http://www.norweco.com/html/lab/Microscope.htm# gives examples of microorganisms
used in wastewater treatment. Students can use this website to view images and videos of
the microorganisms identified in the activity.
 Power Point notes for the Introduction to Bacteria Notes can be found at
Procedure:
1. The information in Appendix 1: “The Microbiology of Activated Sludge” will be used, by the
teacher, as a guide to develop lecture notes, PowerPoint presentation, etc. to introduce the
following to students:
a. activated sludge,
b. the characteristics of microorganisms used in wastewater treatment, and
c. variables affecting the growth of these microorganisms.
Teachers may also access PowerPoints by the author for “Introduction to Bacteria” and
“The Microbiology of Activated Sludge” at www.freewebs.com/tlittle. Upon visiting the site
click on Tech Math to download the presentations.
2. Organize students into laboratory groups of four. Students are to complete the following
procedures for sampling and viewing the representative organisms.
a) Half fill each of six culture dishes with boiled pond or spring water. Label the dishes A through
F. With a dropper, add ten drops of each culture to each of the six dishes. Stir each culture
prior to transferring it to one of the six culture dishes.
b) Mark the fluid levels of each culture dish with tape. To dishes A, B, C, D, and E add three
grains of cooked wheat. Add boiled pond or spring water to each dish as needed to keep the
fluid level constant. These culture dishes will be maintained for students to observe the
organisms in pure culture.
c) Stir the material in the culture dish to be sampled and obtain a sample with a dropper.
Prepare a wet mount slide. Observe the slide with the low power objective lens of your
microscope. Make a sketch of the organism on the “Microbe Trading Cards” table. Observe
and count the number of each species assigned to you by your instructor. Each member of
the group will be responsible for counting a different group of organisms.
d) Sampling Technique. To obtain an average number of organisms, do the following. Count the
number of each species in five different fields of view under the microscope ( count in each of
the four corners of the cover slip and in the center of the cover slip), add the total number,
and divide by five. Students will record the numbers of each species on Data Table 1 for their
group.
e) Add food (wheat grains) to the culture dishes on days 7, 14, 21, 35, and 42. Sample the
cultures prior to adding the food.
(If students maintain the pure cultures over a period of time, bacteria will appear in the culture
dishes and may reach uncontrollable numbers. Students may discover an interesting side
project in studying the relationship between the microorganisms and the bacteria.)
3. Using the information from the discussion and laboratory observations, students are to complete
the “Microbe Trading Cards”
21
Data Table
Classroom Observations of Pure Cultures of Microorganisms
Microorganism
Count
Count
Count
Count
Count
Field #1
Field #2
Field #3
Field #4
Field #5
Sum of
Counts
Average
Count
Paramecium
culture
Mixed rotifer
culture
Euglena culture
Amoeba culture
Tardigrade
culture
Bacteria
Unknowns (sketch):
22
INTRODUCTION TO BACTERIA
STUDENT WORKSHEET
Bacteria
Classifying Bacteria
 Bacteria are prokaryotic organisms, meaning that they do
not have a nucleus or membrane-bound organelles.
 The two different groups of prokaryotes are ________ and
_______________.
 Bacteria are ubiquitous, they live almost everywhere!
 Bacteria have cell walls made of ____________, a complex
carbohydrate.
II. Identifying Prokaryotes
 Read the description of the part and complete the
illustration of a typical prokaryote.
I.
23
basal body - A structure that anchors the base of the flagellum and allows it to
rotate.
capsule - A layer on the outside of the cell wall. Most but not all bacteria have a
capsule.
cell wall - A thin membrane located outside the plasma membrane and within the
capsule.
DNA - The genetic material of the bacterium; it is located within the cytoplasm.
cytoplasm - The jellylike material inside the plasma membrane in which the genetic
material and ribosomes are located.
flagellum - A long whip-like structure used for locomotion (movement). Some
bacteria have more than one flagellum.
pili - (singular is pilus) Hair-like projections that allow bacterial cells to stick to
surfaces and transfer DNA to one another.
plasma membrane - A permeable membrane located within the cell wall. It serves
many functions for the cell, including energy generation and transport of chemicals.
ribosomes - Small organelles composed of RNA-rich granules that are sites of
protein synthesis. The ribosomes are located within the cytoplasm.
III.
Types of Bacteria: There are many different types of bacteria.
A.
Some bacteria are rod-shaped (these are called _______),
some are round (called _______, like streptococcus bacteria),
and some are spiral-shaped (________) or are incomplete
spirals.
B.
Some bacteria need atmospheric oxygen to live (these are
called ___________bacteria), but others do not (these are
called ____________ bacteria; they get their oxygen from
other molecular compounds).
C.
Another way to classify bacteria is by whether or not the
bacteria absorbs a dye called _____________ (a violet dye
named for its developer, the bacteriologist Christian Gram).
Gram positive and Gram negative bacteria have a different type
of cell wall, and therefore, a different reaction to the dye and
to some other chemicals, including antibiotics (chemicals that
can sometimes kill bacteria).
i
Gram-positive bacteria appear ___________ and
ii Gram-negative bacteria appear __________.
24
D.
Diet: Bacteria have a wide range of diets.
Group
________________
________________
________________
________________
E.
Bacteria Respiration
Group
Obligate aerobes
Obligate anaerobes
Facultative anaerobes
F.
G.
Description
Organism that carries out
photosynthesis in a manner similar to
plants.
Organism that obtains energy directly
from chemical reactions involving
inorganic molecules.
Organism that takes in organic
molecules and then breaks them down.
Organism that captures sunlight for
energy and also needs organic molecules
as a carbon source.
Description
Organisms that require a constant
supply of oxygen.
Organisms that must live in the absence
of oxygen.
Organisms that can survive with or
without oxygen.
Reproduction: Bacteria grow in colonies and reproduce rapidly
by asexual budding or fission, in which the cell increases in size
and then splits in two. Bacteria can also undergo sexual
conjugation in which two separate bacteria exchange pieces of
DNA.
Resting Stages: Under unfavorable environmental conditions,
bacteria develop a thick outer wall and enter a dormant phase 25
H.
in this resting state, the bacterium is called an endospore. The
bacteria can remain in this dormant state for long periods of
time, surviving conditions that kill many other organisms.
Importance of Bacteria
i
Decomposers help the ecosystem recycle nutrients.
ii Bacteria live symbiotically with legume plants, converting
atmospheric____________ into a usable form for the
plant.
iii Industry
 Bacteria have been used to clean up oil spills. These oil
digester feed on the long chain hydrocarbons of
petroleum products.
 Bacteria have been used genetically engineered to
produce medicine, for food production, and in
industrial chemistry.
26
Microbe Trading Cards
STUDENT WORKSHEET
Make Your Sketch Here
Ciliate Paramecium
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Paramecium are covered in tiny hairs,
____________, which they wave back and forth to swim and
eat.
Favorite Hangout:__________________
Make Your Sketch Here
Favorite Food:_____________________
Flagellated Protozoans
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Flagellates move quickly using a tail known as a
____________________.
Favorite Hangout:___________________
_________________________________
Make Your Sketch Here
Favorite Food:______________________
Rotifer
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features:The head of the rotifer has a
_________surrounded by __________, that helps to draw
food into their mouth and used for movement.
Favorite Food:______________________
Special Features:Rotifers use their foot to excrete a sticky
substance that allows them to attach to a surface then sift
food.
Make Your Sketch Here
Nematode
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Nematodes look like ________ and are the
largest of all microbes.
Favorite Hangout:_______________
Special Features: Nematodes, unlike other microbes,
can_________________________.
Favorite Food:________________________
27
Make Your Sketch Here
Aquatic Worms
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Are much like terrestrial earthworms, but are
_______.
Favorite Hangout: They can be common in old activated
sludge.
Special Features: Aquatic earthworms have _____along their
body, which allows them to tunnel through floc particles,
ingesting chunks of bacterial floc.
Make Your Sketch Here
Favorite Food:________
Tardigrade (Waterbears)
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features:________________________
Favorite Hangout:______________________
Special Features:______________________
____________________________________
Favorite Foods:________________________
____________________________________
Make Your Sketch Here
Habits Once they grasp the food, they puncture it and suck the
contents out!
Bacteria
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
1. Make up about _____% of the activated sludge
biomass.
2.
These single celled organisms grow in the
wastewater by _____________________________
_____________________________
carbohydrates, fats and many other compounds.
28
Assessment
1. What is the primary job of these microbial employees?
2. Which environmental factors are necessary for the survival of most organisms?
3. Do photosynthesizers survive without food? If so, why?
4. Who is eating whom? Construct a food chain based upon the interactions of the
microorganisms you have observed? Explain the feeding relationships with captions.
29
Appendix 1
Lesson Two
“Meet the Employees”, An Introduction to the Microorganisms
Used in Waste Treatment Facilities”
Completed Classroom Notes
I. Bacteria
II. Activated Sludge- Bacteria in the
Wastewater Treatment Industry
30
Appendix 1: Classroom Notes
Bacteria
Classifying Bacteria
 Bacteria are prokaryotic organisms, meaning that they do
not have a nucleus or membrane-bound organelles.
 The two different groups of prokaryotes are Eubacteria and
Archaebacteria.
 Bacteria are ubiquitous, they live almost everywhere!
 Bacteria have cell walls made of peptidoglycan, a complex
carbohydrate.
IV. Identifying Prokaryotes
 Read the description of the part and complete the
illustration of a typical prokaryote.
III.
31
basal body - A structure that anchors the base of the flagellum and allows it to
rotate.
capsule - A layer on the outside of the cell wall. Most but not all bacteria have a
capsule.
cell wall - A thin membrane located outside the plasma membrane and within the
capsule.
DNA - The genetic material of the bacterium; it is located within the cytoplasm.
cytoplasm - The jellylike material inside the plasma membrane in which the genetic
material and ribosomes are located.
flagellum - A long whip-like structure used for locomotion (movement). Some
bacteria have more than one flagellum.
pili - (singular is pilus) Hair-like projections that allow bacterial cells to stick to
surfaces and transfer DNA to one another.
plasma membrane - A permeable membrane located within the cell wall. It serves
many functions for the cell, including energy generation and transport of chemicals.
ribosomes - Small organelles composed of RNA-rich granules that are sites of
protein synthesis. The ribosomes are located within the cytoplasm.
IV.
Types of Bacteria: There are many different types of bacteria.
A.
Some bacteria are rod-shaped (these are called bacilli), some
are round (called cocci, like streptococcus bacteria), and some
are spiral-shaped (spirilli) or are incomplete spirals.
B.
Some bacteria need atmospheric oxygen to live (these are
called aerobic bacteria), but others do not (these are called
anaerobic bacteria; they get their oxygen from other molecular
compounds).
C.
Another way to classify bacteria is by whether or not the
bacteria absorbs a dye called "Gram stain" (a violet dye named
for its developer, the bacteriologist Christian Gram). Gram
positive and Gram negative bacteria have a different type of
cell wall, and therefore, a different reaction to the dye and to
some other chemicals, including antibiotics (chemicals that can
sometimes kill bacteria).
i
Gram-positive bacteria appear violet and
ii Gram-negative bacteria appear red.
32
D.
Diet: Bacteria have a wide range of diets.
Group
Photoautotroph
Description
Organism that carries out
photosynthesis in a manner similar to
plants.
Organism that obtains energy directly
from chemical reactions involving
inorganic molecules.
Organism that takes in organic
molecules and then breaks them down.
Organism that captures sunlight for
energy and also needs organic molecules
as a carbon source.
Chemoautotroph
Heterotroph
Photoheterotroph
E.
Bacteria Respiration
Group
Obligate aerobes
Obligate anaerobes
Facultative anaerobes
F.
G.
Description
Organisms that require a constant
supply of oxygen.
Organisms that must live in the absence
of oxygen.
Organisms that can survive with or
without oxygen.
Reproduction: Bacteria grow in colonies and reproduce rapidly
by asexual budding or fission, in which the cell increases in size
and then splits in two. Bacteria can also undergo sexual
conjugation in which two separate bacteria exchange pieces of
DNA.
Resting Stages: Under unfavorable environmental conditions,
bacteria develop a thick outer wall and enter a dormant phase 33
H.
in this resting state, the bacterium is called an endospore. The
bacteria can remain in this dormant state for long periods of
time, surviving conditions that kill many other organisms.
Importance of Bacteria
i
Decomposers help the ecosystem recycle nutrients.
ii Bacteria live symbiotically with legume plants, converting
atmospheric nitrogen into a usable form for the plant.
iii Industry
 Bacteria have been used to clean up oil spills. These oil
digester feed on the long chain hydrocarbons pf
petroleum products.
 Bacteria have been used genetically engineered to
produce medicine, for food production, and in
industrial chemistry.
34
ACTIVATED SLUDGE- Bacteria in the Wastewater Treatment Industry
Activated sludge can be defined as "a mixture of microorganisms which contact
and digest bio-degradable materials (food) from wastewater."



Activated sludge is microorganisms.
The Activated sludge process is a biological process.
To properly control the activated sludge process, you must properly control
the growth of microorganism. This involves controlling the items which may
affect those microorganisms.
Bacteria


Make up about 95% of the activated sludge biomass.
These single celled organisms grow in the wastewater by consuming (eating)
bio-degradable materials such as proteins, carbohydrates, fats and many
other compounds.
The Role of Enzymes
Enzymes are compounds that are made by living organisms. Their purpose is to help
biochemical reactions to occur. Almost all biochemical reactions require the
presence of enzymes to cause the reaction to occur.
Enzymes help bacteria in the process of breaking down nutrients, and in rebuilding
broken down nutrients into the new compounds that they require for growth and
reproduction.
Enzymes only do what they are supposed to when environmental conditions are
right. If the conditions are not right the enzymes will not function properly, thus,
the bacteria will not function properly, and they will not survive. If conditions are
right the bacteria will live and prosper.
35
Growth Characteristics
When there is plenty of food available, bacteria use the food mostly for growth
and some for energy.


A growing bacterium mayhave flagella (hair-like structures on the outside of
the cell) which makes it motile, able to move in search of food.
A bacterium reproduces into two bacteria. The cell splits into two smaller
cells and this process occurs over and over again.
When there is very little food available, the bacteria use the limited food to
produce energy and to maintain the cell. Very little is available for growth so less
reproduction occurs.


With little food available, and in an attempt to conserve energy, the
bacterium loses it flagella and thus, its motility.
The waste products start to form a thick slime layer outside the cell wall,
making the cells stick together.
The growth characteristics of bacteria are better understood by studying the
growth curve.




Lag-phase During this phase bacteria become acclimated to their new
surroundings. They are digesting food, developing enzymes and other things
required for growth.
Accelerated Growth-phase The bacteria are growing as fast as they can,
since there is an excess of food. The cells are mostly dispersed, not sticking
together.
Declining Growth-phase Reproduction slows down because there is not an
excess of food. A lot of food has been eaten and there are now a large
number of bacteria to compete for remaining food, so the bacteria do not
have enough remaining food to keep the growth rate at a maximum.
Stationary-phase The number of bacteria is the highest possible, but not
much food is left, so the bacteria cannot increase in number. There is some
reproduction, but some cells are also dying, so the number of bacteria
remain relatively constant. The bacteria have now lost their flagella and have
a sticky substance covering the outside of the cell, allowing them to
36

agglomerate into floc. In fact, the floc get big enough that if aeration and
mixing were stopped, the floc could settle to the bottom.
Death-phase The death rate increases with very little if any growth
occurring. Therefore, the total number of living bacteria keeps reducing.
The bacteria are just trying to keep alive.
F:M (Food to Microorganism ratio)
We measure the amount of biodegradable matter the bacteria use for food by
measuring the amount of BOD (biochemical oxygen demand) or COD (chemical
oxygen demand) in the influent to the aeration basin. We estimate the weight of
microorganisms in the mixed liquor by measuring the amount of volatile suspended
solids (VSS) in the activated sludge. We use this information to form a relationship
called food to microorganism ratio (F/M ratio). The F/M ratio tells us something
about growth and cell condition. If the F/M ratio is high, the bugs normally grow
quite rapidly (because this means there is a lot of "food" available in comparison to
the amount of microorganism); if the F/M ratio is low, the bug normally grow very
slowly (because little food is available for growth).
The Use of Oxygen
Microorganisms need oxygen to live. Oxygen use and be used to determine the
activity of the organisms.
- Actively growing organisms are rapidly metabolizing the food, so they are use
oxygen at a rapid rate.
- We measure the rate at which oxygen is used by a test called the Oxygen Uptake
Rate (OUR), or the Respiration Rate. It is measured in mg O2/hr/gm of MLSS.
- Normally a higher uptake rate is associated with high F/M ratios and younger
sludges and a lower uptake rate is associated with lower F/M and older sludges. So,
if you want a higher uptake rate, more sludge should be wasted. Less should be
wasted if you want a lower F/M ratio.
The Formation of Floc
As bacteria begin growing, they generally develop into small chains or clumps. They
are very active and motile and it is difficult for them to settle. They have not yet
37
developed the slime layer which aids in their sticking together. So, when mixing
occurs, the small chains or clumps are broken up and the bugs are dispersed, and
they will not flocculate or settle.
As the sludge is allowed to age, the bugs lose their motility and accumulate more
slime. Then the clumps and chains are better able to stick together. The clumps
grow bigger and bigger until they form a floc. If the organisms are allowed to
develop properly, under the right conditions, the floc get large and compact and
begin to settle. The mixing in the aeration tank tends to keep the floc small since,
even though the bugs are sticky, the bond formed holding the organisms together
is not very strong. This is good because it allows the cells, food, and oxygen to
contact each other.
Dissolved Oxygen
Oxygen is required by these bugs to metabolize food for cell maintenance and
growth. Although the bugs need oxygen, some bugs can get along with less oxygen
than others.
Each bug must have a dissolved oxygen of at least from 0.1-0.3 mg/L to function
properly. So, it is important to maintain about 2 mg/L of D.O. in the activated
sludge so that the bacteria that are contained in the floc can get oxygen. If the
DO is less than 2 mg/L, the bugs on the outside of the floc use the DO before it
can get to the center of the floc. If this happens, the bugs in the center may die
causing the floc to break up.
The Effects of Mixing
Mixing is required to bring organisms, oxygen, and nutrients together, and to
remove metabolic waste products. If there is not enough mixing, proper treatment
will not take place because of lack of contact between the bugs, their food and
oxygen. If too much mixing is provided, it can cause break up of floc or formation
of unstable floc particles.
The Effects of pH
The enzymes which regulate many of the biochemical reaction in bacteria are very
pH dependent. The optimum pH should be between 7.0 and 7.5 for the proper
activated sludge microorganisms to dominate.
38
The Effects of Temperature
Biochemical reactions are very temperature dependent. Lower temperatures cause
such reactions to be much slower. Thus, more bugs are required to do the same job
during the winter than in the summer.
The Effects of Nutrients
Microorganisms require certain nutrients for growth. The basic nutrients of
abundance in normal raw sewage are carbon (C), nitrogen (N), phosphorus (P), with
the ratio of C:N:P ratio approximately equal to 100:10:1. In addition to C,N,and P,
trace amounts of sodium (Na), Potassium (K), magnesium (Mg), iron (Fe), and many
others are required. In normal municipal sewage, most of these nutrients are
provided.
Most problems with nutrient deficiency occur when there is a lot of industrial
wastes present. When proper nutrients are not available, the metabolism fails and
a kind of bacterial fat (slime) will begin to accumulates around the cell. The cell
slows down in activity because it cannot produce enough enzymes and because
needed nutrients cannot penetrate the slime layer as they should. The sludge will
not settle and BOD removal slows down.
39
Protozoa & Rotifers
The presence of particular types of protozoans is related to effluent quality and plant performance.
Protozoan play secondary but important role in purification of aerobic wastewater.
The protozoans in the activated sludge treatment process fall into four major classes: amoebae,
flagellates, and ciliates (free-swimming, crawling, and stalked).

Amoebae
Amoebae are the most primitive, single-celled protozoans. They move by false feet. They are
frequently present in raw influent, and their presence is short in the aeration basin. Amoebae can
only multiply when there is an abundance of nutrients in the aeration tank. They move very slowly
and it is difficult for them to compete for food when there is a limited amount available. They are
only dominant in the aeration basin for a short time.
They feed on small organic particulates. When amoeba are present in large numbers in the
aeration basin this usually indicates that there has been some sort of shock loading to the plant
(there must be a lot of food available). Their presence may also indicate that there is a low D.O.
environment in the aeration basin, because they can tolerate very low amounts of D.O.

Flagellates
Most flagellates absorb dissolved nutrients. Soon
after amoebae begins to disappear and while
there is still high concentrations of soluble food.
Flagellates and bacteria both feed on organic
nutrients in the sewage so as the nutrient level
declines they have difficulty out competing the
bacteria for soluble food so, their numbers begin
to decrease.
If large amounts of flagellates are present in the
later stages of the activated sludge development
this usually indicates that the wastewater still contains a large amount of soluble organic
nutrients.

Ciliates
Ciliates feed on bacteria not on dissolved organics. While bacteria and
flagellates compete for dissolved nutrients, ciliates compete with other
ciliates and rotifers for bacteria. The presence of ciliates indicate a good
sludge, because they dominate after the floc has been formed and after
most of the organic nutrients have been removed.
o
Free-swimming ciliates - These ciliates appear as flagellates
begin to disappear. As the bacterial population increases, a lot
of dispersed bacteria is available for feeding and as a lightly dispersed floc appears, freeswimming ciliates begin to dominate and feed on the increased numbers of bacteria.
40
o

Crawling ciliates - As floc particles enlarge and stabilize, crawling ciliates graze on floc
particles. Crawling ciliates out compete free-swimming ciliates for food because they can
find food within the floc.
o Stalked ciliates - Stalked ciliates appear in the mature sludge. Within the mature sludge
the crawling and stalked ciliates compete for dominance.
Tardigrades (Water bears)
Tardigrades are small, segmented animals, similar
and related to the arthropods. The name Tardigrada
means "slow walker" and was given by Spallanzani in
1777. The biggest adults may reach a body length of
1.5 mm, the smallest below 0.1 mm. Water bears are
able to survive in extreme environments that would kill
almost any other animal. They can survive
temperatures close to absolute zero, temperatures as
high as 151°C (303°F), 1,000 times more radiation
than any other animal, nearly a decade without water, and can also survive in a vacuum
like that found in space. They are aggressive feeders that move around a lot and feed
continuously. Their favorite foods include microbes such as nematodes, rotifers and
protozoans. Once they have grasped the food they puncture the skin of the food source
and suck the contents out.
Rotifers
Rotifers are rarely found in large numbers in wastewater
treatment processes. The principal role of rotifers is the removal
of bacteria and the development of floc. Rotifers contribute to
the removal of effluent turbidity by removing non-flocculated
bacteria. Mucous secreted by rotifers at either the mouth
opening or the foot aids in floc formation. Rotifers require a
longer time to become established in the treatment process.
Rotifers indicate increasing stabilization of organic wastes.
Factors Influencing Protozoa
Temperature
Most protozoans can survive and reproduce in a temperature range at which activated sludge processes
are carried out. They grow best in ambient temperatures (15-25 ˚C).
pH
Protozoans are more sensitive to pH than floc-forming bacteria. They have an optimum pH range of 7.27.4 and a tolerance range of 6.0-8.0.
Dissolved Oxygen
41
Like bacteria, protozoan must have oxygen to survive. Thus lack of DO will severely limit both the kind
and number of protozoans.
Nutrition
Most municipal wastewater treatment plants, however dilute, contains sufficient nutrients to support most
of the protozoan associated with wastewater.
42
Appendix 2
Lesson Two
“Meet the Employees”, An Introduction to the Microorganisms
Used in Waste Treatment Facilities
MICROBE TRADING CARDS
ANSWER KEY
43
Microbe Trading Cards
Make Your Sketch Here
Ciliate Paramecium
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Paramecium are covered in tiny
hairs, cilia, which they wave back and forth to
swim and eat.
Favorite Hangout: Secondary Treatment,
aeration basin with lots of sludge.
http://www.jcw.org/access/edmicrobes.htm
Favorite Food:Bacteria
Will vary among students.
Make Your Sketch Here
Flagellated Protozoans
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Flagellates move quickly using a
tail known as a Flagella.
Favorite Hangout: Secondary Treatment,
aeration basin with lots of sludge.
Will vary among students.
Favorite Food: Bacteria and food particles
Make Your Sketch Here
Rotifer
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: The head of the rotifer has a
corona surrounded by cilia that helps to draw
food into their mouth and used for movement.
Favorite Food: Bacteria and food particles
Special Features: Rotifers use their foot to
excrete a sticky substance that allows them
to attach to a surface then sift food.
http://www.jcw.org/access/edmicrobes.htm
Will vary among students.
44
Appendix 2: Microbe Trading Cards Key
Make Your Sketch Here
Nematode
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Nematodes look like worms and are the
largest of all microbes.
Favorite Hangout: Secondary Treatment, aeration basin
with lots of sludge.
Special Features: Nematodes, unlike other microbes, can
bite and tear their food.
Favorite Food: Algae and bacteria
http://www.jcw.org/access/edmicrobes.htm
Will vary among students.
Make Your Sketch Here
Aquatic Worms
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Are much like terrestrial earthworms, but
are aquatic.
Favorite Hangout: They can be common in old activated
sludge.
Special Features: Aquatic earthworms have setae along
their body, which allows them to tunnel through floc
particles, ingesting chunks of bacterial floc.
http://www.jcw.org/access/edmicrobes.htm
Will vary among students.
Make Your Sketch Here
Favorite Food: bacteria
Tardigrade (Waterbears)
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Cool Features: Looks like a caterpillar and has claws.
Favorite Hangout: Secondary Treatment, aeration basin
with lots of sludge.
Special Features: They are aggressive feeders, move
around a lot and feed continuously.
http://microshaw.raffish.org/tardigrade.html
Will vary among students.
Favorite Foods: Body fluids of other microbes, such as
nematodes, rotifers and protozoans.
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________
Habits Once they grasp the food, they puncture it and suck
the contents out!
45
Make Your Sketch Here
Bacteria
Check Classification That Applies to This Organism
 Eubacteria  Protista Other_________


Make up about 95% of the
activated sludge biomass.
These single celled organisms
grow in the wastewater by
consuming (eating) bio-degradable
materials such as proteins,
carbohydrates, fats and many
other compounds.
http://www.jcw.org/access/edmicrobes.htm
Will vary among students.
46
Appendix 2: Microbe Trading Cards Key
Microbe Trading Cards Key
Assessment
1. What is the primary job of these microbial employees?
Helpful microorganisms consume organic matter in the wastewater. Bacteria remove nutrients,
like nitrogen and phosphorus.
2. Which environmental factors are necessary for the survival of most organisms?
nutrients, pH, temperature, dissolved oxygen
3. Do photosynthesizers survive without food? If so, why?
Yes, because they are able to produce their own food by the process of photosynthesis.
4. Who is eating whom? Construct a food chain based upon the interactions of the microorganisms
you have observed? Explain the feeding relationships with captions.
May vary among students.
One example follows:
Organic nutrients are consumed by bacteria, which could be preyed upon by other organisms such
as rotifers.
Organic
Nutrients
Bacteria
Rotifers
Tardigrades
47
Lesson 3: THE MATHEMATICS OF POPULATIONS:-
Study of Growth Curves of Waste water Microbes as Function graphs
PURPOSE: To introduce the students to the concept that population growth
curves of any species are function graphs.
1. Allow the students to study population change in Waste water microbes, by
simulation of the population.
2. Allow students to see that most growth curves are linear, exponential,
logistic or even constant functions.
3. The teacher will correlate the lesson to the waste water plant by
introducing the waste water plant through a virtual tour of a waste water
treatment plant (WWTP).The following Internet sites can be used for this
a. http://www.wsd.dst.il.us/vtour.shtml
b. http://www.tampagov.net/dept_wastewater/information_resources/Advanced_Wast
ewater_Treatment_Plant/Virtual_Tour/index.asp?sitemenuhide=n
TIMELINE: One ninety minute period
North Carolina Pre calculus Standard Course of Study
Objective 2.03 For sets of data create and use calculator-generated models of
linear, constant polynomial, exponential and logistic functions.
a. Interpret the constants, coefficients, and bases in the context of the data.
b. Check models for goodness-of-fit; use the most appropriate model to draw
conclusions or make predictions.
c. Translate among graphic, algebraic, numeric, tabular, and verbal
presentations of relations and functions.
d. Define and use linear, constant polynomial, exponential and logistic
functions to model and solve problems.
48
NATIONAL STANDARDS:
NCTM Standard strand:
http://standards.nctm.org/document/chapter7/data.htm
In grades 9–12 all students should— Select and use appropriate statistical
methods to analyze data
a) For bivariate measurement data, be able to display a scatter plot, describe its
shape, and determine regression coefficients, regression equations, and
correlation coefficients using technological tools;
b) Display and discuss bivariate data where at least one variable is categorical.
MATH OBJECTIVES
1. Conceptual Understanding of growth curves as linear, constant polynomial,
exponential and logistic functions.
2. Data collection and analysis
3. Understanding sampling procedures.
4. Graphing
5. Interpret Data
PROCEDURAL STANDARDS
1.
2.
3.
4.
Representation
Reasoning
Communication
Connection
49
HOOK
In the next unit, the students will be learning about growth patterns and curves of
a population of micro organisms in waste water treatment plants, hence they
should be familiarized with various function graphs which they will encounter in
the population study. A mock study and hand graphing is done on a population of
one specific microbe say “Bacteria” found in waste water (represented by fish
crackers) living with other microbes (pretzels) by students sitting in groups of
three. A fishing net (Styrofoam cup) is used to “catch” the waster water bacteria
(fishes) and their number is counted. A graph is drawn with the bacteria count
(fish count) representing their population(y axis) and the sample number
representing time in days(x axis). The shapes of the graphs are categorized as
functions through curve of best fit and further studied.
Material needed
Each group (team of three) needs:





1 paper lunch bag - representing the "Waste water tank"
A supply of goldfish crackers - representing the "Bacteria” in the tank.
A supply of pretzels - representing the “other microbes”.
1 Styrofoam cup - representing the "net"
1 paper plate
PROCEDURE
A. DATA COLLECTION WITH CONSTANT POPULATION
1. Each team receives a paper lunch bag with a packet of goldfish
crackers mixed with a packet of pretzels.
2. The students scoop a sample out of the "tank" with the “net” onto
the paper plate.
50
3. The number of bacteria (fishes) trapped are counted and then
thrown back into the tank keeping the population constant.
4. The students repeat the same procedure eight times and tabulate
the data in the table below.
Sample Number
Number of fish caught in the net
(Representing days) (Representing bacteria population)
1
2
3
4
5
6
7
8
5. Graph a scatter plot of the data with Sample number (days) as
independent variable(x axis) and number of fish representing
bacteria population as the dependent variable(y axis).
6. The students will use graphing techniques and least square
regression analysis to find a best fitting curve for the scatter plot.
7. Analyze the graph and talk about it as a constant function
representing cases where bacteria population is constant and no
growth or decay takes place. These are the days when no food or
oxygen is provided to the microorganisms in the waste water
treatment plants.
51
B. DATA COLLECTION WITH LINEARLY INCREASING POPULATION
a. Each team mixes the goldfish crackers with pretzels back again.
b. The students scoop a sample out of the "tank" with the “net” onto
the paper plate.
c. The number of fishes trapped are counted and then thrown back into
the tank along with a new scoop of goldfish crackers depicting the
birth of a new set of fishes (bacteria). The population of bacteria will
now increase.
d. The students repeat the same procedure eight times throwing in a
new scoop with each new sample and then tabulate the data in the
table below.
Sample Number
Number of fish caught in the net
(Representing days) (Representing bacteria population)
1
2
3
4
5
6
7
8
52
e. Graph a scatter plot of the data with Sample number (days) as
independent variable(x axis) and number of fish representing
bacteria population as the dependent variable(y axis).
f. The students will use graphing techniques and least square
regression analysis to find a best fitting curve for the scatter plot.
g. Analyze the graph and talk about it as a linear function representing
cases where population is growing at a linear rate. These are the
days when no food but only oxygen is provided to the
microorganisms in the waste water treatment plants.
C. DATA COLLECTION WITH EXPONENTIALLY INCREASING POPULATION
h. Each team mixes the goldfish crackers with pretzels back again.
i. The students scoop a sample out of the "tank" with the “net” onto
the paper plate.
j. The number of fishes trapped are counted and then thrown back into
the lake along with a new scoop of goldfish crackers exactly equal to
number caught in the net. This depicts the birth of a new set of
bacteria and the population of bacteria will now increase
exponentially.
k. The students repeat the same procedure eight times throwing in an
extra amount equal to the number of caught fishes in each new
sample. Tabulate the data in the table below.
53
Sample Number
Number of fish caught in the net
(Representing days) (Representing bacteria population)
1
2
3
4
5
6
7
8
l. Graph a scatter plot of the data with Sample number (days) as
independent variable (x axis) and number of fish representing bacteria
population as the dependent variable (y axis).
m. The students will use graphing techniques and least square
regression analysis to find a best fitting curve for the scatter plot.
n. Analyze the graph and talk about it as an exponential function
representing cases where population is growing at an exponential rate.
These are the days when food and oxygen is provided to the
microorganisms in the waste water treatment plants.
54
MATH CONNECTION
1. As a result of this activity, students learn how to gather information about a
large population of living organisms based on a representative sample whose
makeup is similar.
2. The students will be able to see that fish population or any other population
like bacteria and microbes may grow in different fashions in every day life.
3. As a result of this activity, students learn that basic growth curves are
functions graphs. The students will now be ready to analyze growth and
decay in microbial population.
55
ASSESSMENT
1. The students will conduct the same experiment, the fishes trapped are counted
and then the number thrown back should be half of the number caught (converted
to a whole number).
Sample Number
Number of fish caught in the net
(Representing days) (Representing bacteria population)
1
2
3
4
5
6
7
8
2. Graph the scatter plot of the data with Sample number (days) as independent
variable(x axis) and number of fish representing bacteria population as the
dependent variable(y axis).
3. The students will use graphing techniques and least square regression analysis to
find a best fitting curve for the scatter plot. Analyze the graph and write a
paragraph about its behavior, correlating it to actual population of bacteria in a
Waste water treatment lagoon tank.
4. Write a paragraph about the relation between all the four cases of growth curves
studied.
5. What do you think are the variables affecting the change in microbe population
in an actual Waste water treatment lagoon tank?
56
ANSWER KEY
1.
The table would have population readings which will decrease in an
exponential fashion.
2.
The graph over the scatter plot will be similar to the graph below with
population as the dependent variable and sample number as the independent
variable.
3.
The population shows an exponential decay as every time half the
population is got rid of. The number of fishes will decrease at a fast rate initially
but as there will be fewer fishes to fish for in the later stages their number will
practically fall down to zero value. The case can be related to an actual Waste
water treatment lagoon tank where if constant death of bacteria takes place the
result will lead to zero bacteria population and unclean water as bacteria are the
main water cleaners.
4. Case A:
The graph will be a constant function graph.
Case B:
The graph will be a linear function graph.
Case C:
The graph will show exponential growth.
Assessment case: The graph will be an exponential decay graph.
4.
a.
b.
c.
d.
e.
f.
The bacteria population can vary because of,
Changes in available food.
Changes in water and environment contamination.
Changes in available oxygen.
Water born diseases.
Population growth factors such as changes in birth rates.
New bacteria introduced into the population from other sources etc.
57
RUBRIC FOR MATH ASSESSMENT: LESSON 2
THE MATHEMATICS OF POPULATION
Teacher:
MS. SUDEEPA PATHAK
Student:
School:
WILLIAMSTON HIGH SCHOOL
Class:
Objective #1: Upon completing this assignment, you will 1.Learn how Total =
to study, analyze and correlate multivariate graphs.
/ 100
2. Learn how to simulate population study.
1. Conduct the experiment and tabulate the data.
2. Do the above and graph the scatter plot of the data from
the table.
3. Do all the above and find the least square regression
curve fitting the scatter plot, analyze the graph and write
about its behavior.
4. Do all the above and able to correlate all four cases.
5. Do all the above and think about various parameters
which affect the population of bacteria in real life waste
water treatment lagoon tanks.
20
40
60
80
100
58
TABLE USED FOR TABULATING BACTERIA POPULATION (COPIES CAN BE
DISTRIBUTED TO STUDENTS)
Sample Number
Number of fish caught in the net
(Representing days) (Representing bacteria population)
1
2
3
4
5
6
7
8
Sample Number
Number of fish caught in the net
(Representing days) (Representing bacteria population)
1
2
3
4
5
6
7
8
END OF MATH LESSON
59
Lesson 4: Experimental Design, Microbial Growth with a Bench-top Bioreactor
Introduction
Wastewater treatment in wastewater facilities can be done by physical, chemical or biological methods.
Physical and chemical methods are fairly straightforward including; filtering, gravity settling and chemical
reactions. Biological methods use a wide variety of processes and a host of different microorganisms.
These reactions are carried out in large tanks and lagoons (See Figure 1). Bench-top bioreactors can be
used to model the activity of microorganisms. In order to accurately stimulate microbial activity the
conditions of the natural environment must be simulated. Variables such as temperature, oxygen and
nutrient availability have to be controlled. If the vessel is deprived of any of these limiting factors, growth
and metabolic activity of the microorganisms is greatly affected.
Figure 1. Greenville Utilities Commission Wastewater Treatment Facility
This activity enables students to gain knowledge in





An understanding of the mathematics and biology involved in cell growth
Use of specialist apparatus (Vernier probeware; including dissolved oxygen meter, pH meter and
conductivity meter; bioreactors)
Medium preparation
Time-management ( experiment runs for 4-6 weeks)
Technical writing ( data tables, graphs and laboratory reports)
Timeline: One ninety-minute period for initial setup and then once a week collection of data for a period of 4-6
weeks.
North Carolina Standard Course of Study for Biology
Competency Goal 1: The learner will develop abilities necessary to do and understand scientific
inquiry.
1.01 Identify biological questions and problems that can be answered through scientific investigations.
1.02 Design and conduct scientific investigations to answer biological questions.
Competency Goal 5: The learner will develop an understanding of the ecological relationships
among organisms.
5.01 Investigate and analyze the interrelationships among organisms, populations, communities, and
ecosystems.
National Science Education Standards:
CONTENT STANDARD A: As a result of activities in grades 9-12, all students should develop
 Abilities necessary to do scientific inquiry
 Understandings about scientific inquiry
CONTENT STANDARD C: As a result of their activities in grades 9-12, all students should develop understanding
of
 Interdependence of organisms
 Matter, energy, and organization in living systems
 Behavior of organisms
60
Introduction
A population is a group of the same species living together in a certain area. The size and structure of
any population changes over time due to a variety of changing factors including changing rates of births,
deaths, and migration, nutritional resources; space and environmental resources.
Under optimal conditions, a bacteria population can reproduce itself in twenty minutes; this is called its
doubling time. This fast growth period is just one phase of the growth cycle of a batch of bacteria in a
closed system.
Cell Growth
The six phases of microbial growth are summarized in Figure 2 below. The lag phase is considered to be
a time of adaptation with little growth. During the acceleration phase, cell multiplication begins to
increase and eventually reaches exponential growth. The specific growth rate (the slope) is used to
characterize cell growth. During the fourth and fifth phase, cell growth declines and eventually stops
growing. During the final phase, there is a decrease in viable cell count, cells die and cell lysis may occur.
Many variables affect optimum cell growth. In this experiment, students will study the effects of nutrient
availability and aeration on the growth of microorganisms.
decline
phase
acceleration phase
Figure 2. Typical Growth Curve for Batch Fermentation (plot on semi-log graph paper)
WHAT FACTORS AFFECT GROWTH?

Nutrients - Cell constituents and energy sources
ELEMENT
C
H
O
N
S
P
Fe
Na, K, Ca, Cl, Mg, Mn
CELL FUNCTION
organic cell components, energy
water, organic components
water, organic components, respiration
amino acids, nucleotides, coenzymes
amino acids, coenzmyes, enzymes
nucleic acids, phospholipids, coenzymes, ATP
cytochromes, enzymes
transport, ionic balance
61

Physical factors - temperature, oxygen, pH
Temperature- most organisms grow at temperatures favored by humans. Microbes grow in a
small range of temps. their maximum and minimum temps. This often varies by only 30 o C. Every
bacterial species grows at a particular minimum, optimum and maximum growth temperature
Oxygen- a necessity for some organisms and toxic to others. Obligate aerobes require oxygen
to survive. Facultative aerobes can grow in the absence or presence of oxygen. Obligate
anaerobes cannot use molecular oxygen and are sometimes harmed by it.
pH- most bacteria grow best near neutral 6.5 7.5, this is why pickles and sauerkraut are
protected because most bacteria can not survive in that pH.
In this lab activity students will culture microorganisms and macroorganisms associated with wastewater
treatment processes in benchtop bioreactors. Students will investigate the effects of nutrient availability
and oxygen availability on the population growth.
Procedure
Materials

Two five-gallon buckets

Vernier colorimeter probe

2-L pitchers (reactor vessels)


Mixed liquor including Waste Water
Treatment Plant (WWTP) organisms
2 Aquarium aerators (2 pumps, 2 air
stones, and plastic tubing)

Ice cream maker motor assembly

Ice cream maker cap for inner chamber

Galvanized wire

Water-proof glue

Wood slats

Drill

Screws

Parafilm or plastic wrap

50% ethanol

Whole milk

Vernier dissolved oxygen probe
62
Set Up for Control Bench-Scale Treatment:
Figure 3. 5 gallon buckets, aerators
and pumps
1. Assembly of Bench-Top Bioreactor
a. Wash two five gallon buckets with 50% ethanol
prior to experimentation for sterility. Dry
completely.
b. Label the two five gallon buckets “A” and “B”.
c. Add 5.3L of WWTP sludge to each bucket.
d. Make dilution buffered water with 2 Magnesium
Chloride pillows and 2 Potassium Dihydrogen
pillows per four liters of water. Make sure to
make enough to fill two five-gallon buckets.
e. Add 11.7 Liters of the dilution water to both
buckets “A” and “B”.
2. Assembly of Aerators
a. Place an aquarium aerator in each bucket. Make sure to adjust the tubing of the aerator
so that it does not interfere with the baffles of the agitator.
b. Glue the aquarium aerator to the bottom of the bucket with a water-proof sealant, making
sure the positioning of the aerator tubing does not interfere with the motion of the wire
baffles.
3. Assembly of the Agitator
a. Drill four small holes into the cap of the canister (See Figures 4 and 5 below).
b. Attach galvanized wire to each of the holes in the cap to form four wire baffles. Double
the wire, with each baffle having the length of approximately 25 cm. Glue the cap and
wires, now the agitator, to the rotation mechanism of the ice cream maker motor. Allow
this assembly to dry for 24 hours.
Figure 4. Drilled holes in the top of the
ice cream canister.
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Figure 5. Complete assembly of
motor, cap and wires.
4. Attachment of Agitator to Bioreactor
a. Stabilize the agitator, by securing the ice cream motor to slats of wood that are wider
than the diameter of the 5 gallon bucket (See Figure 6 below).
5. Attach the motor and wooden slats to the top of the bucket.
6. Cover the buckets with Parafilm or plastic wrap to prevent splashing.
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Wood slats for support
(we used classroom rulers)
Ice Cream Maker Motor
Ice Cream Churner Motor
Top of Ice Cream Canister
(inner chamber of ice
cream maker)
Aerator ( an
aquarium
air stone)
Galvanized Wire
(Baffles)
for Baffles
Figure 6. Assembled Benchtop
Bioreactor
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5 gallon bucket (Tank)
Students, Tyler and Victor, prepare the dilution
buffer.
Tyler adds the buffered water to the bioreactor
bucket.
Business partner, Jason Manning (Greenville, NC
WWTP), gives suggestions to Tyler for the
experimental setup.
More stirring of the sludge!
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Experiment 1: The Effects of Nutrient Availability with Oxygen Availability






The WWTP mixed liquor in buckets “A” and “B” is spiked with 25 mL of milk.
Solution is examined after 24 hours and sampled by collecting two 100 mL samples per
bucket.
Population estimates of key microorganisms will be quantified by the WWTP laboratory.
Everyday, discard 1000 mL of sludge from each bucket. Replace this discarded amount with
1000 mL of the buffered dilution water. After a weekend, discard 1500 mL of sludge and
replace with 1500 mL of dilution water. Add 25 mL of milk to the sludge. Stir the milk into the
sludge and cover with Parafilm or plastic. Sample the cultures prior to adding the food.
Buckets A and B will receive continuous aeration and agitation throughout the experiment.
Microorganism Inventory Data is then collected twice a week for a 4-6 week period of time.
Experiment 2: The Effects of Oxygen Availability without Nutrient Availability





Solution is agitated and aerated for the duration of the experiment.
No nutrients will be fed during the duration of the experiment.
Solution is examined after treatment. Population estimates of key microorganisms will be
quantified.
Monitor levels of dissolved oxygen using the Vernier Dissolved Oxygen probe, daily.
Microorganism Inventory Data is then collected twice a week for a 4-6 week period of time.
Experiment 3: The Effects of Lack of Oxygen and Nutrients



Solution receives no agitation and no aeration for the retention time of WWTP (24 hours)
Solution is examined after 24 hours. Population estimates of key microorganisms will be
quantified.
Microorganism Inventory Data is then collected twice a week for a 4-6 week period of time.
Note to Teachers: If time does not allow to collect data for these experiments or if the specialized
equipment is not available, please see Appendix 2,Greenville Utilities WWTP Collected Data.
Students can graph this given data and discuss growth patterns and trends.
Table 1
Experiment
1
2
3
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Nutrient
glucose
None
None
Aeration/Agitation
Yes
Yes
None
Microorganism/Macroorganism Inventory Chart
Date/Initials:________________________________________
Microorganism/
Macroorganism
Free-swimming
ciliates
Nematodes
Bioreactor
Vessel 1
Bioreactor
Vessel 2
Bioreactor
Vessel 3
Amoebas
Rotifers
Spirochetes
Water Bears
Bacteria
General Appearance
Colorimeter Reading
Mol/L
pH
Unknowns (sketch):
Comments:____________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
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Data Graph: Colorimetry Results, Absorbance vs. Time
Experiment #1
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Variable: Nutrient Availability (nutrient- whole milk)
Data Graph: Colorimetry Results, Absorbance vs. Time
Experiment #2
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Variable: Oxygen Availability (Aeration and Agitation)
Data Graph: Colorimetry Results, Absorbance vs. Time
Experiment #3
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Variable: Lack of Nutrients and Oxygen
Data Graph: Sample Population Count of Microorganisms/Macroorganisms vs. Time
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Assessment:
o
Which organisms appear to rise and decline the most? The least?
o
Which environmental factors were necessary for the survival of organisms?
o
Draw and label a typical bacterial growth curve in batch culture.

What is occurring in each stage?

What factors limit microbial growth in a bioreactor?

How and for what purpose are microbes maintained in logarithmic/exponential
phase?

How do you know if the bacteria are dead?
o
How would the shape of the graphs change if the experiment were allowed to continue
substantially for a longer period of time? Why?
o
Describe three ways in which our current knowledge of encouraging microbial growth
affects something in your life and three ways in which our current knowledge of
interfering with microbial growth affects something in your life.
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Appendix One
Lesson Four
Experimental Design, Microbial Growth with
a Bench-top Bioreactor
Greenville Utilities
WWTP
Collected Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Appendix 1: Greenville, NC WWTP Data
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Example Data Graph: Sample Population Count of Microorganisms/Macroorganisms vs. Time
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Appendix 2: Wastewater Formula Sheet
Circumference of Circle = (π) (Diameter)
Circle = (π) (Radius)² = (¼) (π) (Diameter)² = 0.785 (Diameter) (Diameter)
Rectangle = (Length) (Width)
Triangle = (½) (Base) (Height)
Volume:
Circular Tank = () (Radius) 2 (Height)
Rectangular Tank = (Length) (Width) (Height)
Cone = (1/3) () (Radius)2 (Height)
Pounds (lbs.)
= (flow MGD) (mg/L) (8.34 lbs/gal)
Sludge Age (days)
= (MLSS mg/L) (Aeration Tank Vol. MG) (8.34 lb/gal)
(Prim. Eff SS mg/L) (Flow MGD) (8.34 lb/gal)
Sludge Volume Index (ml/g)
= (30 min. sett. Solids in ml/L) (1000)
MLSS (mg/L)
Wasting Rate
= Solids to be wasted in lbs/day
(RAS Conc. Mg/L) (8.34 lbs/gal)
B.O.D. (mg/L)
= (Initial DO – Final DO) (300) / Sample in ml
Suspended Solids (mg/L)
=(Wt. 2 – Wt. 1) (1,000,000)
Sample Size in mL
Efficiency (%)
FOOD
MASS
= (Value IN - Value OUT) (100)/ Value IN
= lbs of Incoming Food = (Flow MGS) (Aera. Tank Influlent BOD in mg/l) (8.34 lb/gal)
lbs of Available Biomass (MLVSS) (Aer. Tank Volume in MG) (8.34 lb gal)
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Appendix 3: Wastewater Treatment Vocabulary
A
acidity The quantitative capacity of aqueous solutions to neutralize a base; measured by titration with a standard
solution of a base to a specified end point; usually expressed as milligrams of equivalent calcium carbonate per liter
(mg/L CaCO3); not to be confused with pH. Water does not have to have a low pH to have high acidity.
activated sludge Sludge particles produced by the growth of organisms in the aeration tank in the presence of
dissolved oxygen.
aerated pond A natural or artificial wastewater treatment pond in which mechanical or diffused air aeration is used
to supplement the oxygen supply.
aeration (1) The bringing about of intimate contact between air and a liquid by one or more of the following methods:
(a) spraying the liquid in the air; (b) bubbling air through the liquid; and (c) agitating the liquid to promote surface
absorption of air. (2) The supplying of air to confined spaces under nappes, downstream from gates in conduits, and
so on, to relieve low pressures and to replenish air entrained and removed from such confined spaces by flowing
water. (3) Relief of the effects of cavitation by admitting air to the affected section.
aeration period (1) The theoretical time, usually expressed in hours, during which mixed liquor is subjected to
aeration in an aeration tank while undergoing activated-sludge treatment. It is equal to the volume of the tank divided
by the volumetric rate of flow of the wastewater and return sludge. (2) The theoretical time during which water is
subjected to aeration.
aeration tank A tank in which wastewater or other liquid is aerated.
aerator A device that brings air and a liquid into intimate contact. See diffuser.
aerobic Requiring, or not destroyed by, the presence of free or dissolved oxygen in an aqueous environment.
aerobic bacteria Bacteria that require free elemental oxygen to sustain life.
aerobic digestion The breakdown of suspended and dissolved organic matter in the presence of dissolved oxygen.
An extension of the activated-sludge process, waste sludge is stored in an aerated tank where aerobic
microorganisms break down the material.
aerobic lagoon An oxygen-containing lagoon, often equipped with mechanical aerators, in which wastewater is
partially stabilized by the metabolic activities of bacteria and algae. Small lagoons (less than 0.5 ac [0.2 ha] and less
than 3-ft [0.9-m] deep) may remain aerobic without mechanical aeration. See also anaerobic lagoon.
alkali Generally, any substance that has highly basic properties; used particularly with reference to the soluble salts
of sodium, potassium, calcium, and magnesium.
alkaline The condition of water, wastewater, or soil that contains a sufficient amount of alkali substances to raise the
pH above 7.0.
alkalinity The capacity of water to neutralize acids; a property imparted by carbonates, bicarbonates, hydroxides,
and occasionally borates, silicates, and phosphates. It is expressed in milligrams of equivalent calcium carbonate per
liter (mg/L CaCO3).
ammonia, ammonium (NH3, NH41) Urea and proteins are degraded into dissolved ammonia and ammonium in raw
wastewaters. Typically, raw wastewater contains 30 to 50 mg/L of NH3. Reactions between chlorine and ammonia
are important in disinfection.
ammonification Bacterial decomposition of organic nitrogen to ammonia.
ammonia, ammonium (NH3, NH41) Urea and proteins are degraded into dissolved ammonia and ammonium in raw
wastewaters. Typically, raw wastewater contains 30 to 50 mg/L of NH3. Reactions between chlorine and ammonia
are important in disinfection.
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Appendix 3: Wastewater Treatment Vocabulary
B
bacteria A group of universally distributed, rigid, essentially unicellular microscopic organisms lacking chlorophyll.
They perform a variety of biological treatment processes including biological oxidation, sludge digestion, nitrification,
and denitrification.
bacterial analysis The examination of water and wastewater to determine the presence, number, and identity of
bacteria; more commonly called bacterial examination.
base A compound that dissociates in aqueous solution to yield hydroxyl ions.
biodegradation The destruction of organic materials by microorganisms, soils, natural bodies of water, or
wastewater treatment systems.
buffer A substance that resists a change in pH.
D
decomposition of wastewater (1) The breakdown of organic matter in wastewater by bacterial action, either
aerobic or anaerobic. (2) Chemical or biological transformation of the organic or inorganic materials contained in
wastewater.
dissolved oxygen (DO) The oxygen dissolved in liquid, usually expressed in milligrams per liter (mg/L) or percent
saturation.
F
facultative aerobes Bacteria that can grow and metabolize in the presence, as well as in the absence, of dissolved
oxygen.
foam (1) A collection of minute bubbles formed on the surface of a liquid by agitation, fermentation, and so on. (2)
The frothy substance composed of an aggregation of bubbles on the surface of liquids and created by violent
agitation or by the admission of air bubbles to liquid containing surface-active materials, solid particles, or both. Also
called froth.
food-to-microorganism (F:M) ratio In the activated-sludge process, the loading rate expressed as pounds of BOD5
per pound of mixed liquor or mixed liquor volatile suspended solids per day (lb BOD5/d/lb MLSS or MLVSS).
M
mean The arithmetic average of a group of data
metabolism (1) The biochemical processes in which food is utilized and wastes formed by living organisms. (2) All
biochemical reactions involved in cell synthesis and growth.
mg/L Milligrams per liter; a measure of concentration equal to and replacing ppm in the case of dilute concentrations.
microorganisms Very small organisms, either plant or animal, invisible and barely visible with the naked eye.
Examples are algae, bacteria, fungi, protozoa and viruses.
mixed liquor A mixture of raw or settled wastewater and activated sludge contained in an aeration tank in the
activated-sludge process.
municipal wastewater treatment generally includes the treatment of domestic, commercial, and industrial wastes.
TechMath 2008
Appendix 3: Wastewater Treatment Vocabulary
N
nitrate (NO3) An oxygenated form of nitrogen.
nitrite (NO2) An intermediate oxygenated form of nitrogen.
nitrogen (N) An essential nutrient that is often present in wastewater as ammonia, nitrate, nitrite, and organic
nitrogen. The concentrations of each form and the sum (total nitrogen) are expressed as milligrams per liter (mg/L)
elemental nitrogen.
O
obligate aerobes organisms that require a constant supply of oxygen to survive
obligate anaerobes organisms that cannot live in the presence of oxygen
organic Refers to volatile, combustible, and sometimes biodegradable containing carbon atoms bonded together
with other elements.
oxidized sludge Sludge in which the organic matter has been stabilized by chemical or biological oxidation.
oxygen A necessary chemical element. Typically found as O2 and used in biological oxidation. It constitutes
approximately 20% of the atmosphere.
P
parts per million (ppm) The number of weight or volume units of a minor constituent present with each 1 million
units of a solution in a mixture.
pH A measure of the hydrogen-ion concentration in a solution, expressed as the logarithm (base 10) of the reciprocal
of the hydrogen-ion concentration in gram moles per liter (g/mole/L). On the pH scale (0 to 14), a value of 7 at 25C
represents a neutral condition. Decreasing values indicate increasing hydrogen-ion concentration (acidity); increasing
values indicate decrease hydrogen-ion concentration (alkalinity).
S
scum The extraneous or foreign matter that rises to the surface of a liquid and forms a layer of film there.
sludge The accumulated solids separated from liquids during the treatment process that have not undergone a
stabilization process
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Appendix 4: Answer Key for Assessment Questions
Assessment:
1. Which organisms appear to rise and decline the most? The least?
This will vary depending upon
a.
the environmental conditions of the bioreactor, if the experiment is conducted by
the teacher/student team.
b. the data selected from the supplied Greenville WWTP Microorganism Inventory
Charts.
Over time, typically with good sludge you would probably see flagellates and bacteria
increase over time. Eventually, the bacteria will out compete the flagellates.
2. Which environmental factors were necessary for the survival of organisms?
Student answers may vary, but should include factors such as nutrients, aeration,
agitation, and adequate pH.
3. Draw and label a typical bacterial growth curve in batch culture.
a. What is occurring in each stage?

lag phase: organisms are becoming adjusted to their environment, young
organisms are growing and maturing

exponential phase: rapid growth, more births than deaths

stationary phase: growth slows down, growth is limited by availability of
nutrients and accumulation of toxic wastes, number of births = number
of deaths

death phase: number of deaths exceeds the number of births, population
is declining
Student answers may vary, but should be similar to the Figure 2 Phases of Microbial Growth.
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b. What factors limit microbial growth in a bioreactor?

c.
population counts, availability of nutrients, accumulation of toxins,
oxygen demand, pH
How and for what purpose are microbes maintained in logarithmic/exponential
phase?

Microbes are maintained in logarithmic/exponential growth phase, if a
desired product produced by the microorganisms or as a by-product of
metabolic activity is desired.
d. How do you know if the bacteria are dead?

No metabolic activity detected. STENCH!
4. How would the shape of the graphs change if the experiment were allowed to continue
substantially for a longer period of time? Why?
As the microorganisms continue utilizing the food supply, a point is reached where the
amount of food remaining limits the growth rate of the microorganisms (number of new cells).
Essentially there are too many microorganisms and not enough food to maintain them. This
causes a change in curvature on both the food and microorganisms curve. The growth rate of
the microorganisms as well as their oxygen utilization tapers off. This phase marks the beginning
of a period when the remaining live organisms starts to cannibalize the nutrients available in
their dead neighbors. The living organisms must work harder to obtain food, requiring more
energy, with the result that more end products are produced. In this phase the amount of new
cell producing from the food and complete oxidation of the food to end products for energy for
the existing microorganisms are becoming equal. The total amount of oxygen consumed is
obviously greater, as seen from the curve below.
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LESSON 5; ANALYZING THE DATA:MATHEMATICAL MODELING OF GROWTH CURVES OF MICROBES
PURPOSE:
TO DO REGRESSION ANALYSIS AND FIND CURVE OF BEST FIT FOR
GROWTH CURVES OF MICROBES
1. Allows the students to collect data of changing population of micro
organisms found in the Waste Water Treatment Plant(explained in the
preceding biology lesson module) The organisms will be experimented
under the effect of variable PARAMETERS such as nutrients (food), oxygen
provided (aeration) and agitation (movement). (Math instructors: See
Addendum for pre-prepared population data)
2. Allows the students to draw population vs. time graphs with the uses of TI
calculators or Microsoft Excel
3. Allows the students to identify an appropriate curve of best fit (linear,
quadratic, and exponential) for a set of two-variable data.
4. Allows students to apply a curve of best fit to make predictions within and
beyond a given set of two-variable data.
TIMELINE: One ninety minute period
North Carolina Math Standard Course of Study
Algebra 2
Competency Goal 2: The learner will use relations and functions to solve
problems.
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2.04 Create and use best-fit mathematical models of linear, exponential, and
quadratic functions to solve problems involving sets of data.
a. Interpret the constants, coefficients, and bases in the context of the data.
b. Check the model for goodness-of-fit and use the model, where appropriate,
to draw conclusions or make predictions
Pre-Calculus
Competency Goal 2: The learner will use relations and functions to solve
problems.
2.03 For sets of data, create and use calculator-generated models of linear,
polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.
a. Interpret the constants, coefficients, and bases in the context of the data.
b. Check models for goodness-of-fit; use the most appropriate model to draw
conclusions or make predictions.
Advanced Function and Modeling
Competency Goal 1: The learner will analyze data and apply probability
concepts to solve problems.
1.01 Create and use calculator-generated models of linear, polynomial,
exponential, trigonometric, power, and logarithmic functions of bivariate data to
solve problems.
a. Interpret the constants, coefficients, and bases in the context of the data.
b. Check models for goodness-of-fit; use the most appropriate model to draw
conclusions and make predictions
Technical Math I, II
Competency Goal 2: The learner will use relations and functions to solve
problems.
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2.03 Create, interpret, and analyze best-fit models of linear, exponential, and
quadratic functions to solve problems.
a. Interpret the constants, coefficients, and bases in the context of the data.
b. Check the model for goodness-of-fit and use the model, where appropriate,
to draw conclusions or make predictions.
NATIONAL STANDARDS:
NCTM Data Analysis and Probability Standard for Grades 9-12:
http://standards.nctm.org/document/chapter7/data.htm
Select and use appropriate statistical methods to analyze data.
 For bivariate measurement data, be able to display a scatter plot, describe its
shape, and determine regression coefficients, regression equations, and
correlation coefficients using technological tools;
 Display and discuss bivariate data where at least one variable is categorical.
Formulate questions that can be addressed with data and collect, organize, and
display relevant data to answer them.
 Understand the differences among various kinds of studies and which types
of inferences can legitimately be drawn from each.
NCTM Algebra Standard for Grades 9-12:
http://standards.nctm.org/document/chapter7/alg.htm
Use mathematical models to represent and understand quantitative relationships
 Identify essential quantitative relationships in a situation and determine the
class or classes of functions that might model the relationships;
 Draw reasonable conclusions about a situation being modeled.
MATH OBJECTIVES
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1. Conceptual understanding of growth (and decay) curves as linear, constant
polynomial, exponential and logistic functions.
2. Data collection and study.
3. Understanding sampling procedures.
4. Graphing.
5. Interpreting data and make predictions.
PROCEDURAL STANDARDS
5.
6.
7.
8.
Representation
Reasoning
Communication
Connections
HOOK
Students will learn how to mathematically analyze growth patterns of a population of microorganisms found in the Waste Water Treatment Plant by varying three parameters:
1. Nutrients (food fed as glucose)
2. Oxygen provided (aeration)
3. Agitation (movement)
Students should already be familiar with data analysis and prediction based on
correlation and regression analysis. In the previous lesson, students collected
population growth data from three different experiments performed on organisms
growing in the Waste Water Treatment Plant. In this lesson students will graph
that data using a TI-84 calculator or Microsoft Excel and fit appropriate functions
to their data. The three experiments should produce three different graphs:
constant, linear, and exponential.
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Material needed
1. Population data collected through experiments on microbes (see attached
addendum for simulated data if the students did not collect their own
through the preceding biology lesson).
2. TI graphing calculator OR Microsoft Excel software.
PROCEDURE:
A. DATA PLOTTING AND ANALYSIS OF MICROBE POPULATION
BEING FED WITH NUTRIENTS (GLUCOSE).
1. Students will record population of microbes found in “Waste Water
Treatment experiment” set in their Laboratory on different days and
are constantly fed with glucose as nutrient.
2. The data will be plotted as a scatter plot and a best fitting curve is
analyzed.
3. The students will predict the population of microbes on a certain day,
for example the 22nd day.
A. Plotting the population in number/liter of microbes recorded on
certain days under a varying parameter of nutrient (glucose) fed to the
microbes.
B. Predicting the population on a certain day (for example the 22 day).
1. Enter the data in the calculator
lists. Place the data in L1 and L2.Let
L1 represent the day and L2 represent
population/liters.
Type: STAT, 1 (Edit), then type the
data values into the lists
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2. Prepare a scatter plot of the data.
Type: 2nd, Stat Plot. Resulting
screen is shown at right.
Press: ZOOM, 9 (Zoom Stat).
Sample graph is shown below.
3. Have the calculator determine the
curve of best fit for example the
linear regression.
STAT → CALC #4 LinReg(ax+b)
Include the parameters L1, L2, Y1.
(Y1 comes from VARS → YVARS,
#Function, Y1)
LinReg L1,L2,Y1
y=ax+b
a=13.09073265
b=145.3808831
r2=.9982701159
r=.9991346836
You now have the values of a and b
needed to write the equation of the
line of best fit. See values at the
right.
y = 13.09073265x + 145.3808831
4. To view the graph simply hit
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GRAPH and view the line of best fit.
5. To get a predicted value within
the graph window,
hit
nd
2 : Calc#1value, and type the
desired value such as X=22 for
finding number of microbes on 22nd
day.
The predicted value is 452
microbes/liter of fluid for this data.
C. DATA PLOTTING AND ANALYSIS OF MICROBE POPULATION
UNDER THE EFFECT OF 0.8L/min AERATION and AGITATION of 400
revolutions per min of rotor speed.
1. Students will record population of microbes found in “Waste Water
Treatment experiment” set in their Laboratory on different days and are
constantly provided with oxygen and agitation.
2. The data will be plotted as a scatter plot and a best fitting curve is analyzed,
following the same process as was carried out in Procedure B.
3. The students will predict the population of microbes on a certain day, for
example the 22nd day.
TechMath 2008
D. DATA PLOTTING AND ANALYSIS OF MICROBE POPULATION
UNDER THE EFFECT OF no AERATION and AGITATION or rotor
speed.
1. Students will record population of microbes found in “Waste Water
Treatment experiment” set in their Laboratory on different days and are not
provided with oxygen and agitation.
2. The data will be plotted as a scatter plot and a best fitting curve is analyzed,
following the same process as was carried out in Procedure B.
3. The students will predict the population of microbes on a certain day, for
example on the 22 day.
MATH CONNECTION
4. As a result of this activity, students learn how to graph, analyze and predict
information about a large population of living organisms found in Waste
Water Treatment Plant based on a representative sample in a lab whose
makeup is similar.
5. As a result of this activity, students learn that basic growth curves of micro
organisms found in Waste Water are function graphs that may help to study
and make predictions for whole populations or different populations of
organisms.
6. As a result of this activity students can correlate that the growth and
termination of microbes could be varied according to the needs of the Waste
Water Treatment Plant. The students can understand that waste water sludge
may be loaded with dirt or oily filth and may need more microbes on certain
days as compared to other days for water cleaning. The students can see that,
HOW IN REAL LIFE change in parameters and data through curve fitting
will help them to vary microbe population in the Waste Water Treatment
Plant.
TechMath 2008
ASSESSMENT
1. The same experiment was conducted on a different microbe’s species under the
effect of 0.8L/min aeration and 400 rotations per min of rotor speed in a “Waste
Water Treatment experiment” set in a Laboratory. Students are provided the
population of microbes on different days on the table below:
DAY OF
POPULATION OF MICROBES(NUMBER IN
RECORDING
HUNDRED/LITER)
1
1.3
2
2.7
8
3.5
10
3.7
11
3.8
12
4.0
16
4.2
24
4.25
1. Plot the data as a scatter plot and find the best fitting curve and write its
equation.
2. Analyze the graph and write a paragraph about its behavior, correlate this
population study with one of the three population cases studied in the lesson.
3. What do you think are the variables affecting the change in microbe
population in an actual waste water plant?
TechMath 2008
SOLULTIONS
1. The scatter plot will show exponential growth and the equation will be of
the form y=ab^x.
2. The microbe population in this case will grow exponentially and is very
similar to, Case 2: Where the graph showed exponential growth in
population under the effect of aeration and agitation.
3. The population depends upon,
a. Food and nutrients.
b. Oxygen and environment conditions.
c. Water contamination.
d. The variety of microbes in waste water, etc.
e. Other reasonable suggestions.
TechMath 2008
RUBRIC FOR MATH ASSESSMENT
LESSON 5
ANALYZING THE DATA:-MATHEMATICAL MODELING OF GROWTH
CURVES OF MICROBES
Teacher:
MS. SUDEEPA PATHAK
Student:
School:
WILLIAMSTON HIGH SCHOOL
Class:
Objective #1: Upon completing this assignment, you will 1.Learn how Total =
to study, analyze and correlate multivariate graphs.
2. Learn how to simulate population study.
1. Graph a scatter plot of the data from the table.
2. Do the above and find the least square regression curve
fitting the scatter plot along with the equation of the
function.
3. Do all the above and analyze the graph.
4. Do all the above and able to correlate this case with
three cases analyzed in the lesson.
5. Do all the above and think about various parameters
which affect the population of bacteria in real life waste
water treatment lagoon tanks.
TechMath 2008
20
40
60
80
100
/ 100
ADDENDUM
A. DATA OF MICROBE POPULATION BEING FED WITH GLUCOSE
DAY OF
RECORDING
9
13
21
30
31
31
34
35
POPULATION OF MICROBES(NUMBER IN
HUNDRED/LITER)
260
320
420
530
560
550
590
605
B. DATA OF MICROBE POPULATION UNDER THE EFFECT OF
0.8L/min AERATION and AGITATION of 400 revolutions per min of rotor
speed.
DAY OF
POPULATION OF MICROBES(NUMBER IN
RECORDING
HUNDRED/LITER)
0
2.27
4
3.15
8
3.55
12
3.82
16
3.91
20
3.93
22
3.94
24
3.94
TechMath 2008
C. DATA OF MICROBE POPULATION UNDER THE EFFECT OF no
AERATION and no AGITATION of rotor.
DAY OF
RECORDING
0
4
8
12
16
20
22
24
END OF MATH LESSON
TechMath 2008
POPULATION OF MICROBES(NUMBER IN
HUNDRED/LITER)
2.56
2.57
2.54
2.58
2.60
2.58
2.59
2.52
TechMath 2008