Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Metagenomics wikipedia , lookup
Traveler's diarrhea wikipedia , lookup
Phospholipid-derived fatty acids wikipedia , lookup
Human microbiota wikipedia , lookup
Microorganism wikipedia , lookup
Bacterial cell structure wikipedia , lookup
Bacterial taxonomy wikipedia , lookup
Bacterial morphological plasticity wikipedia , lookup
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. TechMath 2008 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. TechMath 2008 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 TechMath 2008 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! TechMath 2008 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 TechMath 2008 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:____________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ TechMath 2008 Data Graph: Colorimetry Results, Absorbance vs. Time Experiment #1 TechMath 2008 Variable: Nutrient Availability (nutrient- whole milk) Data Graph: Colorimetry Results, Absorbance vs. Time Experiment #2 TechMath 2008 Variable: Oxygen Availability (Aeration and Agitation) Data Graph: Colorimetry Results, Absorbance vs. Time Experiment #3 TechMath 2008 Variable: Lack of Nutrients and Oxygen Data Graph: Sample Population Count of Microorganisms/Macroorganisms vs. Time TechMath 2008 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. TechMath 2008 Appendix One Lesson Four Experimental Design, Microbial Growth with a Bench-top Bioreactor Greenville Utilities WWTP Collected Data TechMath 2008 TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Appendix 1: Greenville, NC WWTP Data TechMath 2008 Example Data Graph: Sample Population Count of Microorganisms/Macroorganisms vs. Time TechMath 2008 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) TechMath 2008 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. TechMath 2008 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 25C 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 TechMath 2008 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. TechMath 2008 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. TechMath 2008 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. TechMath 2008 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. TechMath 2008 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 TechMath 2008 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. TechMath 2008 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 TechMath 2008 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 TechMath 2008 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