I give students access to calculators for this problem, so that the majority of their time is spent reasoning about the best measure to use.
Before this class began, I had the kids read and underline any words what were difficult to understand. While students are working on the means and medians, I circulate around the room and look for underlined works so that I can help support students who need it. After 4 minutes of work time, I have students turn and quickly compare their means and medians with a partner before we start our whole class conversation.
I ask students to comment about what type of student they think Shemar is. I then ask them what they think I, as the teacher, would put in the grade book.
I ask students about the data - did people generally have a good experience on Tuesday night? I ask them what the 1 represents. Drawing from the learning in the previous lessonI ask students what the 1 would do to the mean of the data set.Professional beauty supply store
I ask students if the mean or the median would be a better overall representation of the scenario. In this example, we want an overall idea to know how most people feel about customer service. An exact average, which would be the mean, would be skewed lower because one person had a bad experience at the restaurant. We do not calculate the mean and median for this problem, but I will provide for students at the end of the conversation, so that they can see that the median in this example 9.
The key ideas that come out in conversation and are recorded in the graphic organizer :. As they are working, I circulate around the room and check in with each group. I am looking for:. I also will ask groups to calculate the mean and median of a data set once they've written their response, as a way to justify their thinking. After 10 minutes of partner practice time, students complete the Check for Understanding problem independently. A number of the problems in this lesson ask students to draw a dot plot to represent the data.
It also gives students a visual to use, to decide whether or not there are outliers and to determine if the data is closely clustered. As I circulate, I check the work of problem 4. This problem requires students to create a dot plot and the data set contains an outlier.
I can quickly see whether or not the visual representation is correct. There are many opportunities for questions here. I can ask what would happen if the next two quizzes were 40 and 45 - how would that change your thinking? What if the teacher dropped the lowest score? What measure would make the most sense then?For example, if you counted 24 colonies on the dilution plate you would use the following proportion and solve for X using the following steps.
Note: cfu means colony forming unit which is equivalent to a bacterium as long as the bacteria are single-celled and are not clumps or groups when plated; this is true for many strains of Escherichia coli and other organisms commonly used in the lab. A CFU is basically just a single, viable cell that's capable of dividing and form a colony after some incubation period.
Dilution factor is the same as the dilution you've written above, except the exponent should be positive instead of negative. Not the right answer? Try Yahoo! Science Research 7. Biology CFU calculations A culture was diluted by adding a 0.
Then, 0. And 0.Dilutions - Part 3 of 4 (Calculating Colony Forming Units/ml)
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Carousel Previous Carousel Next.Calculating titer for a virus is a complicated way of saying that a scientist is counting the number of viruses in a particular sample. To calculate virus titers, scientists infect plates of growing bacteria with viral solutions at varying concentrations and figure out the number of viruses in the original solution by counting the bacteria that have died due to the viral infection. Since viruses can grow to incredibly high concentrations, you need to dilute them in order to count them effectively.
Each tube represents a ten-fold dilution of the virus. Mix the tube well. This is your first ten-fold dilution. Continue this pattern to create a serial dilution series. You will end up with 9 tubes of 9 ml and 1 tube of 10 ml. The viral loads in your tubes will be diluted anywhere from 10 times your first tube or times your second tube to ten billion times your final tube. Take 10 tubes of tryptone soft agar and 10 Petri plates and label them to correspond with your serial dilution tubes.
Loosen the caps so that they do not pop off in the heat and then place your agar tubes in a beaker of boiling water. This will melt the agar so that you can pour it into Petri plates. Transfer your tubes to a hot water bath set at a minimum of 45 degrees Celsius.
This will ensure that your agar does not solidify in the tubes before you have a chance to pour it into a Petri dish. Add two drops of bacterial culture to your agar and mix it gently. These are the bacteria that will be killed, allowing you to count the number of virus particles in a particular solution.
Add 1 ml of each serial dilution to its corresponding agar tube while the tubes are still in the hot water bath. Mix each tube and then pour each tube into the Petri plate with the corresponding label. This will create a thin layer of agar that has been inoculated with bacteria and viruses in each plate. Let the plates grow overnight in an incubator.
Take your plates out of the incubator and examine them. You should see cloudy areas throughout the plate where bacteria have grown, except for small clear spots called plaques. These plaques are patches of dead bacteria, and each plaque represents one virus.Dilution is the process of making a solution weaker or less concentrated. In microbiologyserial dilutions log dilutions are used to decrease a bacterial concentration to a required concentration for a specific test method, or to a concentration which is easier to count when plated to an agar plate.
I have created this guide to provide a better understanding of dilutions and should be used as a guideline, not a replacement for laboratory procedures. A log dilution is a tenfold dilution, meaning the concentration is decreased by a multiple of ten.
To complete a tenfold dilution, the ratio must be The 1 represents the amount of sample added. The 10 represents the total size of the final sample.
For example, a sample size of 1 ml is added to 9 ml of diluent to equal a total of 10 ml. Example: dilution — if the concentration is 1, CFU, a one log dilution will drop the concentration to CFU. Multiple dilutions are required to decrease the sample concentration by multiple logs. A serial dilution is the stepwise dilution of a substance in a solution. Usually, the dilution factor at each step is constant, resulting in a geometric progression of the concentration in a logarithmic fashion.
After you have calculated the individual dilutions for each tube, multiply the dilutions when using serial dilutions. Serial dilutions are the culmination of a number of diluted tubes used in order to get smaller dilutions.
How to Calculate CFU/ml?
Following is a graphic representation of these dilutions:. You incubate the plates for 24 hours, after which you obtain the following results:. Friend's Email Address.
Your Name. Your Email Address. Send Email. Skip to content. Leave a Reply Cancel reply Comment. Enter your name or username. Enter your email. Enter your website URL optional. Search for: Type text and hit enter to search. Close Menu. Share this Article Like this article? Email it to a friend!It is imperative that you utilize your best aseptic technique. Not all bacterial cells produce colonies, as some bacteria tend to clump or aggregate, and some are nonviable.
Ideally only plates with colonies are used. Plates with less than 25 colonies do not have a statistically significant number of colonies. When the approximate number of bacteria is unknown, plate a wide range of dilutions. In this way you will have at least plates within the countable range to use in your calculations.
If more than one plate is countable, average the counts together. Because dilutions are large when counting bacteria, exponents are used. Answers should be written with two significant figures in proper scientific notation, i.
Then 4 serial fold dilutions are made. To arrive at a final dilution, multiply successive dilutions together. How many CFUs were in the original sample?
To graph these data, start the spreadsheet software package Microsoft Excel. Directions are for Microsoft Office For example, enter the exponent 5. With the mouse, start in cell A1 and drag the mouse to B5. Your data cells and only your data cells should be highlighted. If data graphed are not correct, click series and enter the correct X and Y values. Step 3 : Add appropriate title, X and Y units. Change axes, gridlines, legend, etc. Step 4 : Indicate if you want the chart as a new sheet or as an object in present chart.
Once you have your graph, click on the y axis and change scale to logarithmic. You can also add more hatch marks to make it easier to read the graph. If you click on the graph and choose print, it will size graph to full page.
Figure 1. Linear trendline added. You can use the graph to determine the generation time. Choose two points on the graph between which the population doubled and determine the time it took for this to happen.
For DNA, the sample is loaded onto an agarose gel and subjected to an electrical current. Numerous markers are commercially available, so DNA size may be determined. The 11 bands produced by this digest are shown in Figure 2.
These fragments are suitable for sizing linear double-stranded DNA from bp.A colony-forming unit CFU, cfu, Cfu is a unit used In microbiology to estimate the number of viable bacteria or fungal cells in a sample.
Viable is defined as the ability to multiply via binary fission under the controlled conditions. Counting with colony-forming units requires culturing the microbes and counts only viable cells, in contrast with microscopic examination which counts all cells, living or dead.
The visual appearance of a colony in a cell culture requires significant growth, and when counting colonies it is uncertain if the colony arose from one cell or a group of cells. Expressing results as colony-forming units does not distinguish.
The purpose of plate counting is to estimate the number of cells present based on their ability to give rise to colonies under specific conditions of nutrient medium, temperature and time. Theoretically, one viable cell can give rise to a colony through replication. However, solitary cells are the exception in nature, and most likely the progenitor of the colony was a mass of cells deposited together.
Streptococcus or clumps e. Estimation of microbial numbers by CFU will, in most cases, undercount the number of living cells present in a sample for these reasons. This is because the counting of CFU assumes that every colony is separate and founded by a single viable microbial cell. The plate count is linear for E.Dell xps 15 9550 battery 97whr
Typically ten-fold dilutions are used, and the dilution series is plated in replicates of 2 or 3 over the chosen range of dilutions. An advantage to this method is that different microbial species may give rise to colonies that are clearly different from each other, both microscopically and macroscopically. The colony morphology can be of great use in the identification of the microorganism present. Alternatively it is possible to decrease the average number of cells per CFU in some cases by vortexing the sample before conducting the dilution.
However many microorganisms are delicate and would suffer a decrease in the proportion of cells that are viable when placed in a vortex. Concentrations of colony-forming units can be expressed using logarithmic notation, where the value shown is the base 10 logarithm of the concentration. Colony-forming units are used to quantify results in many microbiological plating and counting methods, including:. However, with the techniques that require the use of an agar plate, no fluid solution can be used because the purity of the specimen cannot be unidentified and it is not possible to count the cells one by one in the liquid.
Counting colonies is traditionally performed manually using a pen and a click-counter. This is generally a straightforward task, but can become very laborious and time-consuming when many plates have to be enumerated. Colonies can be enumerated from pictures of plates using software tools.
The experimenters would generally take a picture of each plate they need to count and then analyse all the pictures this can be done with a simple digital camera or even a webcam. Since it takes less than 10 seconds to take a single picture, as opposed to several minutes to count CFU manually, this approach generally saves a lot of time. In addition, it is more objective and allows extraction of other variables such as the size and colour of the colonies.
In addition to software based on traditional desktop computers, apps for both Android and iOS devices are available for semi-automated and automated colony counting. The integrated camera is used to take pictures of the agar plate and either an internal or an external algorithm is used to process the picture data and to estimate the number of colonies. Many of the automated systems are used to counteract human error as many of the research techniques done by humans counting individual cells have a high chance of error involved.
Due to the fact that researchers regularly manually count the cells with the assistance of a transmitted light, this error prone technique can have a significant effect on the calculated concentration in the main liquid medium when the cells are in low numbers. Completely automated systems are also available from some biotechnology manufacturers. Some of the automated systems such as the systems from MATLAB allow the cells to be counted without having to stain them. This lets the colonies to be reused for other experiments without the risk of killing the microorganisms with stains.
However, a disadvantage to these automated systems is that it is extremely difficult to differentiate between the microorganisms with dust or scratches on blood agar plates because both the dust and scratches can create a highly diverse combination of shapes and appearances.
The Most Probable Number method counts viable cells and is useful when enumerating low concentrations of cells or enumerating microbes in products where particulates make plate counting impractical. From Wikipedia, the free encyclopedia. For the human hematopoietic cell, see Hematopoietic stem cell.For additional information, contact Guodong Zhang.
The aerobic plate count APC is intended to indicate the level of microorganism in a product. The conventional plate count method for examining frozen, chilled, precooked, or prepared foods, outlined below, conforms to AOAC Official Methods of Analysissec.
The suitable colony counting range 10 is The automated spiral plate count method for the examination of foods and cosmetics 5outlined below, conforms to AOAC Official Methods of Analysissec.
Appropriate Measure of Central Tendency
For procedural details of the standard plate count, see ref. Guidelines for calculating and reporting plate counts have been changed to conform with the anticipated changes in the 16th edition of Standard Methods for the Examination of Dairy Products 2 and the International Dairy Federation IDF procedures 6. Using separate sterile pipets, prepare decimal dilutions of 10 -210 -310 -4and others as appropriate, of food homogenate see Chapter 1 for sample preparation by transferring 10 ml of previous dilution to 90 ml of diluent.
Avoid sampling foam. Shake all dilutions 25 times in 30 cm 1 ft arc within 7 s. Pipet 1 ml of each dilution into separate, duplicate, appropriately marked petri dishes. Reshake dilution bottle 25 times in 30 cm arc within 7 s if it stands more than 3 min before it is pipetted into petri dish. For milk samples, pour an agar control, pour a dilution water control and pipet water for a pipet control.
Add agar to the latter two for each series of samples. Add agar immediately to petri dishes when sample diluent contains hygroscopic materials, e. Pour agar and dilution water control plates for each series of samples. Immediately mix sample dilutions and agar medium thoroughly and uniformly by alternate rotation and back-and-forth motion of plates on flat level surface. Let agar solidify. Do not stack plates when pouring agar or when agar is solidifying.
Official Methods of Analysis 3 does not provide guidelines for counting and reporting plate counts, whereas Standard Methods for the Examination of Dairy Products16th ed. Report all aerobic plate counts 2 computed from duplicate plates.
For milk samples, report all aerobic plate 2 counts computed from duplicate plates containing less than 25 colonies as less than 25 estimated count. Report all aerobic plate counts 2 computed from duplicate plates containing more than colonies as estimated counts. Counts outside the normal range may give erroneous indications of the actual bacterial composition of the sample.
Dilution factors may exaggerate low counts less than 25and crowded plates greater than may be difficult to count or may inhibit the growth of some bacteria, resulting in a low count.
Report counts less than 25 or more than colonies as estimated aerobic plate counts EAPC. Use the following guide:.
Computing and recording counts see refs 68.
To avoid creating a fictitious impression of precision and accuracy when computing APC, report only the first two significant digits. Round off to two significant figures only at the time of conversion to SPC.
For milk samples, when plates for all dilutions have no colonies, report APC as less than 25 colonies estimated count.
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