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= Welcome to Christina Ferrara's EDUC 519 Math Wiki! =


 * For the topic of my performance task, I have chosen probability and data analysis. The task has been designed to be appropriate for an 8th grade Algebra I class.**


 * The following NCTM standards for grades 6-8 (http://standards.nctm.org) will be addressed:**

Understand and apply basic concepts of probability:
 * Understand and use appropriate terminology to describe complementary and mutually exclusive events;
 * Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.

Instructional programs from prekindergarten through grade 12 should enable all students to—


 * create and use representations to organize, record, and communicate mathematical ideas;
 * select, apply, and translate among mathematical representations to solve problems;
 * use representations to model and interpret physical, social, and mathematical phenomena.

Students understand that data analysis and probability have important uses in real life and are able to apply their knowledge to such situations. Students understand how to formulate and predict outcomes of experiments using basic probability. Students understand what makes multiple events complementary or mutually exclusive.
 * The enduring understandings for the task will be:**

Why is it important to understand basic data analysis and probability? What types of jobs depend on probability calculations? How? How does one decide whether multiple events are complementary or mutually exclusive?
 * The essential questions for the task will be:**

Textbook (chapter on probability and odds), paper and a writing utensil, calculator, computer with PowerPoint software or posterboard & markers.
 * Materials needed:**

For additional ideas or help, see me or visit these websites: http://www.onlinemathlearning.com/complementary-events.html http://www.onlinemathlearning.com/mutually-exclusive-events.html http://people.richland.edu/james/lecture/m116/sequences/probability.html


 * Task:**

You are working on your first project at company XYZ to develop a new drug to treat chronic headaches. The first 13 reports from the clinical trials have just arrived, and your boss wants you to analyze the information and provide a panel of people reviewing the drug with some very preliminary results. Here is the data you have to work with:
 * Consider **

Patient A went from having 12 headaches/week to 11 headaches/week. Reported side effects included runny nose and constipation. Patient B went from having 7 headaches/week to 8 headaches/week. No reported side effects. Patient C reported no change in headaches. Reported side effects included runny nose, fatigue, and blurred vision. Patient D went from having 10 headaches/week to 4 headaches/week. Reported side effects included runny nose. Patient E went from having 12 headaches/week to 17 headaches/week. Reported side effects included blurred vision and constipation. Patient F went from having 13 headaches/week to 11 headaches/week. Reported side effects included runny nose and fever. Patient G reported no change in headaches. No reported side effects. Patient H went from having 2 headaches/week to 1 headaches/week. Reported side effects included runny nose and constipation. Patient I went from having 12 headaches/week to 11 headaches/week. Reported side effects included runny nose and constipation. Patient J went from having 5 headaches/week to 0 headaches/week. Reported side effects included blurred vision. Patient K went from having 20 headaches/week to 1 headache/week. Reported side effects included runny nose. Patient L reported no change in headaches. Reported side effects included runny nose and blurred vision Patient M reported no change in headaches. No reported side effects.

1. Create a graph to represent the number of patients with each observed side effect. HINT: Be sure to include a section for “no side effects observed.” 2. Create a visual representation of your choice (graph, table, etc.) to illustrate to the drug panel the number of people taking the drug that saw an improvement in their headaches.
 * Evaluate the data **

3. Dr. Z asks: Based on your report, what is the probability of a patient suffering from a runny nose? Both a runny nose and blurred vision? Any side effect at all? 4. Mrs. Y asks: Based on your report, what would you tell your company the odds are of seeing improvement in a patient taking the drug? 5. Mr. X asks: Theoretically, is it possible for the probability of having no side effects to be .6 while the probability of having a runny nose is .5? Explain. 6. Mrs. Y asks: Theoretically, is it possible for the probability of having a runny nose to be .5 and the probability of having a fever to be .7? Explain. 7. Miss Ferrara: Based on the current numbers, what side effects would you recommend the company include on the label of the drug? Why? 8. Mr. X informs you that 4 more patient’s results have come in. None reported a change in headaches or experiencing side effects. How does this affect your answers to questions 3 and 4? Does it affect your answer to question 7? 9. Miss Ferrara asks: Based on your answer to question 8, why are small sample sizes considered not as reliable as large sample sizes in drug studies?
 * Analyze the data – You’ve presented the information. Now you have to answer the panel’s questions. **


 * Your creations from questions 1 and 2 should be prepared in a PowerPoint presentation or on a poster board. The rest of the questions should be answered thoroughly on a sheet of paper to be collected. Be prepared to present your report to the class if asked, as well as answer and explain any of the accompanying questions! **

Project to be scored using the below scoring guide (25 points):


 * Points || Criteria ||
 * 5 || The visual representations of the data were chosen and created in a way that portrays an understanding of the important information related to probability and data analysis. ||
 * 10 || All questions were answered completely, with all thought processes evident. ||
 * 5 || Accuracy of data interpretation and question answers ||
 * 5 || Presentation to class conveyed a strong understanding of the task and underlying concepts ||