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The New Illinois Learning Standards for Algebra II / Math II Statistics and Probability

The New Illinois Learning Standards for Algebra II / Math II Statistics and Probability. Julia Brenson. The Four Components of a Statistical Investigation*. 1) Formulate a question 2) Design and implement a plan to collect data 3) Analyze the data by measures and graphs

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The New Illinois Learning Standards for Algebra II / Math II Statistics and Probability

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  1. The New Illinois Learning Standards for Algebra II / Math IIStatistics and Probability Julia Brenson

  2. The Four Components of a Statistical Investigation* 1) Formulate a question 2) Design and implement a plan to collect data 3) Analyze the data by measures and graphs 4) Interpret the results in the context of the original question *Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report American Statistical Association http://www.amstat.org/education/gaise/GAISEPreK-12_Full.pdf

  3. The New Illinois Learning Standards Algebra II and Math II

  4. Statistics Standards for Algebra II/Math IIMaking Inferences & Justifying Conclusions

  5. Statistics Standards for Algebra II/Math IIConditional Probability and the Rules of Probability Big Ideas • Provide opportunities for students to independently determine if a problem is asking for an AND, OR, or conditional probability. • Provide data from real life problems. Ask students to calculate probabilities and interpret probabilities in the context of the problem. • Students should be able to create and interpret two-way frequency tables, diagrams, probability trees, and other graphical displays. • Determine if two events are independent or dependent, and interpret what this means in the context of the problem.

  6. Examples of events which are likely to be dependent: • The event that a student spends more time on homework and studying and the event that the student’s test average goes up. • The event that the amount of snow is above average in a given winter and the event that the number of show shovel sales is also above average for that winter. • The event that a randomly selected passenger on the Titanic was a woman and the event that the passenger survived. • Example of events which are independent • The event that a 2 is rolled on the first roll of a dice and the event that a 2 is rolled on a second roll of a dice. • The event that a couple’s first child is a boy and the event that a couple’s second child is a girl.

  7. Statistics Standards for Algebra II/Math IIConditional Probability and the Rules of Probability Addition Rule The probability that event E or Event F occurs can be found by:

  8. Statistics Standards for Algebra II/Math IIConditional Probability and the Rules of Probability Activity: Conditional Probability Four Square

  9. Statistics Standards for Algebra II/Math IIConditional Probability and the Rules of Probability Duct Tape Therapy • Read The Efficacy of Duct Tape vs Cryotherapy in the Treatment of Verruca Vulgaris (the Common Wart). • Complete the table below using the data available in the “Results” section of the text found on page 972. Sample Questions: • Given that a patient had complete resolution, what is the probability that they received the Duct Tape Occlusion Therapy? • Is complete resolution independent of the type of treatment received? 22 4 26 15 10 25 37 14 51

  10. Statistics Standards for Algebra II/Math IIConditional Probability and the Rules of Probability Activities: • Titanic(www.illustrativemathematics.org) • Duct Tape Therapy (The Efficacy of Duct Tape vs Cryotherapy in the Treatment of Verruca Vulgaris (the Common War) available as a free download from JAMA Pediatrics http://archpedi.jamanetwork.com/article.aspx?articleid=203979&resultClick=1) • Lengthening the School Day (http://www.smarterbalanced.org/).

  11. Statistics Standards for Algebra II/Math II Fit a Function to Data: Non-Linear Functions Be sure to include work on fitting functions to non-linear data! Kamataka Task Adapted from PARCC Item Development ITN 2013-31 Appendix F

  12. Acknowledgements and Resources Chance, B. & Rossman, A. (Preliminary Edition). Investigating Statistical Concepts, Application and Methods. Duxbury Press. Chance, B., et al. Rossman/Chance Applet Collection. Retrieved from http://www.rossmanchance.com/. Chicago Tribune. (2014, April). Chicago Bears. Retrieved from http://chicagosports.sportsdirectinc.com/football/nfl-teams.aspx?page=/data/nfl/teams/rosters/roster16.html Daily Mail. (2012, December 2). What are the odds? New study shows how guessing heads or trails isn’t really a 50-50 game. Retrieved from http://www.dailymail.co.uk/news/article-2241854/What-odds-New-study-shows-guessing-heads-tails-isnt-really-50-50-game.html. Duggan, M. & Brenner, J. (2013, February 14). The Demographics of Social Media Users – 2012. Retrieved from http://www.pewinternet.org/2013/02/14/the-demographics-of-social-media-users-2012/. Focht, D., Spicer, C, and Fairchok, M. (2002). The Efficacy of Duct Tape vs Cryotherapy in the Treatment of Verruca Vulgaris (the Common Wart). 156 (10) pp. 971-974. Retrieved from http://archpedi.jamanetwork.com/article.aspx?articleid=203979&resultClick=1.

  13. Acknowledgements and Resources Franklin, C., Kader, G., Mewborn, J. M., Peck, R., Perry, M. & Schaeffer, R. (2007) Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework. Alexandria, VA: American Statistical Association. McCallum, B., et al. (2011, December 26). Progressions for the Common Core State Standards in Mathematics (draft) 6-8 Statistics and Probability. Retrieved from http://commoncoretools.files.wordpress.com/2011/12/ccss_progression_sp_68_2011_12_26_bis.pdf. McCallum, B., et al. (2012, April 21). Progressions for the Common Core State Standards in Mathematics (draft) High School Statistics and Probability. Retrieved from http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_sp_hs_2012_04_21_bis.pdf. Moore, D. & McCabe, P. (1989). Introduction to the Practice of Statistics. New York, NY: W. H. Freeman. Oakes, J. “Causation verses Correlation” Grossmont. Retrieved July 7, 2013, from www.grossmont.edu/johnoakes/s110online/Causation%20versus%20Correlation.pdf Peck, R., Gould, R., & Miller, S. (2013). Developing Essential Understand of Statistics for Teaching Mathematics in Grades 9-12. Reston, VA: The National Council of Teachers of Mathematics, Inc.

  14. Acknowledgements and Resources Peck, R., Olsen C. & Devore J. (2005). Introduction to Statistics and Data Analysis. Belmont, CA: Brooks/Cole. Peck, R. & Starnes, D. (2009). Making Sense of Statistical Studies. Alexandria, VA: American Statistical Association. Ramsey, F. & Schafer, D. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis. Boston, MA: Brooks/Cole, Cengage Learning. Rossen, J. (2014, January 15). Taste Test Pits Fine Chocolate Against Cheaper Brands. Retrieved from http://www.today.com/video/today/54076112#54301611. Rossen, J. (2014, February 26). Underage Alcohol Buys. Retrieved from http://www.today.com/video/today/54076112#54515111. Rossman, A. (2012). Interview With Roxy Peck. Journal of Statistics Education, 20(2). pp. 1 – 14. Retrieved from http://www.amstat.org/publications/jse/v20n2/rossmanint.pdf. Rossman, A., Chance, B., & Von Oehsen, J. (2002). Workshop Statistics Discovery With Data and the Graphing Calculator. New York: Key College Publishing.

  15. Acknowledgements and Resources Scheaffer, R., Gnanadesikan, M., Watkins, A., & Witmer, J. (1996). Activity-Based Statistics. New York: Springer-Verlag. Stickgold, R., James, L. & Hobson, J. (2000). Visual discrimination learning requires sleep after training. 3(12) pp. 1237-1238. Retrieved from http://www.nature.com/neuro/journal/v3/n12/pdf/nn1200_1237.pdf. Strayer, D. and Johnston, W. (2001, November 6) 12(6). Driven to Distraction: Dual-Task Studies of Simulated Driving and Conversing on a Cellular Telephone. Pp. 462-466Retrieved from http://www.psych.utah.edu/AppliedCognitionLab/PS-Reprint.pdf. The Institute for Preventative Sports Medicine. (2001) Study finds break-away bases effective in professional baseball. Retrieved from http://www.noinjury.com/articles/bases.htm.

  16. Online Resources Census at School. http://www.amstat.org/censusatschool/ Consortium for the Advancement of Undergraduate Statistics Education. http://causeweb.org/ Engage NY. http://www.engageny.org/mathematics Illustrative Mathematics. http://www.illustrativemathematics.org/ Inside Mathematics. http://www.insidemathematics.org Mathematics Assessment Project. http://map.mathshell.org/ Math Vision Project. http://www.mathematicsvisionproject.org/ NCSSM Statistics Institutes. http://courses.ncssm.edu/math/Stat_Inst/links_to_all_stats_institutes.htm

  17. Online Resources PARCC Model Content Frameworks. http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsNovember2012V3_FINAL.pdf PARCC Mathematics Evidence Tables. https://www.parcconline.org/assessment-blueprints-test-specs Smarter Balanced Assessment Consortium. http://www.smarterbalanced.org/ Statistics Education Web (STEW).  http://www.amstat.org/education/STEW/ The Data and Story Library (DASL). http://lib.stat.cmu.edu/DASL/ The High School Flip Book Common Core State Standards for Mathematics. http://www.azed.gov/azcommoncore/files/2012/11/high-school-ccss-flip-book-usd-259-2012.pdf

  18. The New Illinois Learning Standards for Algebra II / Math IIStatistics and Probability Julia Brenson Lyons Township High School jbrenson@lths.net

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