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The New Illinois Learning Standards for Eighth Grade Statistics and Probability

The New Illinois Learning Standards for Eighth Grade Statistics and Probability

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The New Illinois Learning Standards for Eighth Grade Statistics and Probability

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  1. The New Illinois Learning Standards for Eighth GradeStatistics 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 Eighth Grade

  4. Statistics Standards for 8th Grade * See Evidence Statement 8.D.2 (content from Grade 7 including 7.SP.B) and 8.D.3 (Micro-models) from the PARCC Evidence Table – Grade 8 PBA

  5. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data What is bivariate data? bi - means two variate – means variable Bivariate data is data about two variables. If the two variables are numeric, we examine the relationship between the two variables using a scatterplot. If the two variables are categorical, we organize the data in a two-way frequency table and look for an association.

  6. Statistics Standards for 8th GradeInvestigate Patterns of Association in Bivariate Data Which is the best interpretation of the scatterplot? A. As heights go up, weight increases. B. As heights go up, weight tends to increase. C. If you get taller, you will get heavier. D. Taller football players tend to be heavier football players. Below is a graph of the heights and weights of currently rostered Chicago Bears (April 2014). http://chicagosports.sportsdirectinc.com/football/nfl-teams.aspx?page=/data/nfl/teams/rosters/roster16.html

  7. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Example: Shoe Rating and Price From the Engage NY website – Grade 8, module 6 (www.engageny.org) Is there a relationship between price and the quality of athletic shoes? The data in the table below are from the Consumer Reports website. 𝒙= price (in dollars) and 𝒚= Consumer Reports quality rating The quality rating is on a scale of 𝟎 to 𝟏𝟎𝟎, with 𝟏𝟎𝟎 being the highest quality.

  8. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data • Create a scatterplot, choosing appropriate scaling for each axes. • Do you see any pattern in the scatter plot indicating that there is a relationship between price and quality rating for athletic shoes? • Some people think that if shoes have a high price, they must be of high quality. How would you respond?

  9. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Example: Deep Water From the Engage NY website – Grade 8, module 6 (http://www.engageny.org/sites/default/files/resource/attachments/math-g8-m6-teacher-materials.pdf) Does the current in the water go faster or slower when the water is shallow? The data on the depth and speed of the Columbia River at various locations in Washington State listed on the next slide can help you think about the answer.

  10. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Example: Deep Water

  11. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Example: Deep Water The Deep Water Task provides an opportunity for students to work independently through the steps of creating a scatterplot, fitting a line to the data, and interpreting the slope, y-intercept, an ordered pair, and the relationship between depth and velocity in the context of the problem.

  12. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Example: Florida Alligators The American Alligator can live up to 50 years in the wild. Males have an average length of 11 feet, and females have an average length of 8 feet. The data shown in the scatterplot on the next slide was collected from 25 American alligator captured in Florida. 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

  13. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Activity: Florida Alligators Describe the relationship between the length in inches and the weight in pounds for this sample of Florida Alligator. Be sure to comment on any interesting features of the scatterplot.

  14. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data The PARCC Evidence Tables for the Eighth Grade PBA indicates that eighth graders may be asked to do a task that requires applying knowledge or skills from 7.SP.B. Bear Hugs, an activity that is shared by Subhash Bagui and Mary Richardson on the Statistics Education Web (STEW), is an activity about arm span and age. Students are first asked to create box plots comparing the arm span of male and female students (7.SP.B). They then proceed to create and interpret a scatterplot of age versus arm span. http://www.amstat.org/education/stew/pdfs/BearHugs.pdf

  15. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data A look at sample activities for 8.SP.1-3 • Oil Changes and Engine Repair Adapted from an NCTM Illuminations’ activity • Bike Weights and Jump Heights NCTM Illuminations • Animal Brains Illustrative Mathematics • US Airports, Assessment Variation Illustrative Mathematics • Patterns in Scatter Plots – Lesson 7 Classwork EngageNY • Determining the Equation of a Line Fit to Data – Lesson 9 Problem Set EngageNY

  16. Statistics Standards for 8thGrade Investigate Patterns of Association in Bivariate Data Questions In what order would you use these activities in a unit? What questions did you particularly like? What questions are different than what we might typically ask students? Do you have suggestions for improvement of or additions to these activities?

  17. Statistics Standards for 8th Grade Investigate Patterns of Association in Bivariate Data 8.SP.4 Summarize categorical data in two categories Big Ideas: • Review the difference between numeric data and categorical data. • Explain that frequency refers to the count of the data. Relative frequency is a proportion. • Analyze relative frequencies and assess possible associations and trends in the data.

  18. Statistics Standards for 8th Grade Investigate Patterns of Association in Bivariate Data Association of two categorical variables • There is an association between two categorical variables if the row (or column) conditional relative frequencies are different from row to row (or column to column) in the table. • The greater the difference between the conditional relative frequencies, the stronger the association.

  19. Statistics Standards for 8th Grade Investigate Patterns of Association in Bivariate Data Activity: Music and Sports Adapted from Illustrative Mathematics (http://www.illustrativemathematics.org/illustrations/1098) Is there an association between whether a student plays a sport and whether he or she plays a musical instrument? To investigate this question, each student in your class should answer the following two questions: 1. Do you play a sport? (yes or no) 2. Do you play a musical instrument? (yes or no)

  20. Statistics Standards for 8th Grade Investigate Patterns of Association in Bivariate Data Music and Sports Summarize the class data in a two way frequency table. Questions: 1. Of those students who play a sport, what proportion play a musical instrument? 2. Of those students who do not play a sport, what proportion play a musical instrument? 3. Based on the class data, do you think there is an association between playing a sport and playing an instrument?

  21. Statistics Standards for 8th Grade Activities • 8-SP Oil Changes and Engine Repair • Bike Weights and Jump Heights NCTM Illuminations • Florida Alligators • Shoe Rating and Price (www.engageny.org ) • Deep Water (www.engageny.org) • 8.SP Animal Brains (http://www.illustrativemathematics.org/illustrations/1520) • 8.SP US Airports, Assessment Variation (http://www.illustrativemathematics.org/illustrations/1370)

  22. Statistics Standards for 8th Grade More Activities • Scatter It! (Predict Billy’s Height) Statistics Education Web (STEW) (http://www.amstat.org/education/stew/pdfs/BearHugs.pdf) • Bear Hugs Statistics Education Web (STEW) (http://www.amstat.org/education/stew/pdfs/BearHugs.pdf) • 8-SP-4 Music and Sports Activity adapted from: (http://www.illustrativemathematics.org/illustrations/1370) • Census at School ( http://www.amstat.org/censusatschool/)

  23. Statistics Standards for 8th Grade Census at School (http://www.amstat.org/censusatschool/) Statistics Education Web (http://www.amstat.org/education/stew/)

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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

  29. 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

  30. The New Illinois Learning Standards for Eighth GradeStatistics and Probability Julia Brenson Lyons Township High School jbrenson@lths.net