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Using Statistics in Mathematics Classes

Using Statistics in Mathematics Classes. Shelby Aaberg , Nebraska Master Teaching Fellow, Scottsbluff High School Jason Vitosh , Nebraska Master Teaching Fellow, Falls City High School. Mathematical models describe structure. Statistical models describe variability around the structure.

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Using Statistics in Mathematics Classes

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  1. Using Statistics in Mathematics Classes Shelby Aaberg, Nebraska Master Teaching Fellow, Scottsbluff High School Jason Vitosh, Nebraska Master Teaching Fellow, Falls City High School

  2. Mathematical models describe structure. • Statistical models describe variability around the structure. How Statistics is Not Just Mathematics?

  3. Students Discover a Distribution Shape Students Develop a Winning Strategy Roller Derby

  4. Mathematical Questions “What is the probability of rolling an 8 with a pair of number cubes?” “What is the expected value when rolling a pair of number cubes?” • Statistical Questions “What is a winning strategy in a game of Roller Derby?” “Explain if a winning strategy guarantees success?” VS. Asking the “Right” Questions

  5. Student Distribution Results

  6. Four sets of data • Same LSRL slope • Same LSRL y-intercept • Same r value • Same r2 value • WILDLY DIFFERENT SCATTERPLOTS Anscombe’s Quartet HTTP://MATHLETICISM.NET/?P=160

  7. Students explore permutation counting methods. • Students consider probability and randomness. Counting Sixlets

  8. Two equally qualified scholarship candidates • Candidate 1: ACT Math Subscore of 33 • Candidate 2: SAT Math Subscore of 550 • You are the scholarship committee chairperson. Who should get the scholarship? Scholarship Committee HTTP://MATHLETICISM.NET/?P=1065

  9. Dot Plots • Stem & Leaf Plots • Box & Whisker Plots • Histograms Pennies Pennies Pennies

  10. Mathematical Practices • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning Common Core State Standards High School Statistics Categories 1) Interpreting Data (HSS.ID) 2) Inferences & Conclusions (HSS.IC) 3) Conditional Probability (HSS.CP) 4) Making Decisions (HSS.MD)

  11. Problems- The Birthday Problem The Monty Hall Problem Lottery Problems Your Own Raffle Free Throw Stats & Prob Books- • Proofiness, Charles Seife • The Lady Tasting Tea, David Salsburg • Damned Lies and Statistics, Joel Best • How to Lie with Statistics, Darrell Huff • Naked Statistics, Charles Wheelan • NCTM Developing Essential Understanding of Statistics-Grade 9-12 • NCTM Implementing the Common Core State Standards through Mathematical Problem Solving-High School • NCTM Developing Essential Understanding of Statistics-Grade 6-8 • NCTM Bridging the Gap Between CCSS and Teaching Statistics • NCTM Teaching Mathematics through Problem Solving-Grades 6-12 Resources & Ideas Websites- http://mathleticism.net http://apstatsmonkey.com http://mathcoachblog.com/ www.geogebra.org

  12. Shelby Aaberg UNL MTF, Scottsbluff NE saaberg@sbps.net • Jason Vitosh UNL MTF, Falls City NE jvitosh@fallscityps.org Contact Info

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