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Welcome to Common Core High School Mathematics Leadership

Welcome to Common Core High School Mathematics Leadership. Summer Institute 2014. Session 9 • 26 June 2014 What a Difference a (statistical) Test Makes. Today’s Agenda. Homework review and discussion Group presentations: Grade 9, Lessons 3 and 17 Break

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Welcome to Common Core High School Mathematics Leadership

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  1. Welcome to Common Core High School Mathematics Leadership Summer Institute 2014 Session 9 • 26 June 2014 What a Difference a (statistical) Test Makes

  2. Today’s Agenda • Homework review and discussion • Group presentations: Grade 9, Lessons 3 and 17 • Break • Grade 9, Lesson 19: Interpreting Correlation • A glimpse forward: Statistical Tests • MKT assessment • Closing remarks

  3. A few moments from XKCD…

  4. A few moments from XKCD…

  5. A few moments from XKCD…

  6. Activity 1 homework review and discussion Table discussion Discuss your write ups for the Day 8 homework tasks: • Compare your strategies with others at your table • Reflect on how you might revise your own solution and/or presentation

  7. Activity 1 Homework review and discussion Day 8 homework: • See the Problem Set for Lesson 2. Complete Problem 2 (the Obedience School for Dogs) • Reflection on teaching:Based on your current progress with the resources, reflect on the following: • Do you feel you are able to identify lessons for the students you will teach next fall? Explain how you think your students may react to this material. • Do you feel prepared or comfortable in presenting selected lessons to your students? Explain. • What topics or lessons are you the most uncomfortable with at this time? Explain why you selected these lessons.

  8. Learning Intentions and Success Criteria We are learning to… • Identify the differences between correlation and causation • Describe the nature of correlation in a data set • Compare data sets and determine whether differences are statistically significant

  9. Learning Intentions and Success Criteria We will be successful when we can: • Interpret the value of a correlation coefficient as a measure of the strength and direction of a linear relationship • Provide multiple explanations for why correlation does not imply causation, using contextual data sets • Define statistical significance and identify appropriate tests of statistical significance using contextual data sets

  10. Activity 2 Grade 9, Lesson 3 (Michelle, Lindsay, Allison) Estimating Centers & Interpreting the Mean as a Balance Point EngageNY/Common Core Grade 9, Lesson 3

  11. Activity 3 Grade 9, Lesson 17 (Heather, Melissa, Jenny) Analyzing Residuals EngageNY/Common Core Grade 9, Lesson 17

  12. Activity4Grade 9, Lesson 19 Interpreting Correlation EngageNY/Common Core Grade 9, Lesson 19

  13. Activity 4Lesson 19: Interpreting correlation Put the three scatter plots in order from weakest to strongest correlation.

  14. Activity 4Lesson 19: Interpreting correlation Which of these two has a stronger linear relationship?

  15. Activity 4Lesson 19: Interpreting correlation • In your small groups, complete and discuss Exercises 13-17.

  16. Break

  17. Activity 4Lesson 19: Interpreting correlation S-ID.6 • Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. • Fit the function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. • Informally assess the fit of a function by plotting and analyzing residuals. • Fit a linear function for a scatter plot that suggests a linear association. S-ID.7 • Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S-ID.8 • Compute (using technology) and interpret the correlation coefficient of a linear fit. S-ID.9 • Distinguish between correlation and causation.

  18. Activity 5 A Glimpse Forward When are differences statistically significant? Content for a capstone statistics course

  19. Activity 5 Statistical Tests & Significant Differences • When is a difference statistically significant? • If we had two populations’ responses to the same question, how could we know whether the differences were “noise” or real?

  20. Activity 5 Statistical Tests & Significant Differences You have a curfew of midnight. What choice best describes what you will probably do? • You don’t call and come home when it suits you. • You finally call after you are already late and make excuses. • You call to tell your parents you will be late. • You get home on time.

  21. Activity 5 Statistical Tests & Significant Differences You have a curfew of midnight. What choice best describes what you will probably do? • You don’t call and come home when it suits you. • You finally call after you are already late and make excuses. • You call to tell your parents you will be late. • You get home on time.

  22. Activity 5 Statistical Tests & Significant Differences Basic tests for statistical hypothesis testing: • z-test comparing populations means, assumes a normal distribution, standard deviations known • t-test comparing populations means, relaxed conditions and assumptions, standard deviation not known • Chi-square test categorical data, assumes a normal population (Pearson’s, Fisher’s exact, Yates…) A basic version of most tests can be done online or with Excel.

  23. Activity 5 Statistical Tests & Significant Differences

  24. Activity 4reflecting on standards aligned to lessons 12, 13 & 15 • How can you distinguish between linear and nonlinear associations in data by looking at a scatter plot? • What are the characteristics of linear, quadratic, and exponential relationships and/or associations in data? • How can you tell whether a linear model is a good fit to data? Closing questions for lessons 12, 13 & 15

  25. Learning Intentions and Success Criteria We are learning to… • Identify the differences between correlation and causation • Describe the nature of correlation in a data set • Compare data sets and determine whether differences are statistically significant

  26. Learning Intentions and Success Criteria We will be successful when we can: • Interpret the value of a correlation coefficient as a measure of the strength and direction of a linear relationship • Provide multiple explanations for why correlation does not imply causation, using contextual data sets • Define statistical significance and identify appropriate tests of statistical significance using contextual data sets

  27. A few words on the graduate project…

  28. Activity 6Statistics Knowledge Assessment MKT AssessmentGo to: http://bit.ly/UWM-LOCUS or http://dev-artist.gotpantheon.com/take/xaYNkXbEm8 Access code: xaYNkXbEm8

  29. Thank you! See you in the fall: September 17Location TBD

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