9.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION 9 21 JAN 2015 THOUGHTS ON DEVIATION

9.2 TODAY’S AGENDA  Welcome Back!  Deviation, Part 1 (pedagogical): Considering Access and Equity  Association and Independence: Returning to Two-Way Tables  Break  Deviation, Part 2 (statistical): Calculating & Interpreting Standard Deviation  Planning Time / Background Knowledge Review  Closing remarks & For Next Time

9.3 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to…  Connect key statistics and probability ideas and constructs between the middle and high school grades  Identify and understand issues of equity and access in the teaching and learning of mathematics  Make comparisons between categorical data sets  Describe variability in numerical data sets

9.4 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can:  Describe how constructs and terminology about key statistics and probability ideas evolve in grades 6-8  Identify ways in which we address access and equity in our teaching and systemic constraints on access and equity  Identify whether or not an association exists in categorical data and whether two constructs are independent  Calculate and describe the meaning of standard deviation

9.5 SOME REMINDERS…  Please Mike with possible coaching session visit times ASAP!  If you are taking the course for graduate credit, please consult the syllabus regarding the Teaching and Learning Case Study assignment  We have six meetings this spring  Because of parent conferences in three districts, we would like to change the March 4 th meeting to February 25 th.

9.6 ACTIVITY 1 DISCUSSING ISSUES OF ACCESS AND EQUITY PRINCIPLES TO ACTIONS

9.7 ACTIVITY 1 DISCUSSING ISSUES OF ACCESS AND EQUITY Organization of Principles to Actions  Effective Teaching and Learning (8 Mathematics Teaching Practices  Essential Elements  Access and Equity  Curriculum  Tools and Technology  Assessment  Professionalism

9.8 ACTIVITY 1 DISCUSSING ISSUES OF ACCESS AND EQUITY  For the demographic dimension listed at your table, consider the following:  What do you do to foster access & equity with this specific group in your classroom?  What are the systemic challenges you face in your district with respect to access & equity with this specific group?

9.9 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN BIVARIATE CATEGORICAL DATA ENGAGE NY GRADE 11, LESSON 4

9.10 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA  Is there an association evident in the asthma data? Attend to both the rows and the columns. No household member smokes At least one household member smokesTotal Student indicates he or she has asthma Student indicates he or she does not have asthma Total

9.11 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA  Based on the values, what are the conditional relative frequencies based on row totals?  If we interpret each of the conditional relative frequencies based on the rows as a probability, explain each probability in words. No household member smokes At least one household member smokesTotal Student indicates he or she has asthma Student indicates he or she does not have asthma Total

9.12 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA Having asthma and having a member of your household who smokes are independent by examining the following row probabilities: The probability of a person with asthma who does not have a family member who smokes. The probability of a person who does not have asthma who has a family who smokes. The probability of a person who has a family who smokes. If independent, then all of the above probabilities would be equal. Based on the probabilities based on the rows, are these events independent?

9.13 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA  Based on the values, what are the conditional relative frequencies based on column totals?  If we interpret each of the conditional relative frequencies based on the columns as a probability, explain each probability in words. No household member smokes At least one household member smokesTotal Student indicates he or she has asthma Student indicates he or she does not have asthma Total

9.14 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA Having asthma and having a member of your household who smokes are independent by examining the following column probabilities: Given that a person does not have a family member who smokes, the probability that this person has asthma. The probability of a person who has at least one family who smokes, the probability that this person has asthma. The probability that a person selected has asthma. If independent, then all of the above probabilities would be equal. Based on the probabilities based on the columns, are these events independent?

9.15 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA What is the connection between association and independence? How does our challenge with meaningful difference come up again? How could we produce a distribution that would examine the meaningful differences?

9.16 ACTIVITY 2 ASSOCIATIONS AND INDEPENDENCE IN CATEGORICAL DATA Meaningful difference in population means (Grade 7) Association between variables in categorical data using two-way tables (Grade 11) Tests of statistical significance (numerical and categorical) Plus standards (Stats or AP Stats)

Break

9.18 ACTIVITY 3 STANDARD DEVIATION ENGAGE NY GRADE 9, LESSONS 5 AND 6

9.19 ACTIVITY 3 STANDARD DEVIATION The Corporate Average Fuel Economy (CAFÉ) standards, first introduced in 1975, are a set of regulations intended to promote continuous improvement in fuel economy (and energy efficiency) in cars and light trucks in the United States. A 2011 agreement between the Obama administration and 13 large automakers led to two key provisions:  Fuel economy will be increased to 54.5 mpg by 2025  Benchmarks were set for each model year from

9.20 ACTIVITY 3 STANDARD DEVIATION Passenger CarsLight Trucks Footprint of 41 ft 2 of less Footprint of 55 ft 2 or more Footprint of 41 ft 2 of less Footprint of 75 ft 2 of less CAFEEPA window sticker CAFEEPA window sticker CAFEEPA window sticker CAFEEPA window sticker How close is a given auto manufacturer to meeting the CAFE targets in the 2015 model year? Data from

9.21 ACTIVITY 3 STANDARD DEVIATION  What tools could we use to determine how close Kia is to meeting the 2015 fuel economy standards? ModelNotesMPG Rio Eco1.6L, 4 cyl31 Rio1.6L, 4 cyl31 Forte1.8L, 4 cyl31 Forte2.0L, 4 cyl29 Forte Koup2.0L, 4 cyl28 Forte 52.0L, 4 cyl28 Soul Eco2.0L, 4 cyl27 Optima2.4L, 4 cyl27 Soul1.6L, 4 cyl26 Soul2.0L, 4 cyl26 Forte Koup1.6L, 4 cyl25 Forte 51.6L, 4 cyl24 Sportage FWD2.4L, 4 cyl24 Optima2.0L, 4 cyl24 ModelNotesMPG Sorento FWD2.4L, 4 cyl23 Sportage FWD2.0L, 4 cyl23 Cadenza3.3L, 6 cyl22 Sportage AWD2.4L, 4 cyl22 Sorento AWD2.0L, 4 cyl21 Sportage AWD2.0L, 4 cyl21 K9003.8L, 6 cyl21 Sedona SX3.3L, 6 cyl21 Sorento FWD3.3L, 6 cyl21 Sedona3.3L, 6 cyl20 Sorento AWD3.3L, 6 cyl20 Sedona SXL3.3L, 6 cyl19 K9005.0L, 8 cyl18

9.22 ACTIVITY 3 STANDARD DEVIATION  Calculate the mean and mean absolute deviation (MAD) for the Kia data set  Using the provided histogram, mark the mean and one MAD on either side  How many data points are within 1 MAD of the mean? ModelNotesMPG Rio Eco1.6L, 4 cyl31 Rio1.6L, 4 cyl31 Forte1.8L, 4 cyl31 Forte2.0L, 4 cyl29 Forte Koup2.0L, 4 cyl28 Forte 52.0L, 4 cyl28 Soul Eco2.0L, 4 cyl27 Optima2.4L, 4 cyl27 Soul1.6L, 4 cyl26 Soul2.0L, 4 cyl26 Forte Koup1.6L, 4 cyl25 Forte 51.6L, 4 cyl24 Sportage FWD2.4L, 4 cyl24 Optima2.0L, 4 cyl24 ModelNotesMPG Sorento FWD2.4L, 4 cyl23 Sportage FWD2.0L, 4 cyl23 Cadenza3.3L, 6 cyl22 Sportage AWD2.4L, 4 cyl22 Sorento AWD2.0L, 4 cyl21 Sportage AWD2.0L, 4 cyl21 K9003.8L, 6 cyl21 Sedona SX3.3L, 6 cyl21 Sorento FWD3.3L, 6 cyl21 Sedona3.3L, 6 cyl20 Sorento AWD3.3L, 6 cyl20 Sedona SXL3.3L, 6 cyl19 K9005.0L, 8 cyl18

9.23 ACTIVITY 3 STANDARD DEVIATION  x is each individual value  x bar is the sample mean  n is the number of values  But why n–1? (We’ll come back to this…)

9.24 ACTIVITY 3 STANDARD DEVIATION  Calculate the standard deviation for the Kia data set  Using the provided histogram, mark the mean and one SD on either side  How many data points are within 1 SD of the mean? ModelNotesMPG Rio Eco1.6L, 4 cyl31 Rio1.6L, 4 cyl31 Forte1.8L, 4 cyl31 Forte2.0L, 4 cyl29 Forte Koup2.0L, 4 cyl28 Forte 52.0L, 4 cyl28 Soul Eco2.0L, 4 cyl27 Optima2.4L, 4 cyl27 Soul1.6L, 4 cyl26 Soul2.0L, 4 cyl26 Forte Koup1.6L, 4 cyl25 Forte 51.6L, 4 cyl24 Sportage FWD2.4L, 4 cyl24 Optima2.0L, 4 cyl24 ModelNotesMPG Sorento FWD2.4L, 4 cyl23 Sportage FWD2.0L, 4 cyl23 Cadenza3.3L, 6 cyl22 Sportage AWD2.4L, 4 cyl22 Sorento AWD2.0L, 4 cyl21 Sportage AWD2.0L, 4 cyl21 K9003.8L, 6 cyl21 Sedona SX3.3L, 6 cyl21 Sorento FWD3.3L, 6 cyl21 Sedona3.3L, 6 cyl20 Sorento AWD3.3L, 6 cyl20 Sedona SXL3.3L, 6 cyl19 K9005.0L, 8 cyl18

9.25 ACTIVITY 3 STANDARD DEVIATION Mean ±1 MAD Mean ±1 SD

9.26 ACTIVITY 3 STANDARD DEVIATION For this data set, we eliminated hybrid and electric vehicles in the line. How do you think including those vehicles would have changed our analyses? For full data on Chevy, Honda, and Kia, with analyses that include and exclude electrics and hybrids, see the second tab of the spreadsheet at

9.27 ACTIVITY 3 STANDARD DEVIATION Why might we use Standard Deviation as compared to Mean Absolute Deviation?

9.28 ACTIVITY 3 STANDARD DEVIATION Center, shape, and spread (Grade 6) Variability and MAD (Grade 6) Standard Deviation and residuals (Grade 9) Normal distribution and curve modeling (Grade 11) Assumptions of statistical tests (Statistics/ AP Statistics)

9.29 ACTIVITY 4 PLANNING AND BACKGROUND KNOWLEDGE SUPPORT

9.30 ACTIVITY 4 PLANNING AND BACKGROUND KNOWLEDGE SUPPORT  In the next few weeks, we’ll be tackling some fairly meaty high school probability and statistics concepts:  The Normal Distribution  Sampling (Sample Variability)  Margin of Error  As groups yet to teach plan, gather in one of the three small groups above to discuss some background ideas related to each concept

9.31 FOR NEXT TIME  A theme for spring: Analyzing our Teaching using the 8 Math Teaching Practices  Each week, bring in a small set of artifacts related to your teaching  Identify 1-2 of the Mathematics Teaching Practices that you think these artifacts embody, and be prepared to briefly share them with a small group

9.32 FOR NEXT TIME  Identify a coaching window for us to come visit soon!!!  Complete the problem set for Grade 9, Lesson 5 (provided)  Respond to the following prompt: Today we discussed issues of access and equity. Identify one aspect of your (or your district’s) mathematics teaching/program that you would to think more about with respect to access and equity. How is this aspect of your (or the district’s) practice restricting access and/or equity, and what might you do to change it?  Bring in artifacts for analysis and discussion.  Stay tuned to your for some survey data collection for more on SD…