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Welcome to Common Core High School Mathematics Leadership

Welcome to Common Core High School Mathematics Leadership. Summer Institute 2014. Session 3 • 18 June 2014 Variability: Describing it, displaying it, and modeling with it. Today’s Agenda. Special Guest: Adam Guttridge , Milwaukee Brewers Homework review and discussion

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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 3 • 18 June 2014 Variability: Describing it, displaying it, and modeling with it

  2. Today’s Agenda • Special Guest: Adam Guttridge, Milwaukee Brewers • Homework review and discussion • Grade 6, Lessons 6 and 9: Mean and MAD • Reflecting on CCSSM standards aligned to lessons 6 and 9 • Break • Grade 6, Lessons 12 and 13: The IQR and Box Plots • Reflecting on CCSSM standards aligned to lessons 12 and 13 • Group presentation planning time • Homework and closing remarks

  3. Special GuestAdam Guttridge Milwaukee Brewers Baseball Club Manager–Baseball Research & Development

  4. Activity 1 homework review and discussion Table discussion Discuss your write ups for the Day 2 homework tasks: • Compare your strategies with others at your table • Reflect on how you might revise your own solution and/or presentation

  5. Learning Intentions and Success Criteria We are learning to… • Describe, conceptualize, and calculate measures of center in context • Describe the variability of a set of data relative to measures of center

  6. Learning Intentions and Success Criteria We will be successful when we can: • Calculate the mean and median in a data set • Understand the mean related to “fair shares” and use a fair shares strategy to calculate the mean • Calculate, display, and describe interquartile range in a data set

  7. Activity 2 Lessons 6 and 9: Mean & MAD Measures of Variability in Near-Symmetric Distributions EngageNY/Common Core Grade 6, Lessons 6 and 9

  8. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation • On the large white board, put a sticky note up that corresponds to the number of hours of sleep you got last night. • How would you describe the center of the distribution of our dot plot? • How might we determine the mean without calculating it?

  9. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation • Give each person at your table the same number of Unifix cubes as they reported hours of sleep last night. • Use a fair share strategy to find the mean number of hours of sleep at your table.

  10. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation • Complete the Lesson 6 Exit ticket with a partner or group of 3.

  11. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation • Complete Lesson 9, exercises 1-3. • In what order would you classify the 7 cities’ temperatures, from least variability to most variability?

  12. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation • Find the mean temperature for City G • For each month’s temperature, find the deviation from the mean temperature. • What do you notice about your deviation values? Mean absolute deviation = (sum of the absolute values of the deviations from the mean) ÷ (number of data points)

  13. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation • Complete Lesson 9, Exercise 7 with a partner or group of three.

  14. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation Review the following CCSSM Grade 6 content standards: 6.SP.A.2 6.SP.A.3 6.SP.B.4 6.SP.B.5 • Where did you see these standards in the lesson you have just completed? • What would you look for in students’ work to suggest that they have made progress towards these standards? Reflecting on CCSSM standards aligned to lessons 6 and 9

  15. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation 6.SP.A.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. G.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B.4: Display numerical data on plots on a number line, including dot plots, histograms, and box plots. 6.SP.B.5: Summarize numerical data sets in relation to their contexts.

  16. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation Look across the set of Standards for Mathematical Practice. • Recalling that the standards for mathematical practice describe student behaviors, which practices did you engage in, and how? • What instructional moves or decisions did you see occurring during the lesson that encouraged greater engagement in the SMP? Reflecting on CCSSM standards aligned to Lessons 6 and 9

  17. Break

  18. Activity3Lessons 12 & 13: The IQR and Box Plots Measures of Variability in Skewed Distributions EngageNY/Common Core Grade 6, Lessons 12 & 13

  19. Activity 3 Lessons 12 & 13: The IQR and Box Plots Consider the following: • In what situations might you want or need to know where the border between the top half and the bottom half of a set of data is? • What questions might you ask about your data when you know where this border point lies?

  20. Activity 3 Lessons 12 & 13: The IQR and Box Plots • With your pair or group of 3, work on exercises 1, 2, 3, 5, and 7 from Lesson 12.

  21. Activity 3 Lessons 12 & 13: The IQR and Box Plots • Using frequency tables to find median…

  22. Activity 3 Lessons 12 & 13: The IQR and Box Plots • How do you think the data from these restaurants was collected, and what problems might there be with the data? • What would you consider typical and what would you consider atypical for each restaurant?

  23. Activity 3 Lessons 12 & 13: The IQR and Box Plots • With your pair or group of three, work on exercises 2, 4, 5, and 6 from Lesson 13. NOT a statistical question.

  24. Activity 3 Lessons 12 & 13: The IQR and Box Plots Consider the following: • What are the conditions under which you might choose to summarize a set of data using: • The mean • The MAD • The IQR? • How does the statistical question you are investigating relate to this decision?

  25. Activity 3 Lessons 12 & 13: The IQR and Box Plots Create three different contexts for which a set of data collected related to those contexts could have an IQR of 𝟐𝟎. Define a median for each context. Be specific about how the data might have been collected and the units involved. Be ready to describe what the median and IQR mean in each case.

  26. Activity 3 Lessons 12 & 13: The IQR and Box Plots • Complete the Exit Ticket for Lesson 13.

  27. Activity 2 Lessons 12 & 13: The IQR and Box Plots Review the following CCSSM Grade 6 content standards: 6.SP.A.2 6.SP.A.3 6.SP.B.4 6.SP.B.5 • In what ways did the work on these two lessons add to your understandings of the standards? Reflecting on CCSSM standards aligned to lessons 12 & 13

  28. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation 6.SP.A.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. G.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B.4: Display numerical data on plots on a number line, including dot plots, histograms, and box plots. 6.SP.B.5: Summarize numerical data sets in relation to their contexts.

  29. Activity 2 Lessons 6 & 9: Mean & Mean Absolute Deviation Look across the set of Standards for Mathematical Practice. • Recalling that the standards for mathematical practice describe student behaviors, which practices did you engage in, and how? • What instructional moves or decisions did you see occurring during the lesson that encouraged greater engagement in the SMP? Reflecting on CCSSM standards aligned to Lessons 6 and 9

  30. Activity 4 group presentation planning time • During Week 2 of the institute, you will present (in groups) one of the following engageny lessons: • Grade 6, Lessons 2, 3, 4, 5, 16 • Grade 8, Lesson 6 • Grade 9, Lessons 3, 17 • For the rest of our time today, you should study these lessons, decide which one you wish to present, and find a group with which you will present.

  31. Learning Intentions and Success Criteria We are learning to… • Describe, conceptualize, and calculate measures of center in context • Describe the variability of a set of data relative to measures of center

  32. Learning Intentions and Success Criteria We will be successful when we can: • Calculate the mean and median in a data set • Understand the mean related to “fair shares” and use a fair shares strategy to calculate the mean • Calculate, display, and describe interquartile range in a data set

  33. Activity 5 Homework and Closing Remarks • Due to our tight timeframe, no content homework this evening. • In your reflection tonight, address the following:Tonight, we touched on mean, mean absolute deviation, median, and interquartile range. As students learn to calculate and represent these quantities, how might we support them in developing both the procedural fluency with these quantities alongside the conceptual understanding that will help them know when and how to make use of them?

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