Welcome to Common Core High School Mathematics Leadership

3.1

WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIPSUMMER INSTITUTE 2014

SESSION 3 • 18 JUNE 2014VARIABILITY: DESCRIBING IT, DISPLAYING IT, AND MODELING WITH IT

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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

3.3

SPECIAL GUESTADAM GUTTRIDGEMILWAUKEE BREWERS BASEBALL CLUB

MANAGER–BASEBALL RESEARCH & DEVELOPMENT

3.4

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

3.5

LEARNING INTENTIONS AND SUCCESS CRITERIA

We are learning to… Describe, conceptualize, and calculate measures of center

in contextDescribe the variability of a set of data relative to

measures of center

3.6

LEARNING INTENTIONS AND SUCCESS CRITERIAWe will be successful when we can:Calculate the mean and median in a data setUnderstand the mean related to “fair shares” and use a

fair shares strategy to calculate the meanCalculate, display, and describe interquartile range in a

data set

3.7

ACTIVITY 2 LESSONS 6 AND 9: MEAN & MADMEASURES OF VARIABILITY IN NEAR-SYMMETRIC DISTRIBUTIONS

ENGAGENY/COMMON CORE GRADE 6, LESSONS 6 AND 9

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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?

3.9

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.

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ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

Complete the Lesson 6 Exit ticket with a partner or group of 3.

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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?

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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)

3.13

ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

Complete Lesson 9, Exercise 7 with a partner or group of three.

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Review the following CCSSM Grade 6 content standards:6.SP.A.26.SP.A.36.SP.B.46.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?

ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

Reflecting on CCSSM standards aligned to lessons 6 and 9

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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.

ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

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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?

ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

Reflecting on CCSSM standards aligned to Lessons 6 and 9

Break

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ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTSMEASURES OF VARIABILITY IN SKEWED DISTRIBUTIONS

ENGAGENY/COMMON CORE GRADE 6, LESSONS 12 & 13

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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?

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

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With your pair or group of 3, work on exercises 1, 2, 3, 5, and 7 from Lesson 12.

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

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Using frequency tables to find median…

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

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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?

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

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With your pair or group of three, work on exercises 2, 4, 5, and 6 from Lesson 13.

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

NOT a statistical question.

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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?

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

3.25

Create three different contexts for which a set of data collected related to those contexts could have an IQR of . 𝟐𝟎Define 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.

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

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Complete the Exit Ticket for Lesson 13.

ACTIVITY 3 LESSONS 12 & 13: THE IQR AND BOX PLOTS

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Review the following CCSSM Grade 6 content standards:6.SP.A.26.SP.A.36.SP.B.46.SP.B.5 In what ways did the work on these two lessons add to your

understandings of the standards?

ACTIVITY 2 LESSONS 12 & 13: THE IQR AND BOX PLOTS

Reflecting on CCSSM standards aligned to lessons 12 & 13

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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.

ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

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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?

ACTIVITY 2 LESSONS 6 & 9: MEAN & MEAN ABSOLUTE DEVIATION

Reflecting on CCSSM standards aligned to Lessons 6 and 9

3.30

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.

ACTIVITY 4 GROUP PRESENTATION PLANNING TIME

3.31

LEARNING INTENTIONS AND SUCCESS CRITERIA

We are learning to… Describe, conceptualize, and calculate measures of center

in contextDescribe the variability of a set of data relative to

measures of center

3.32

LEARNING INTENTIONS AND SUCCESS CRITERIAWe will be successful when we can:Calculate the mean and median in a data setUnderstand the mean related to “fair shares” and use a

fair shares strategy to calculate the meanCalculate, display, and describe interquartile range in a

data set

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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?

ACTIVITY 5 HOMEWORK AND CLOSING REMARKS