Chapter 5: Stories Quantitative Data Tell, Continued (Days 34-35)

Today in Stats, I take advantage of having finished the main text in Chapter 5 to give the review questions that I mentioned in yesterday's post. For starters, on the Warm-Up, I ask two questions from the homework that only involve converting data from inches to millimeters -- saving the questions on how such rescaling affects statistical measures for later.

Then I have the students take a few short notes. The emphasis here is on measures of center (mean, median, and mode) vs. measures of spread (range, interquartile range, and standard deviation). I show them a handy chart revealing that rescaling (multiplying and dividing all data values) affects all measures, but shifting (adding and subtracting all data values) only affects measures of center -- measures of spread remain unchanged.

Then I move on to a quick thumb activity. Students show me their thumbs up if a measure changes (for example, "Multiplying all data values by two does what to the mean?") and their thumbs down if the measure doesn't change (for example, "Adding three to all values does what to the range?") And after doing this, I return to last night's homework, which they can finally understand. ("Multiplying all data values by 25.4 does what to the mean?")

This is followed by markers and whiteboard to draw boxplots, since many students are still confused with identifying outliers. Then I cap off the class with an Exit Pass -- and yes, I do give them the question I mentioned in yesterday's post. ("If F = 1.8C + 32, converting from degrees Celsius to degrees Fahrenheit does what to the range?") Of my four students, two guys are definitely clever enough to figure out the trick (multiplying affects the range, but not adding), while the other two are still struggling (especially the special ed student). I only wish that I'd given this Exit Pass yesterday -- a range of 15 degrees C converts readily to 27 degrees F (matching yesterday's date), but today I give a messy range of 15.6 degrees C and use rounding in order to make the answer come out to 28 degrees F. (By the way, this explains why when we convert temperature intervals from C to F, we don't add 32 -- an interval is simply a range with just two data points, the endpoints.)

I give the review assignment for the students now, since I leave 25 minutes early to rush home in time for the AP Calculus webinar on Zoom. (The actual Calculus class goes smoothly as well, since Section 2.8 -- "What does f' say about f?" -- is a short lesson, leaving me more time for non-text examples.)

I learn many things at the webinar. The presenter -- himself an experienced Calc teacher -- tells me that the AP emphasizes all four ways to present functions (verbally, numerically, algebraically, graphically). Our Calc text presents these four ways from the very start in Section 1.1, and sometimes I even choose such questions from the text as Warm-Ups. I just need to make sure that I don't gloss over these questions and make sure that the students fully understand them. There is one more Zoom session, a week from today.

Tomorrow is an Ethnostats day, so it's back to Twitter. I need to push the students to finish their climate change posters, so that they can start a writing assignment based on Greta Thunberg's UN speech.

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