Stats, Common Core Style

Today in Stats, I give the Chapter 5 Test on the stories that quantitative data tell. But unfortunately, due to a key error on my part, the test doesn't go as smoothly as it should have. Here's what happens -- I begin with the Warm-Up, as always. I try to give a question that will help the students on the test as well -- this saves time, since Warm-Up time also doubles up as test review time. I choose a homework question on stem-and-leaf plots, analyzing the margins of victory from Super Bowl I to XLIII for the median/quartiles. But here's the problem -- stem-and-leaf plots appear on the  Chapter 4 Test , not Chapter 5. In other words, I was looking at the wrong chapter! Moreover, in trying to draw the stem-and-leaf plot, I keep missing one of the data values, and so there are only 42 leaves instead of 43. I end up wasting time trying to figure out which value I'm missing -- all of this to solve a problem that has nothing to do with today's test. This forces me to r...

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 d...

Today in Stats, we continue with the next three pages in Chapter 5, "Stories Quantitative Data Tell." These pages discuss how measures of center and spread are affected if each data point is multiplied or divided by a constant. Unfortunately, the students appear to be confused by this concept. The example in the book involves converting data from kilograms to pounds -- that is, multiplying by 2.2. There is a histogram where all the weights are divided into bins of 10 kg each -- that is, 50-60 kg, 60-70 kg -- but when these are converted to pounds, they become 110-132 lbs., 132-154 lbs. and so on. These non-multiples of ten are hard to find on the histogram where the scale is marked in tens. And this confuses the students. What should have been a simple concept -- when you multiply (or rescale) the data, all the key numbers (mean, median, mode, range) are multiplied by that constant -- is instead obscured by that strange factor of 2.2. I try to give a simpler example involves ...

Yesterday was the fall equinox -- it occurred at 12:21 PM Pacific time. As I mentioned on the old blog, I want to choose an extra pencil giveaway between the first day of school and Halloween -- and that I should select either Back to School Night or the fall equinox. Since Back to School night was a bit too early in this district, I decided to make the equinox my giveaway day instead.  The true equinox moment -- 12:21 -- was during fourth period Ethnostats. I gave pencils to most of the students -- one guy was summoned to the office and left before 12:21, so he never got a pencil. Today in Stats, we continue with the next six pages in Chapter 5, "Stories Quantitative Data Tell." These pages show how to graph boxplots on the TI calculator, introduce timeplots, and discuss how measures of center and spread are affected if each data point is raised or lowered by a constant. All of this occurs in fifth period, of course. This is the first general Stats class since the collapse o...

NOTE: Yesterday I posted some confusing information about the date of final exams here. I've since received corrected information, and so I have edited out the incorrect date from yesterday's post. Today in Stats, we continue with the next six pages in Chapter 5, "Stories Quantitative Data Tell." These pages continue with boxplots and show how they can be used to compare changes in data over time. But after school, the schedule changes that I proposed in yesterday's post become official. The lone guy in my first period Stats class has agreed to move to my fifth period. His previous fifth period class was art, and the art teacher will enroll him in her first period class, even though it's a slightly different art class. And so starting on Thursday, the next time that odd periods meet, I will have first period conference, third period Calculus, and fifth period Stats -- now my only general Stats class. At the same time, the principal tells me that she is in con...

I'll begin with a description of today, in "A Day in the Life" format. This is my monthly posting day -- my school has a minimum day on one Monday per month. By the way, the dates of these monthly minimum days aren't announced in advance (so it isn't something simple like "the third Monday of each month," even though today is indeed the third Monday of September). 8:00  -- First period arrives. This is the first of two general Stats classes. As of now, this class has just one student -- and as of now, this class still exists. As I mentioned last week, there's a possibility that this class will disappear, with the one guy moving to fifth period. I tell this guy that in last week's quiz, he'd earned the highest grade of all four general Stats students. He scored 70 out of 75 -- but arguably, it should have been 69 out of 75. It has to do with a quirk of how the Illuminate website works. Even though I'm able to weight the constructed respons...

Today in Stats class, I give the first quiz of the year. The quiz covers Chapter 4 of the text, which is on Exploring Quantitative Data. Before the quiz, I continue Sarah Carter's idea to do a different dot plot everyday. Since today's Thursday, I choose Carter's topic from last Thursday, "How many concerts have you attended in your lifetime?" But my classes continue to shrink as some students are transferring to another school -- now my fifth period class has just three students, in addition to the single student in my first period. And of this quartet, two of them have seen just one concert while the others haven't seen anyway. So this doesn't lend itself to a very strong dot plot. Carter's idea of dot plots based on the students' data is excellent, but my classes are so tiny. In fact, the superintendent has contacted our school and informed us that three of the classes here are too small and need to be combined. Naturally, this includes my Stats...

Today in Stats, we continue with the next six pages in Chapter 4, "Exploring Quantitative Data." These pages cover mean and standard deviation. One of the examples in the text is about cancelled flights from 1995-2005. There was one outlier during that stretch -- September 2001, with 20% of all flights being cancelled due to 9/11. Last weekend we commemorated the twentieth anniversary of the September 11th attacks. I often tell my students the story of where I was on 9/11, close to the anniversary. With the date falling on the weekend, and with it fitting today's lesson perfectly, I tell my Stats students the story. I'll repeat it here (as I first posted on my original blog): In the year 2001, I was an undergrad student at UCLA. I had just completed my second year and decided to take two classes over the summer. (These summer classes, along with my AP credits, would allow me to complete my bachelor's degree in just three years.) Notice that since UCLA is on the qu...

Today in Stats, we continue with the next three pages in Chapter 4, "Exploring Quantitative Data." These pages cover quartiles, the interquartile range, and the 5-number summary. I decide to follow Sarah Carter's suggestion of starting with a different dot plot each day. Today's dot plot is on the number of hours of sleep last night. But the idea of doing sleep hours, as opposed to some other quantitative data, comes not from Carter, but from the Ethnostats lesson set up two years ago. Indeed, now that I finally have some of those lessons, my general Stats and Ethnostats classes are now starting to diverge. As usual, I'll focus more on the general Stats classes here, and save Ethnostats lessons for Twitter. Yet both classes contribute to the sleep hours dot plot. My classes are so small, and so I want to collect data from all my Stats classes in order to get more information. In general Stats, I begin with the Warm-Up and aforementioned dot plot. Then I move on to...

Today in Stats, we continue with the next six pages in Chapter 4, "Exploring Quantitative Data." These pages cover one more type of distribution -- the dotplot -- as well as the mode, median, and range of a particular distribution. This means that it's time for another Sarah Carter activity. That's because Carter blogs and tweets extensively about dotplots: https://mathequalslove.net/how-many-states-have-you-visited-map/ And so I decide to do this "How many states have you visited?" activity today. Since my classes are so small, I'm including all of my Stats classes -- both general and Ethnostats -- in the dotplot. I begin by telling them that I've visited fifteen states -- California, Arizona, New Mexico, Texas, Oklahoma, Kansas, Missouri, Colorado, Utah, Nevada, Maryland, Louisiana, Mississippi, Alabama, and Florida. Meanwhile, the most states visited by any of my students so far is five. Two of my students have never been to any state outside Cali...

Today is Rosh Hashanah, the Jewish New Year. The LAUSD always closes for both of the High Holidays, Rosh Hashanah and Yom Kippur. It also closes for Admission Day -- but even though California was admitted as a state on September 9th, 1850, the district observes it on the Friday before Labor Day. Thus this year, the district observes a big five-day weekend from Friday to Tuesday. Then again, none of this is relevant to me. My current district closes for neither Admission Day nor the Jewish holidays, and so this was just an ordinary three-day Labor Day weekend for me. And I spent this past weekend grading the exams in Stats and Calculus. I have only a single guy in first period and four students in fifth period Stats, so only five students took the Chapter 3 Stats test. Of those five students, three of them scored 80 out of 100. There was also one girl who scored 70 (after having missed the first three weeks of school) and one guy who earned a 50. (He's a special ed student -- there...

And now Blaugust is over -- or is it? Notice that Shelli's husband -- the only person who's really leading Blaugust this year since Shelli herself is skipping it -- has declared a full five-week blogging period. So according to him, the official leader, this challenge extends into the first days of September. It's strange thinking of Labor Day as the first big milestone of the school year, since back in the old days, school didn't even start until after the September holiday. Now I work at a district with nearly a full month of school before Labor Day. Ten percent of the year will be completed by tomorrow. On my old blog, I once referred to the first few weeks of school as the Willis unit -- named for Paul Willis, a British education theorist. Another name is the Wong unit -- named for Harry Wong, an author who wrote extensively about the first days of school. Or we can just call it Blaugust. At any rate, now is a good time to reflect upon the start of my school year. O...