Day 132 Measures of Variation Introduction

6th Grade Math Standards: 6.SP.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.

6.SP.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.

The Learning Objective: Find the range of a data set

Quote of the Day: "Learning is defined as a change in behavior. You haven't learned a thing until you can take action and use it." - Don Shula

Agenda:

1. Self-Assessment
2. Review Quiz
3. Get the central tendencies of Derek and Michael in partners 
4. Ask what the difference is in the data between the two after students agree that the central tendencies for each student is identical
5. Ask students to define range or tell students if nobody knows
6. Do the rest of the problem with Derek and Michael
7. Give examples of outliers (my age, months hockey players were born in in Canada, home runs in a baseball season by Sammy Sosa from 1993-1998, etc.)
8. Homework models (could serve as tickets to leave additionally)

The Assessment: I circumvented the room as students worked on the central tendencies in Step 3 of the directions. Off-hand I would say about 60% of the students recognized that Michael needed a 0 on the quiz he had on division. I pointed this out to students. They seemed to remember what mean, median, and mode were after I gave them a little time to work this out. It was a perfect sheet to have when most students had not been in class since last Thursday (three days ago).

I also asked students to think of a range that would give them an answer of 20 and to come up with their own outlier examples to ensure that they knew enough about the definition to identify how these numbers could fit into a problem.

Glass Half-Full: In one class today, I asked why they believed our mean was about 6 or 7 points away from the other two classes. I did not do it with a threatening or sarcastic tone. I simply asked it curiously to evoke some of their ideas. One student brought up paying attention and others said we did not have enough practice. It was good feedback. My personal opinion is that in terms of classroom management that particular group has a harder time working in partners as we did on the study guide the day before the quiz. I had their attention though after we as a class came to this realization and it helped in going over the quiz. Hopefully that makes up for the 6 or 7 percentage point drop between the two classes as they seemed to pay attention more thoroughly when I reviewed the quiz.

Overall today was a classic example of mood winning over the students. I was not in a joking mood, but I was extremely tolerant of the needs of needy students. I had students go to their lockers, but only at logical points in the course of the class. I used please and thank you to get students to work. My listen to lecture ratio was a little more tilted in the side of listening than usual. More than anything what helped with this was the students previous learning experiences with the three central tendencies. It was a well-timed lesson.

One Regret: So many steps, so little time. I read Malcolm Gladwell's book Outliers over the summer. There were interesting anecdotes from this book that analyze why outliers came to be and I wish I had more time to share these nuggets because it's a great example of math telling a story.

Link of the Day: Great article on Emojis although it does talk a little too much about alcohol for my liking.