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: Identify three measures of variation; identify three measures of central tendency; find all measures of central tendency given the data set; find all measure of variation given the data set; find a missing value in a data set given all values but one and the mean; differentiate a statistical question from a non-statistical question
Agenda:
- Collect the Weekly Quizzes
- Explain the dilemma of how many ways people can sit next to each other if two people are in the room, three people in the room, etc.
- Pass out and read over the directions for the test
- Take the test
- Determine how many combinations of people can sit next to each other if there are 4 people in a group, 5 people in a group, 6 people in a group, and 7 people in a group
- How many handshakes take place if each person in a group of two shakes hands with the other? A group of 3? 4? 5? 6? 7?
- If there are three people chosen among 3 people to be allowed to drop out of school and only attend Red Sox games, how many possible groups can be chosen? What about if there are 4 people and only 3 can be chosen? If there are 5 people and only 3 can be chosen? 6? 7?
The Assessment: The test went relatively well. Based on the study guide from the previous class I was not surprised to see students struggle most with finding a missing data value given the mean. I also was not surprised with the students struggling to identify what measure of central tendency was most appropriate given the data set.
Glass Half-Full Take: Today was the day before a vacation, so it was good to have something to go to after the test where students could work independently and be somewhat engaged. I borrowed all three of the items featured in the agenda 5-7 from a book called The Number Devil. I loved the book and thought it was both curriculum and age appropriate.
One Regret: As part of that after test activity, I had the students share their work on Google Docs. We have not used Google Sheets in my class and I'm not sure if the students have had any experience with this. It was not something I went over in great detail with the students beforehand and I decided that students usually are better equipped to handle technology than me and that the details were not necessary. I was wrong.
Students were simply typing messages to one another into the cells and not being as productive as they could have been in solving the problems. They did not struggle with the technology, but the task I gave them with the spreadsheet was rather vague. What I should have had them do was create a page with their name and their partners name on the page. Then the students could submit that page to me as a sort of bonus answer. Instead I made the page public and left the directions relatively vague. Even students that knew what they were doing had their work erased by other students who could edit the page. In my last class I expressed my disappointment with the students lack of focus. In reality I'm more to blame than any of the students for the lack of planning. I will know better next time at least.
Link of the Day: I was reading this blog post about if we have mathematical ceilings and loved two analogies. "Try asking adults about their math education: They refer to it like some sort of NCAA tournament. Everybody gets eliminated and it's only a question of how long you can stay in the game." And then this, "if you're missing one simple understanding - that these graphs are simply the x-y pairs satisfying the equation - they you're a broken futon. You're missing a piece which future learning will crucially depend."
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