6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
The Learning Objective: Interpret dot plots to find measures of center and variation
Quote of the Day: "Each student in this class will get an A for the course. However, there is one requirement that you must fulfill to earn this grade: Some time during the next two weeks, you must write me a letter dated next May... and in this letter you are to tell, in as much detail as you can, the story of what will have happened to you by next May that is in line with this extraordinary grade." They [the students] were to discuss insights, milestones, and even competitions won. "I am interested in the attitude, feelings, and worldview of that person who will have done all she wished to do or become everything he wanted to be." - from How to Win Friends & Influence People by Dale Carnegie
Agenda:
- Jumpstart
- Review the homework
- Dot plots notes on central tendency and variation
- Dot plot notes on central tendency and variation independent practice
- Work on the weekly quiz
The Assessment: In coordination with the quote of the day, I promised students that if they could prove to me they could find measures of variation and central tendency by looking at a dot plot that we would have no homework. It instantly helped add value to the assessment which was step four in the agenda. I gave the students two problems to do on their own from this step.
In all honesty, students proving their knowledge in the formative assessment and not needing to do homework is generally just good teaching practice. The homework I have typically given this year is done only because I run out of time to more properly give a formative assessment.
Glass Half-Full Take: The ease with which students are able to answer what the purpose of a dot plot is useful is refreshing for me. When they understand the more basic purpose, it makes the rest easy. All the students demonstrated on the formative assessment from the last class that they knew at least two purposes for the dot plot and now some of the students can state as many as nine purposes.
- Find the mean
- Find the median
- Find the mode or peak
- Find any possible outliers
- Find the quartiles and interquartile range
- Find the range
- Find any possible gaps
- Find any clusters
- Find how many pieces of data are in the data set
One Regret: I only wish that I could have gotten the students out of their seats at some point during class. Perhaps next time I teach this lesson, I will have them go to the recycle bin to throw their paper away once the jumpstart finishes. The way this class was designed, it was essentially 100 minutes of desk work (although in truth if students were optimally focused it's really 50 minutes).
Link of the Day: Good take on high school preparation for college by Grant Wiggins. A couple of counterpoints from me:
- High school is not college. The maturity level and hormones are not the same, so why should we treat it as such? College classes are longer, but is that really what we should do with high school classes?
- What about those students in high school that are not going to move on to college? In fairness to Mr. Wiggins, he does make this caveat at the end of the article.
- Advocacy from the students is another thing that must happen gradually. In my own experience many times I didn't seek out my professors for extra help, but my peers.
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