Day 133: Manipulating the Mean

6th Grade Math Standards: 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.

Quote of the Day: From the book 26 Irrefutable Laws of Powerful Relationships. It's too long to type, but it's about a teacher who did not give up on her student and the student eventually became an adult who won a Pulitzer.

Question from Yesterday (as always from a student): Why do the numbers come out to decimals? What happens to the decimals when they are divided by 5 (will they always terminate or will some repeat)?

The Learning Objective: Manipulate the mean of a data set

Assessment: I gave the students their scores using X2 without showing them the average and had the students do three things:

1. Determine their average right now (this part they did just fine)
2. Find how their average could increase by three points (this was much harder)
3. Find how their average could decrease by three points (this was the same as number two, but they ran out of time before they could finish in some cases)

Agenda:

1. Complete a graphic organizer of central tendencies
2. Do several practice problems that vary in their degree of difficulty for finding the three measures of central tendency (mean, median, mode). I found out today through another student that there are other measures of central tendency.
3. Give an example of another student's grade (I made up the information on the fly and used 72, 72, 90, 83 as the scores). Have students calculate the mean and what's needed to bring the grade up to an 83.
4. Have students calculate their own grade and the scores necessary to bring that grade up or down by three points

Glass Half-Full: I really enjoyed teaching and being a teacher today. Perhaps it was the extra hour and a half of sleep I got last night or the two days that I essentially did not teach for because of MCAS testing. I think more likely though is that I enjoyed giving students only a couple issues to dive into and getting them to dive in deep to those issues.

Finding their own mean served a dual purpose of getting them to meet today's objective and also give them awareness of how their grade is scored (which many of them seem to be unaware of). Only about half the students were able to manipulate their averages, so we still have some work to do tomorrow, but I loved that they were challenged and really had to put the pieces of the puzzle together. We broke this problem down with the Polya Problem Solving method.

Regrets: None. Some students did not get the skill according to the exit ticket, but I'm not worried. We will continue to work on it tomorrow. It felt good to have them challenged, to give them time to struggle, and to help some students work it through.

Link of the Day: Interesting read on reward systems among other topics.