Day 126 Manipulating the Mean

6th Grade Math Standards: 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.

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 a missing value in a data set given the mean and other data values

Agenda:

1. March Madness Day 8
2. Students were given this problem which purposely leaves out information such as what numerical values are equivalent to a B+, A-, and C+ so that they could ask questions and have an opportunity for critiquing the reasoning of one another
3. We did another problem in which they had to determine what grade (a 225%) made going from a 60 average to a 93 average possible.
4. If there was time we closed out with one more problem that was similar to the Bethel problem earlier, but this time the problem had several more assessment and involved critiquing around rounding grades (is a 79.8 a C+ or B-?). 

The Assessment: The March Madness was done with TurningPoint software. The top results among the three classes asked for correctness looked like this:

Division of fractions 86%

Percent proportion 81%

Write a ratio 64%

Length of a side in CP 71%

Overall, pretty good results. Students were also assessed by a partner and myself who was circumventing the room during our class.

Glass Half-Full: The students struggled and we needed only one or two problems to make that possible. Students were truly forced to think with this activity. 

One Regret: For some students, I think this lesson comes too fast. I need to do a better job with small numbers of showing how the mean can change when a data value that is lower than the mean is added and how it changes when a data value that is high as added to the data set.