Students find equations, which best-fit the data, using different regression models built into their calculators. The best method of handling this data, is to break the data into sections and fit different periods of time with different equations. Using their models, they predict when the patient will be released from the hospital, and when the blood counts will rise to certain important levels. This is actual data, used with permission, of white blood counts following a stem cell transplant.
Before the Activity
Before the activity: Students should already understand the different types of regressions used in the calculators STAT/CALC menu. They should also have knowledge of why some functions should be piece-wise functions over the domain.
Instructor should print off the Word document called "Don's Data" Worksheet. The instructor may not want to use this if he/she wants the students to make more of the decisions. The instructor should also print off the Excel document called "Don's Data through Oct 21." I would suggest that THIS time the instructor NOT put the lists into the TI-Navigator™ and send them to them.
Students need to make some major decisions on how to enter this data, such as how to handle the change in months, how they want to break up the data into shorter periods of time, and why that is appropriate. This discussion can be a whole class discussion or by teams.
During the Activity
The students try to get the best possible fit, to all the data, by using their STAT/CALC menu. Encourage them to try different regression models, such as Linear, Quadratic, Cubic, Exponential, and Power.
It seems to make sense that parts might show exponential growth of the cells. Around the bottom, as the white blood cell count approached zero, the parabola might fit fairly well. Constantly do screen captures of their efforts, giving suggestions as they go. I suggest you assign teams of three.
As they progress, grade their various scatterplots, with lines fit through them, before they go on to the next set of dates. Just view screen captures as the teams finish tasks assigned on the worksheet.
After the Activity
You may modify the data slightly and ask them to do the activity again as an individual quiz, again grading screen captures when students ask you to do so.
Much of the assessment, of this activity, is done through the teacher viewing screen captures, to immediately see the goodness-of-fit.