CA I.5 Modeling Change in Applied Data using Mathematica
Purpose: To learn to use a CAS (Mathematica) to visualize characteristics of change in numerical data and in associated modeling functions through graphing. Students will learn to enter a table of data, create a scatterplot of that data, define a function, graph a function, evaluate a function for a particular input value and show multiple graphs together.
Classroom Procedure: Students work on this activity in pairs while we spend our time helping students as they get stuck. We may have a few whole class discussions but mostly students are working through the activity and asking us individually as they have problems.
Ideas this Activity Builds On: This activity is an immediate follow on from the previous activity CA I.4. It asks students to graphically evaluate their conclusions from that activity and emphasizes the graphical characteristics that we concluded linear and exponential functions would have.
Introduction/Motivation of the Activity: The main motivator for this activity is the desire to have a way to visualize if the models we found in CA I.4 were good models. We already discussed how we might numerically think about whether they are good models but for some students the visual will be much more effective. It is also important for us to be able to move between numerical, symbolic and graphical forms of a function which this will allow the students to do.
Need to Establish by the End of Activity/Wrap-Up:
How to use Mathematica for everything listed in the purpose
How to conclude visually if your modeling function is a "good" model for the data set.
Additional Notes: There are no synthesis questions to this activity - in some ways this activity itself is really a synthesis to CA I.4. If you are not using Mathematica in this class this is a good time to introduce any technology that you are using and if possible to visualize the functions and data that they worked with in the previous activity.