# CAS with Probability

 Using CAS with probability lessons can make learning fun and allow students to do experiments on a device instead of gathering data, flipping coins and rolling number cubes the old-fashioned way.  Sorry teachers but the students like the devices, and it will save you money and storage space if you keep it digital. Let’s start with random samples involving population.  TI has a FREE activity called Interrogating the Data that works great.  The data is a random sampling of 7th grade math scores.  It starts with the question:  “Why might one use a sample instead of collecting data from an entire population?”  The handheld generates a random sampling for the students.  You do not have to come up with the numbers.  Let the technology do the work for you.  Here is a screenshot of the samples: You can use the TI-Navigator CX CAS system to capture student handheld screens to display on your screens for discussion and self-checks.  A CAS handheld will allow a student to compare not only the table but different data displays to compare which is the best display to analyze the data.  A dot plot and stem plot is shown below, but you can also look at a histogram.  You can even compare all of the samples on one page. With technology students can customize the color and axis to investigate to their individual style.  Next the CAS will allow students to calculate the mean of the sample and absolute deviation using formulas in the spreadsheet which leads into major discussions on the data. Instead of focusing on how to do the calculation at this time you can focus on the following: 1.    What does the formula mean? 2.    Why is it necessary to calculate the absolute value? 3.    What is learned by calculating the Mean Absolute Deviation? This is applying the mathematics instead of just doing the mathematics.  Students can then make predictions using their analysis of the data instead of a textbook created problem with no meaning.  The CAS handheld will also allow the students to interact with the graphs by hovering over different parts of the graph on the screen to see other important values as shown in the screenshot below: This particular activity gives students other types of population data to study also. Now let’s look at experimental and theoretical probability.  Using the One and One Equals Win activity from the TI website, the CAS handheld has a basketball player simulation to analyze probability of making a shot and a basic spinner simulation.  Screenshots are shown below.  The CAS handheld allows students to calculate the theoretical probability then do the experimental probability and compare the two.  This will save time in the classroom and still allow the most important discussion to take place:  Are the experimental outcomes different from the theoretical and why?  Then finally give the students a basketball scenario and let them use the probability experiment to predict the outcome of the game based on the data.  The TI activity provides a scenario but you can create your own if you choose.  A sample table is shown below: It is easy to see that technology is the way to improve motivation for learning probability.  The TI-Nspire CAS handheld comes with pre-made activities and simulations for this purpose and has the calculation and graphing capabilities working together.  Whatever data is put in the table is automatically connected to a graph for manipulation and analysis.  I will never use physical number cubes again. 