Students should engage and be hands-on with mathematics as much as possible. One of the activities I loved was the Sum of Two Dice, whether in my middle school classes or in my Algebra classes. That’s the great thing about mathematics – you can take an activity/concept and make it more or less rigorous depending on the questions you ask.
I am sure many of you have done this activity – I am choosing it for this post because it’s a nice way to demonstrate how the Casio ClassWiz (fx-991EX) scientific calculator allows you to create frequency tables and with the QR code, see an online visualization of the data.
First thing – have students roll two dice and collect some data – i.e., the number on each die and then the sum of the two together. If you don’t have die (or don’t want to hear all the noise!) you can utilize the random integer option on the calculator to simulate rolling die. I usually had my students in pairs to do this – one record, one ‘roll’. Then have them tabulate the frequency of each sum and create a new table with possible sums & frequency.
The next step is to have them make a histogram of their own frequency table and then compare to other students. In my example, students only rolled 24 times each, so everyone’s graph will look different and not be what we expected (more 7’s). Great discussions can come from these observations.
Hopefully, discussions lead to the idea that each group only collected a small sample of rolls, and that if we had more samples,
perhaps the distribution of data would be more what we expected – i.e. more sums of 7 appearing. Here’s where having a class emulator is a great tool – you can display one frequency table and collect the class data. So – same sums, but combine each groups frequency to get a total frequency for the whole class.
Once you collect the class data, you can then create a new histogram. With the ClassWiz you can easily do so just by creating a QR code of the table data, and, with the emulator, go directly to the visualization. You can also do this with the SmartPhone App Edu+ if you have that option. The nice thing about the emulator is you can immediately pop the visualization up and begin discussions and comparisons of whole class histogram versus individual groups. Being able to immediately see the visualization with only a scientific calculator, is powerful, especially as you can quickly compare between previous “one-group” histogram and current “whole-class”.
There are so many ways to use this activity – I use to use it with TinkerPlots, graphing calculators, students hand-drawing the graphs. The ClassWiz and its ability to create QR codes and online visualizations is another way to help students make meaning out of the math they are doing, especially when they only have a scientific calculator to use, as most middle school students do. Hopefully this gives you some more options. I have included a short video clip on how to actually create the frequency table, QR code, and online graph using the ClassWiz fx-991EX. Try it!