Spreadsheets, Patterns, and Exponential Growth
- Karen Greenhaus
- Jun 12
- 3 min read
I want to focus on the newest Casio graphing calculator, the fx-CG100 Classwiz. The lesson I am sharing today is using the Spreadsheet Menu Icon. You will note that the shared PDF has images from another graphing calculator, the fx-CG50, but, the beauty of Casio technology is that the functionality is very similar, though with this new calculator, due to its tabs vs. function keys, it is slightly different navigation. The video below is specifically using the fx-CG100 so you can see the difference in navigation, but I have also included a link to a video using the fx-9750GIII and the fx-CG50 so you will see that connection.
I chose an activity from the Fostering Algebraic Thinking with Casio Technology (2013) that I thought would be of interest to students because it deals with money and payment for summer jobs, something that many students can relate to. It's a take on a problem that has been around for awhile - i.e. what would you rather earn - a consistent amount every day(in this example, it's $1,000) for a period of a month OR a penny the first day, and then doubling the amount paid each day for 30 days. Obviously, not knowing anything about exponential growth, most students will look at the guaranteed amount and think that is the better deal because a penny on day one seems ridiculous. This is an activity where you want students to record the amounts and look at the patterns and come to the realization that 'doubling' really increases very quickly. Tables, graphs, calculations all come into play in this activity and it's a really fun way to introduce exponential growth and using mathematics to reason and think about problems instead of just jumping in and making a conclusion.
You will see in the video that I am utilizing the fx-CG100 emulator, available on the ClassPad.net workspace. This is an amazing tool for engaging your students, and as they work along with the handheld, you can model and demonstrate and focus on the visuals and patterns and have some good class discussion. You could model the problem with them, or start it off and then send them into small groups to complete the tables and then come back and discuss their observations. You could create the graphs and ask questions - i.e. what do you notice, what do you wonder, how are the graphs different/similar, etc and have them discuss and reach some conclusions. Lots of options. The key here is the data collection, the multiple representations, the questions you ask and the discussions you have with students to help THEM discover the exponential pattern and come up with an equation. The PDF of the activity below offers some good questions that help get students thinking and connecting.
The Spreadsheet Menu is a good one to utilize for this problem for its ability to use the cells to create calculations that will then fill in the entire cell for you. This also means students are really looking at the problem and determining what expression is going to do a calculation of doubling the previous day's amount. This leads to good discussion as well. They basically use the given information - constant amount for one column, and then doubling of previous days amount for the second column. There is then the ability to look at the data in the spreadsheet and compare visually what is happening to what is happening in the table. Then, again using spreadsheet capabilities, you can sum the two different options and really see the difference in total, which then connects back to the growth patterns. It's a great activity for showing exponential growth and comparing constant rate to exponential as well.
Here is the PDF of the activity - if you have any other Casio graphing calculator (fx-9750GIII or fx-CG50) you will see the steps for using the function keys.
The video below shows how to use the fx-CG100 CW graphing calculator, with the tabs, to start this problem.
Here is an older video that shows how to set up the Spreadsheet and work with formulas and graphs with the fx-9750GIII (the fx-CG50 will have the same steps).
