Spreadsheets in Geometry

This is a guest post shared by Pinedale High School Math teacher Christy Zakotnik.  It describes a lesson plan she used which integrates spreadsheeting to develop student understanding of Geometry concepts.  

 

Area is a topic students start to address in elementary school and we continue to build on it into high school.  By the time they finish Geometry in high school, students are expected to be able to work backwards through the formulas and be able to comprehend find areas of more complicated figures, too.  For example, given the side length of a regular heptagon, find its area.  And of course: if you are given one base of a trapezoid, the height and the area, find the length of the other base.  The whole point is really to get them to think algebraically about a situation.  What are the many steps that you go through to solve the problem?  How do you isolate a variable so that you can use the new version of the formula over and over again?

Wait a minute—formula that you can use over and over?  That is a spreadsheet.  Rather than the usual chapter test for our unit, students completed a series of tasks on a spreadsheet in Excel.  The tasks increased in difficulty as students progressed through the assignment.  For Parts I and II, I checked students’ work face-to-face as complete and correct and gave them verbal feedback so they could fix any problems.  This check ensured that everyone knew how to input formulas using Excel and understood the concept of the assignment.  (Added bonus—half of the project was graded before I even opened a file.)  They were mostly on their own for Parts III and IV as the cognitive complexity increased.  Students chose to work with a partner or to complete the project individually, but they were allowed to share ideas and communicate throughout the project.  Students had access to textbooks and notes, but they were not to use the internet (many of the formulas we want them to develop could be found there).  Assignments were submitted as attachments through Edmodo. Here is an example of a student project.  If you make a copy (file>make a copy), you can experiment with changing the variables to calculate the unknown elements (highlighted in blue).  

This is a great example of watching students work from concrete to abstract.  As the tasks grew in difficulty, we encouraged students to use pencil and paper to work through specific examples and use those examples to generalize the process.  This generalization became the formulas they used in Excel.  When inputs changed in the spreadsheet, the outputs changed accordingly.

Here is a link to the assignment sheet I shared with students on this project.

I would like to thank Glen Egbert for helping me set up the project and doing everything in his power to make the process as smooth as possible.  Also, I’d like to thank Lindsay Abercrombie, paraprofessional, for diving in and helping students in the lab.  Lindsay’s previous experience with Excel proved invaluable and her eagerness to work with students was refreshing.