I begin class by asking students to tell me what they know about “square roots". I use polleverywhere.com* to collect responses on the board and set the stage for the day’s lesson. In my past experience, students might say things like “It un-does the x squared” …etc. It is unlikely that the responses will mentioned what the function might look like on a graph, which is okay since that is the topic for our investigation today. As the teacher, I make certain NOT to tell students if they are right or wrong in order to promote healthy discussion. This helps serve as an even greater motivation for the lesson. In my experience, any time you ask students to define or explain a concept it hooks them right from the start because they want to see if they are correct!
* PollEverywhere is an excellent classroom instructional tool. Teachers can create an account for free and instantly set up and save multiple polls. Students can respond to the polls via computer, iPad, or cell phone text message (standard messaging rates apply). The website is very user friendly and great for entry and exit polls. Results can appear in a variety of ways, both public and private, and can be illustrated in word clouds or bar graphs.
To begin the class, I provide my students with an introduction to the features of Geogebra. I use the free online version. I have found that it works great as a graphing utility and has an app option for all of you iPad users out there! Tools like Geogebra are critical to really get to the heart of the Common Core since it provides easy access to multiple dynamic representations which provides a new platform for generating discussion with students. It is also a great way to teach students a tool to use strategically! (MP5)
Although my students have iPads, I do not ask them to download the Geogebra app during class. This takes a long time on our school network. Instead, however, I direct them to the free version of the site found on the internet. The link has been provided in the above paragraph.
Students quickly catch on to the features of Geogebra. To start, I have them graph linear equations because they are familiar with what the results should look like. Just for fun, I ask them to graph the line y=2x+1. Rather than giving them a second equation after this, and just giving them another one, I ask them to graph a line perpendicular to the first line. This reviews a few Algebra I concepts and the students learn to delete lines if they "guess" incorrectly! One key note to make to the students as you roll out Geogebra is that they need not type the "y=" or "f(x)=" portions of the equations/functions to be graphed.
To wrap up the lesson and send the students home with a small homework assignment, I ask them to take time to analyze their graphs and note any patterns or observations. It is important to give them an example to two, without directly giving them the answers... in fact, emphasize to them that there may be MANY correct answers!
It is usually necessary to provide the students with a concrete example since this is a "non-traditional" activity. I demonstrate on the board what this might look like if we were graphing different types of LINES...instead of radicals. If our graphs were lines, I ask the students, what types of patterns would we see in correspondence with the equations? What generalizations might we make? After noting things like the slope being negative, they get the picture as to what I want them to do with their Geogebra graphs. This is a great way to emphasize MP2 (reasoning abstractly) and MP7 (make use of structure - BIG TIME!).
FUTURE LESSON NOTE: It is important to print the follow along sheet SINGLE SIDED as students will cut these graphs out in an upcoming lesson where they will sort and group the graphs based on their properties.