In the opening for this lesson I want to give students a quick overview of how to use the Desmos online graphing calculator (MP5). Once students open the Desmos applet from Desmos.com, I let them play around with typing in different functions that they have seen in past lessons. This will allow students to familiarize themselves with the interface and how to type functions into the calculator.
In today's investigation, students will explore how to write equations that represent transformation of functions. The students will be using the Desmos online calculator as a tool to experiment with different ideas and check their thinking. As students move through each section of the investigation they will deepen their understanding of the structure of the various transformations (MP7). Students will begin to see commonalities between each of the various functions and how similar transformations are preformed on those functions.
While students are working I can move around the computer lab (or classroom) and facilitate or monitor progress. As an extension, I show students who finish early how to use sliders to check various constant values relatively quickly (transformation_2_sliders). I then ask students to experiment with putting sliders into the other functions they have been working with to show how the function is effected (MP2).
As a check for student understanding, I have students construct a "How To" guide for transformations of functions. Students will work with a partner to demonstrate their thinking about how to translate a function in various directions in the plane. To end this particular class, students will work with their partner to begin to layout how they will make their "How to" guide (MP3). They will begin to choose the functions they would like to use and the equations to represent those functions.
In the next class, students will construct the actual "How To" guide and these can be displayed for future reference.