Sample Lesson Plan: Transforming Other Parent Graphs
Link to a PDF of the lesson: TOPG Lesson Plan
Link to Geogebra: Click here!
Link to original lesson and extra material: Click here!
Link to Geogebra: Click here!
Link to original lesson and extra material: Click here!
A Bit About the Lesson:
This lesson should be implemented after students have studied parabolas and their parent graph, y=x^2. In this investigation students will use what they have learned about transforming the graph of y=x^2 to transform four new parent graphs. We will also be using Geogebra, an online graphing tool, to aid our learning of functions. As a group, they determine how to make the graph of any function move left, right, up, and down and how to stretch it vertically, compress it vertically, and flip it. Each group member should choose one of the parent functions given in the lesson to investigate. By investigate I mean that I want the students to sketch the graph, identify the domain and range, and label any important points of asymptotes. After students have done that without use of technology they will graph and check your work using a program called Geogebra and write an equation to demonstrate each transformation they discover. Finally, the students discover a general equation for all four parent functions. In the about video I have described a bit about Geogebra and how the students may use it during the class period and at home for homework.
Geogebra is a great online graphing tool that has many other uses as well. For this task I asked the students to graph their functions in the program. I chose Geogebra because I felt it was a great technology to aid me in teaching the content. This lets the students alter the functions and see how the graph responds to the equation. You can also do the reverse and move the graph and see how the equation changes due to the movement of the graph. By being able to directly see the graph move as a result of a change in the equation and vice versa really enriches the lesson by providing feedback on the students hypotheses. I can remember learning this material and having a difficult time visualizing what was really happening to the graph when I changed the equation. This technology would have instantly cleared up my misconceptions about the equations if it was used in the class that I had learned it in. Without this technology I feel many more misconceptions would arise that could be taken care of by students discovering the material with the applet. At the end of the lesson I give some homework using Geogebra as well. I great feature of this program is that you can locate the technology from any computer.
This technology allows me to take a step back and let the students do the real learning by discovery. They can make educated guesses in how they think the graph will change when they change the equation. Then the students can test their guesses themselves using Geogebra and come to conclusions on their own. My role as a teacher can become more of a facilitator instead of a lecturer. Without the technology this lesson may be more lecture based causing a decrease in student to student discourse and lower student participation. It would also not allow for as much student accountability of material and group work. The use of Geogebra in this lesson took it from a somewhat typical “boring” mathematics class to an interactive engaging lesson. This promotes much better material retention.
On the flip side all technology has the ability to glitch and Geogebra is not immune to it. Possible pitfalls in the lesson could arise from an internet crash or the inability to rent a laptop cart of computers for the classroom. This tool has the ability to be downloaded onto a computer or be used directly from the internet however without initial access to the internet it is difficult to put the applet onto each laptop. This may be a time consuming process for a teacher if there happens to be an internet crash that day. To overcome this I would advise downloading the applet to your computer and then to a zip drive so that in the event occurs you are able to upload it onto the computers while the students start on the individual work first. Overall Geogebra can be a great asset to a mathematics (and even science too!) classroom.
Geogebra is a great online graphing tool that has many other uses as well. For this task I asked the students to graph their functions in the program. I chose Geogebra because I felt it was a great technology to aid me in teaching the content. This lets the students alter the functions and see how the graph responds to the equation. You can also do the reverse and move the graph and see how the equation changes due to the movement of the graph. By being able to directly see the graph move as a result of a change in the equation and vice versa really enriches the lesson by providing feedback on the students hypotheses. I can remember learning this material and having a difficult time visualizing what was really happening to the graph when I changed the equation. This technology would have instantly cleared up my misconceptions about the equations if it was used in the class that I had learned it in. Without this technology I feel many more misconceptions would arise that could be taken care of by students discovering the material with the applet. At the end of the lesson I give some homework using Geogebra as well. I great feature of this program is that you can locate the technology from any computer.
This technology allows me to take a step back and let the students do the real learning by discovery. They can make educated guesses in how they think the graph will change when they change the equation. Then the students can test their guesses themselves using Geogebra and come to conclusions on their own. My role as a teacher can become more of a facilitator instead of a lecturer. Without the technology this lesson may be more lecture based causing a decrease in student to student discourse and lower student participation. It would also not allow for as much student accountability of material and group work. The use of Geogebra in this lesson took it from a somewhat typical “boring” mathematics class to an interactive engaging lesson. This promotes much better material retention.
On the flip side all technology has the ability to glitch and Geogebra is not immune to it. Possible pitfalls in the lesson could arise from an internet crash or the inability to rent a laptop cart of computers for the classroom. This tool has the ability to be downloaded onto a computer or be used directly from the internet however without initial access to the internet it is difficult to put the applet onto each laptop. This may be a time consuming process for a teacher if there happens to be an internet crash that day. To overcome this I would advise downloading the applet to your computer and then to a zip drive so that in the event occurs you are able to upload it onto the computers while the students start on the individual work first. Overall Geogebra can be a great asset to a mathematics (and even science too!) classroom.