Learning Objective:
Understand how the graph of 
changes under the transformations 
and 
Task
In pairs, create a screencast that demonstrates your understanding of how changing variables 
for and 
for changes the graph of . The graphs should be transformed using sliders and the graphing tool on www.desmos.com and the screencast should include audio commentary by both students.
Instructions
1. Go to Desmos Graphing Calculator and learn how to create sliders to change the values of variables and .
2. Investigate how changing for and for changes the graph of by testing various functions (for example: linear, rational, quadratic, cubic, exponential, logarithmic, trigonometric, modulus). You will need to test a wide range of values for and and take notes on when and how the graph changes.
3. Once you understand the effects of and , you are ready to create your screencast. Plan out what you want to show and a script for what you want to say. You can watch a sample screencast that I created for this task at the bottom of this post.
4. Be sure to check the assessment rubric so that you know what you should include and how you will be assessed.
5. Submit your screencast as a .mp4 video file to the assignment on our Google Classroom page.
Assessment
| Criteria | No Marks | Partial Marks | Full Marks |
|---|---|---|---|
| Use of Desmos and Sliders | Does not contain sliders | Sliders are used but do not change the graphs correctly | Sliders are used correctly and effectively |
| Understanding of Transformations | Little to no understanding of how and transform the graphs is demonstrated |
Some understanding of how and transform the graphs is demonstrated |
Strong understanding of how and transform the graphs is demonstrated |
| Depth of Investigation | The effects of and are not investigated |
The effects of and are investigated but in a general sense |
The effects of and are investigated for different ranges of values such as  |
| Audio Commentary | Both students do not present or the audio is difficult to hear | Both students present but the investigation results are unclear | Both students present and the investigation results are clear and the commentary is effective |
Resources
Desmos Graphing Calculator
How to use Desmos Sliders
How to make a Quicktime Screen Recording
I recently taught a unit on transformation of functions with my Grade 10 Math class and although I used an inquiry-based activity with a worksheet for them to fill out and demonstrate their understanding, I felt that there was room for the students to investigate on their own rather than completing a task just to fill in an answer. When I developed my own enhanced lesson, I realized how much understanding is needed in order to present on a topic and therefore felt that having students create their own presentation in the form of a screencast would require them to have a strong understanding of the learning objective. In the activity, I had students use Desmos Graphic Calculator which they are familiar with from other lessons, and get “hands-on” with the slider functionality which allows them to see how changes they make effect graphs in real time. I provided a sample screencast for students to refer to so they have an idea of what is expected. At first, I was undecided about providing this as I feared students would simply copy the format and all the submissions would seem the same. However, I have found from experience that when the task is too open-ended with little guidance or structure, students have a more difficult time reaching the learning objective. Also, this task requires much more investigation than the sample I provided which force students to have to inquire further. Finally, I provided a rubric on how they will be assessed so that students are aware of exactly what is required for the task. Some of the descriptors are also my way of guiding the students what exactly they need to be considering when studying this topic.
Kaz,
Great lesson! I love how in your video exemplar they see exactly what the possibilities are and then have the chance to play with it themselves when creating their own screen capture. I too agree that in this case, the exemplar is really necessary otherwise students would probably get hung up just getting started rather than actually playing and learning in Desmos. I also really like your rubric. For the Audio Commentary portion would the mark they receive there be part of their summative mark or would it be formative? Great job again!
Abbi
Hi Kaz,
I will have to look into the Desmos Graphing Calculator. My first questions is, is this a higher level Grade 10 math class? Are all of the students getting these concepts or is this more of an extension project for the higher level students? I am asking as I am thinking of some of my Grade 9 students who struggle in math, and can see them struggling with these tasks. As an extension however, it is great to allow the students an opportunity to visualize how these functions can change. As Abbi noted, I love the exemplar where students can see exactly what it is that you are looking for. Great task.
Markku