Author: MaryAnn Moore
Hold onto your hats, folks, because I am about to share with you the best task that I have ever assigned my students. Ever! It's no secret that I am in love with the Desmos Free Graphing Calculator (learn more about Desmos here). I use the thing almost daily in my teaching. And sometimes I use it even when I'm not teaching. I've been a major fangirl of Desmos and the whole Desmos team ever since I learned about it 3 years ago. And for about the same amount of time, I've been crazy jealous of my online teaching friends, like Bob Lochel, who teach upper grades and get to do Desmos Conic Section Art Projects with their students. I knew there had to be a way to scale this down for my 8th graders - whose focus is entirely on linear functions, but I couldn't quite figure out how to structure it. Fear not, though. The ever-creative Fawn Nguyen solved the problem for me last spring when she wrote about the Desmos Puppy House task that she gave her 8th graders.
Here's the gist of how it works:
1. Students sketch a puppy house on graph paper. The requirements are: at least 5 horizontal lines, at least 5 vertical lines, at least 6 slanted lines, at least 1 image of a puppy in the doorway or a window. They are welcome to use more lines. They are welcome to use curved lines, but they will have to figure those out on their own. They are welcome to swap out the puppy for a kitten or a dragon. (Turns out some of my students are NOT dog people. Go figure.) They can make their puppy house into a Puppy Palace if they want, just so long as they meet the minimum requirements. I showed them the images of the houses from Fawn's blog post and it really helped spark their creativity and raise the bar, so by all means, feel free to share my examples. I graded the sketch as a practice assignment.
2. Teacher draws axes onto student's completed sketch. This idea came from this Parabola Art blog post by Mary Bourassa. Mary explains her reasoning behind this: "This is my answer to the multitude of parabolic art graphs that are already out there - even if they took someone else's design (which they would have a hard time doing as I make them create their sketch in class), they would have to move all the equations to fit the axes I forced on them." Whether you have students draw the axes onto their sketch or whether you draw it for them, I would strongly recommend that you put the axes on there. I didn't do this for all of my students, but the students who had the coordinate grid on their sketches had a much easier time writing the equations.
3. Students write equations of their lines onto the sketch. This year I only asked students to write the slope next to each line. However, when it came time to graph, many students really struggled to put the pieces together even with the slopes already written (good thing I still have 5 more months to get slope-intercept form ingrained into their brains). Therefore, in the future, I will have them write on their sketches the exact equations for all of their vertical and horizontal lines and the approximate equations of their slanted lines (something like y=3x+?). I thought about teaching them point-slope form so that they could write the exact equations for the slanted lines also, but in the end I liked forcing them to use guess and check in Desmos to figure out the y-intercept. Through the guess-and-check process, many developed a deeper understanding of how the y-intercept affects the graph of a linear function. If we have time later in the year, we may do another Desmos Art assignment using Point-Slope form. I graded writing the slopes/equations of each line on the sketch as another practice assignment.
4. Start Graphing! I went over the basics of creating accounts/logging in first and then used this handout to teach them about creating domain and range restrictions. Some students caught on much more quickly than others. The next day I gave them a very short quiz at the beginning of class and then they had the rest of the time to work on their Puppy Houses. The following day, most students were finished with everything except the puppy. I taught them how to put the Puppy into their graph, taught them how to share the link to their graph, how to access the Google Form to turn it in, and then they had the rest of the class period to either finish their Puppy House or, if they were finished, play Desmos Polygraph Lines. I graded the final graph as an performance assessment.
Was it an investment of time? Absolutely, although I think I can pull it off in less time next year. But was it worth it? No doubt about it! I have never seen my students so excited about any task I've ever given them. On the second day of graphing, when the clean-up music started playing, there were cries of disappointment from my students - who were so engrossed in their line art. Their creativity and dedication to this task blows my mind. Several of my 8th grade students learned how to graph circles, inequalities, sine functions, and how to use variables and sliders to animate parts of their graphs. I didn't teach them any of that but they wanted it, so they learned it! I feel like a proud parent - there were honestly a couple of these graphs that had me in tears when I opened them. When is the last time that your students created a piece of mathematics that was so beautiful that it brought tears to your eyes? For me, it was a first. I want to print out all of their graphs and plaster them all over my refrigerator. I will restrain myself, though, and instead I will plaster a few of my favorites into a slide show at the end of this blog post. Thanks again to Fawn and Desmos for making this happen for me and my students.
About the author: MaryAnn Moore (@1mooreorless) is the editor and lead writer of the UCTM blog. She teaches 8th and 9th grade math in Davis School District. When not teaching, MaryAnn enjoys playing violin, running, cooking and traveling. You can contact her at firstname.lastname@example.org.
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