As you can see in the top left picture collage, I had students mark off their intervals by 0.5 and label the whole numbers. I then demonstrated how I could write Maria's name using horizontal, vertical, and diagonal lines. I then displayed my color coded graph so students could see how I wrote the equations with the domain and range restrictions.
Many students started and were successful with a lot of noticing of vertical lines being x=-2 if the line went through -2 on the x axis. They then realized they would have to limit the range to stop it from going all the way up and down.
Some students realized that they couldn't use y=mx+b for some diagonal lines when if they extended it the y-intercept would be off the page. So, there was a need to introduce y=m(x-h)+k or vertex form of a linear function. I told students it basically meant a line with a slope of m still, but it passed through the point (h,k).
Above you can see a student color coding the parts of her name to the equations she wrote. In the top right of the collage, this student finished first... Possibly because her first name had no diagonal lines.
Students were really open to helping each other answer each others questions about their graph and equations.
As you can see, students who had finished were able to use the Desmos iPhone app to start inputting their equations and see their creations come alive. For students whose parents restricted downloading of apps I instructed them to go to desmos.com in Safari and make sure they logged into their school gmail account to save their work.
I thought about how I could scaffold this activity better to reach all of my students on day 2, and I came up with the following Google Slides. I'd love some feedback on these. The lesson plan is to introduce learning goals and success criteria first (which can later be used as a rubric possibly). Also, show students the artifact that they could eventually print out with all their hard work. Then, instead of telling them exactly how to write each equation, I showed a slide with the equation matched to it's line segment on the graph. I asked students to notice. The slide right after that is a summary of the discussion points I anticipate that we would review. Some of the language refers to a YouTube video called Slope Dude Says under my Jokes tab at the top of the page where an increasing line is "puff puff positive," a decreasing line is "niiice negative" and a horizontal line is "zero fun." I showed this to students because they kept forgetting to put the negative sign after correctly identifying the vertical and horizontal growth of a line.
Below is an idea I had to help students setup their graph for export. I want them to notice all the options that are on in the default Desmos graphing window after clicking on the wrench icon in the top right of the screen. To prepare the graph to export it as an image, students will notice the grid, axis numbers, gridlines, and x and y axis need to be unchecked. The graph also needs to be in projector mode. I screen shotted these when I was on my iPhone app so they could see it easier.
Also, all equations must be the color black, and Desmos shared with me a faster way to do this. You click the gear icon to the right of the plus button in your equations window, and then can click on each color and change it to black.
The default settings are above. You can also see that I haven't changed the color of the lines yet.
The above settings show the correct settings as well as the equations in black.
If you look at the slides, I show the example of "Mr. Joyce." When I printed this, it printed as individual letters. My next iteration is below. I spelled out my daughter's name with parabolas, absolute value, linear, and exponential functions. This time though I created a rectangular prism around the name. I then matched the heights of the prism and the letters and then changed the letters to a "hole" in Tinkercad. So, as you can see, the letters made a hole in the prism. I want to compare this to an embossed or raised look where the letters are sticking up above the plate next time and see which looks better.
So, we have our 2nd week of 8th grade testing next Monday and Tuesday and I have arranged for the local librarian Debbie to come in with the portable 3D printer, give them an introduction, answer questions, print out a sample so they can watch it work, and then have them finish their graphs and prep them to be exported so they can put it in Tinkercad and make the name plate. Then they can export it as a .STL file and be ready to go. Once again, I learned all of this by reading John Stevens' blog post, which is linked in my first blog post, entitled "My First Desmos 3D print."
I also created a Padlet wall so students could post their work for myself and other students to see.