This is definitely not a new idea on the web, but this is my first time doing a functions pictures project with my students! I am really excited to see the final outcome. What a GREAT way to teach restricted domain, technology / math notation, piecewise graphs, solving for y in a formula, and to review function transformations!
Here are my students' projects from Algebra 2. Stay tuned for my Calculus students' projects (which include an integral component). The basic requirements in Algebra 2 were to use quadratic, linear, and absolute-value functions. Some of the kids took the liberty to learn about sideways parabolas (which had to be turned into square root functions in order for them to limit its domain), circles and ellipses, and one student learned about using matrices to solve for coefficients, to help him find cubic functions to fit his points.
I think a writing component is essential for this particular project, when done in Algebra 2. Even though they were able to create the functions with only a minor amount of help from me and each other, it was when they had to write down their explanation of the impact of every parameter on the graph, that they really learned. They learned the correct math vocabulary, the specificity of the language, and for some kids who needed extra conceptual reinforcement, this was a great time for them to slow down and to make sure that they articulated once more the horizontal and vertical transformations and vertical scaling. I find now that I can grab any kid from my Algebra 2 classes, sit them down in front of any of the basic functional forms, and they can correctly analyze the parameters instead of mixing them up, as they kept doing earlier this year. Great stuff.
WIN. This project is really a MUST in Algebra 2, and (judging from my Calculus students' great enthusiasm for it) worth repeating at a later age, with greater detail and more complex requirements. It also fit beautifully with our annual Arts Fest, which will happen next week. I'm putting these bad boys on display, along with the Calculus designs (to come in a separate post).
Thank you, teachers of the interwebs, for your generous sharing of ideas!!!