I teach High School Math, both the A.P. as well as two remedial sections. I have always loved math and have always wanted to teach it, though I haven't yet been teaching that long.
I know that for Valentine's Day there are various ways to get students to come up with functions that, when graphed, will produce a heart shape. However, I am not sure which is the best way to present a simple version so that even the least experienced and least comfortable mathematician in my remedial class will be able to participate in a meaningful way. I bet you recall (or at least have access to) a lot of ways way that one can get a heart-shape produced on a graph. Would you be so kind as to give me some way to present a relatively simple approach?
Here's a way to present a situation so that -- without even realizing it until it is interesting enough to actually see for oneself -- either the entire class working together at the board or smaller groups of students working on large-format graph paper will see a heart emerge on the surface:
Put this on the board:
(x2 + y2 – 1)3 – (x2)(y3) = 0
Have the students draw the usual coordinate x and y axis, and have them try to plot as many points as they can. It is easier than it looks, especially with your guidance. Perhaps, just for the holiday, why not encourage the use of calculators? And wait until they see what appears on the paper!
Hope this helps, and...