I'm so excited. I taught the graphing r= 4 sin(theta), r = 2 cos(theta) + 3 and such today, and I think THIS method will stick more successfully than what I've done in the past.
Two years ago at the NCTM Atlanta Conference, a teacher from North Dakota shared her strategy, and it made so much sense, and this year I adapted it and tried it.
I made up a packet where I have 12 such graphs mapped out on a rectangular coordinate system. I don't even label which ones they are. Right next to these graphs are blank polar coordinate systems. The tick marks (or angle marks) on each are divided the same (into pi/6). This ND teacher stressed to make the connection between "y = f(x)" and "r = f(theta)" and link x to theta and y to r and to keep mentioning it. Then you transfer each point from (x,y) to (r,theta) accordingly, and voila! You have your graph.
On the front page I had 3 similar ones, and after they/we graphed all three, then we refreshed our memory on what the equations were. Then we discussed what the connection was between "amplitude BIGGER/smaller than vertical shift" was, etc.
We got through 4 in class, and they have the rest for homework. I'm thinking it will work, because even I can now remember what the graphs should look like by doing such an analysis (whereas before, I had to refresh my memory each year).