How do you sketch r=theta? I don't really understand polar coordinates.

First, make sure that the tutee understands using radians, and get them to do some examples of swapping between radians and degrees to ensure familiarity.Then explain to the tutee that they already intuitively know how to use polar coordinates. If I asked them where something was in the room, they would probably point and tell me how far away it is. This is exactly the concept of polar coordinates: you need an origin (you), an angle theta (the direction you point) and a distance r (how far away the object is). Get the tutee to do some examples of swapping between cartesian and polar coordinates until they are comfortable with the concept (use the whiteboard).Then ask the tutee to think about r=theta. Get the tutee to plot easy points (eg: theta =0, pi/2, pi etc). Then get them to think about a pencil centred at the origin with the point drawing out the curve (as it increases in length) until they succeed in drawing the curve. Then show them a computer generated version https://www.wolframalpha.com/input/?i=plot+r%3Dtheta Extension: Ask the tutee to sketch r=0.5theta and r=2theta