A successful conference or series of conferences will give you something to share with the class. I like to discuss highlights with the class and share some of the many valuable ideas that students could take away form the lesson. With the shape and plane example, I would have all students look at some of the pyramid problems and have a student who how to draw the plane of intersection and teach why the intersection is a trapezoid and when the intersection will match the shape of the base. I have a collection of plastic 3D shapes that I hand out to help students visualize how planes and 3D shapes cross. They can show this directly to the class as long as they draw the intersection as the class watches and turn the shape to show the trapezoid formed on the intersection. I also like to have the student demonstrate the problem using the document camera. This way the class can watch an up close demonstration on a projector and I have the ability to take a snap shot of the demonstration for review.
As a class we would applaud this student and their ability to share their idea. Many students leave a conference willing and able to teach others about the concept. For the rest of the year, I know I can have this student help others on this topic. They become a teacher that can help me in the room.