Edges, Vertices, Polyhedra, Cones and Cylinders, OH MY!

Today a group of grade 3 students asked if cylinders and cones had edges (the line where the flat face meets the curved face) and if the point on a cone is a vertex.  

If you consider the textbook definition, an edge is the line where two faces meet and faces are always flat surfaces.  A vertex is the point where three edges meet.  Given these definitions, cylinders and cones have neither vertices or edges.

But I know that the point of a cone is called a vertex, because the axis of a cone is a line through the vertex and the center of the base.  If the point of a cone is a vertex, then do cones and cylinders have edges?

I looked on the web (Math Forum) and found that the textbook definitions are for polyhedra, i.e. 3D shapes made up of only flat faces.  The problem is that there is no other word to label the place where the flat face meets the curved face on either a cylinder or a cone.  Math Forum recommended extending some definitions:  edges would still be the line where two faces meet but we could have a "curved edge" (both words are necessary).  A face is flat but we could have a "curved face" (again, both words necessary).  So a cylinder would have two faces and one curved face, and two curved edges but no vertex.  A cone would have one face and one curved face, one curved edge, and a vertex.  But this seems a bit confusing for me, let alone the kids.

So does anyone else have any definitive mathematical terms or solutions to this?

Multiplication/Division Aid

     One of the "tools" we can use with our students who struggle to memorize the multiplication table and who get stopped in problem solving by their lack of math facts is "Numbers That I Hear When I Count."  On each of the strips below are the multiples of the numbers 2-9.  If a student needs to multiply 6 x 6, he/she would flip to the "Numbers That I Hear When I Count By 6's" and count down then over to the sixth number to find the answer "36."

     Likewise, if a student is trying to divide 56 by 8, he/she would flip to the "8" card and look for the number closest to "56", then count the position of "56" on the card..."56" will be the 7th number so 56 divided by 8 is 7.  For division with remainders, if a student was attempting to divide 76 by 8, they would go to the "8" card and look for the closest number to 76 without going over it.  That number would be 72 which is the 9th number.  So 76 divided by 8 is nine with a remainder of 4.

     Of course we would still want students to memorize their facts.  But in the meantime, this tool may help them solve other problems without the frustration and labor of "guess and check."

     And I just hope I got all the numbers right!