Mental Math - Is It Dead?

I had another terrifying experience while teaching Geometry this week.

I was working through a problem in our book and the last question was to find the area of a triangle with specific vertices.  We had already found the coordinates of all three of the vertices and the lengths of the sides of the triangle.  Our last step was to multiply 1/2 * 9 * 12.  I immediately wrote 54 on the board and started to go on to the next thing...when several of the students started to say wait how did you get 54 so fast?  I said well, half of 12 is 6 and 6 * 9 is 54.

They were amazed that you could multiply like that - they all wanted to pull out their trusty calculators and type it all in.  In fact after I explained that you could take 1/2 of either number and then multiply that by the other number, they continued to be amazed.  Some of them were convinced that you need to take 1/2 of both 9 and 12 and multiply that together.

Wow, this is a real problem!  Wish I had a solution...

Halloween Joke a Little Late:  I was walking in the hall this week behind one of my fellow math teachers and I was listening in on a conversation he was having with a student.  The student said, Mr. H, what are you going to be for Halloween?  Mr. H said, I'm going to be a fraction - everyone is scared of them!