Algebra problems to get you thinking

My 8 year old son wanted to learn calculus the other day.  So, I thought he should study a little algebra first.  Here are a series of problems that are similar to the ones that I gave him:

x-5 = 10

He had no problem with that one

2X = 10

He thought that X needed to be a digit in a number that started with 2.  After I explained that it really was 2 times x = 10, he was able to figure it out.

Then combining the two operations:

2x -5 = 15

No problem with that one.

x^2 = 9

Needed a review on squares.  We only covered the positive answer to this problem.  I have not gotten into negative numbers with him yet.

x^2 + 4 = 20

This is the one that we are currently stuck on. 

Do you have suggestions on how to teach an eight year old algebra and calculus?  Leave them in the comments below. 

MSAM: Successful first semester

I just completed my first semester the Masters in Applied Mathematics program at the University of Houston.  I had to take an undergraduate class that was required for the graduate classes I need to take.

“Advance Multi-variable Calculus” by Dr. G. G. Johnson was a very good class that filled in many of the whole that I had in my understanding of calculus and the techniques behind mathematical proofs.  It had a different format than the lecture/exam types of class that have been the standard class structure.  It is easy in those lecture/exam classes to go through the entire the class without actually having to think or learn.  This class was taught in a “give problem”/”work problem”/”defend solution” method.  There were only 3 or 4 days of lectures.  The rest of the time was spent with students at the board working problems with the professor and the other students asking questions.  This ensured that there was no “weakness” in the student’s understanding of the problem and the solution.  The only downside were the days that students were at the board that did not really understand the solution or sometimes, even the problem.

Anyway, I have to report that this first class turned out very successful!

Next semester, I am considering taking a class on the math behind options: http://www.math.uh.edu/%7Elowe/Math5397/Math5397-syllabus.pdf