Math Algorithms

I have been working on my elementary math endorsement, so I have been thinking a lot about math lately.  We are getting ready to begin learning about double-digit addition.  I know from previous experience that this is not easy for my students, and I now attribute that to the fact that I have always taught them using the standard algorithm (don't be afraid of the word, it simply means a systematic procedure for solving problems).  The standard math algorithm looks like this:

You're probably all familiar with this way of adding two-digit numbers since it is the way that most of us learned how to do it in elementary school.  I have been learning that there are several different ways to add numbers.  There are two in particular, that when I learned about them, my response was "this makes so much sense!  Why didn't my teachers teach me this way?"  So, I have decided that instead of weeks and weeks of hand-holding trying to get my students to understand the standard way, I am going to start with a simpler version called the expanded form algorithm.  This seems a logical place to begin since my students already know what expanded form is, and isn't that how teaching works?; taking what is known and extending to what is not known?  Here is how the expanded form algorithm works.

Once students are comfortable with this method and can do it easily, I will introduce numbers in the ones place that add to greater than 10, and we will repeat the process until they have mastered it.  Then we will move on to this format:

When have students have mastered this, we can move on to the standard method of regrouping.  Students will now know three ways to add two-digit numbers, so if one doesn't make sense to them, they have two others to choose from.  I'm a bit nervous about this since I 've never taught it this way, but the more I think about it, the more sense it makes.