Using Chip Models for Adding/Subtracting Integers

My district has adopted a new curriculum, Connected Mathematics 3 (CM3).  Right now we are working on Integers and CM3 has students use a chip model to introduce adding and subtracting integers.  I LOVE this type of model for adding.  I've used it for years (and even developed my own game called "Close to Zero").

For subtracting, I'm torn.  It is not the way my mind thinks about integers.  But in an effort to avoid putting my preferences on my students, I wanted to make an effort to teach it this way in case it helps some of my students "see" what is going on with subtracting.

It works like this:
Pink = Negative and Blue = Positive

If I have a problem such as -4 - 3…

Start with 4 pink chips to represent -4:

We want to subtract positive 3.  There are not 3 blue chips available… so add 3 zeros (a pair of a positive and negative).  We can do this because adding zeros does not change the value.

Now, go ahead and subtract 3.

You are left with 7 pink chips, which equals -7.

I have to say that some students are doing really well with this model.  However, I have some students getting pretty confused.  You can see some of their thinking on their math blogs.

I plan to also show them how to use a number line to add and subtract as well.  Does anyone have experiences with subtracting with the chip model?  How did it go for you?