Kal-El began the dot game today! The dot game is direct preparation for abstract addition without manipulatives. In this game dots made with the tip of a pencil or marker serve as counters rather than stamps. The exchange or "carrying" process is the star of the show. It is great fun to get back into working with more than two addends (we did some work with multiple addends in the stamp game, but not a lot). Kal-El was excited to have the new 10,000's category as well.
He created a "10,000 bar" in honor of the new category.
We chose to do the dot game in the "AMI style" as opposed to the "AMS style." Throughout the entire math sequence, AMI puts a greater emphasis on letting the child create his or her own equations rather than using prepared slips. This is not always convenient if you are trying to be sure they get through all of the appropriate variations so I sometimes resort to either the prepared slips or writing equations into the math books in advance. (Another way to solve this problem is to give the child parameters for creating their equations on a given day.) However, the dot game is an excellent time to let them loose and write their own. There aren't variations to be concerned about and they really can't write an improper equation for this apparatus. So, we did it the AMI way.
Another thing I love is that AMI starts BIG. The AMS presentations I saw started with a three addend equation on a prepared slip. However, we know in Montessori math that it is the BIGNESS of things that makes the greatest impression. In most things the child will retain a much clearer picture in their mind of the concept if you show it to them the first time really BIG. So, Kal-El's first equation had eight addends. We had planned on 10 but ran out of room.
Another notable difference is that the AMI style only uses two colors of writing utensils and you don't have to switch between them repeatedly to do the work. I find the AMS style with five colors of pens and the constant switching to be super tedious. There were a lot of other subtle differences I noticed from presentation to presentation regarding things like which direction to record the dots or the timing of the carrying. Some presentations direct you to cross out the rows of ten dots, some don't. Some have you cross out the dots you record below for the carrying, some don't. I don't think those differences really matter as long as you are consistent. I chose whichever methods involved the least amount of switching pens and the fewest opportunities to skip a step.
Here is Kal-El's first completed equation. His sum was 50, 029. I don't know if that is absolutely "correct" because it would be easy to lose a dot here or there. The point is the process of recording and carrying, not accuracy. Kal-El thinks this work is great fun.