We've worked with exchanging values for a while (ie exchanging ten units for a "ten bar" or exchanging ten "ten bars" for a hundred square), and then one day, he asked me what happened when you add 2 sets of numbers together.
So, I began by presenting single digit addition to my son.... WAY too boring for him. We moved on to double and triple digit numbers -- much more of his liking.
For those of you who are not familiar with Montessori, please understand that this is NOT "memorizing facts" that he is regurgitating. Instead, he is manipulating blocks to determine an answer. This is known as concretely exploring addition, which, I feel, leads to a better understanding of "number sense" -- a very hard skill to learn.
To add to the self-selection of this activity, I allowed him to select the numbers from our hundred number tiles. He would then lay out the blocks, combine the values, and then determine the resulting number.
Here it is a little more pictorally... From our hundred number tiles, he selected 78 and 51. He then laid out the blocks to represent 78 (7 blue "ten bars" and 8 green units) and 51.
He then combined the blocks together, and then counted each set of blocks. If a set of blocks was over ten, he would excitedly exchange them from our "block bank" and get the next larger unit. This was the case with the "ten bars" -- 7 "ten bars" + 5 "ten bars" was more than 10, so he exchanged 10 of the "ten bars" for a red hundred square.
Finally, he would find the number cards that corresponded with that number, and combine them together. Even though it is not shown above, he did result with 129, once the number cards were combined together to form one number.
Finally, MANY people have asked me why I use Math-U-See blocks rather than the traditional Montessori golden bead materials. Well, it's quite simple.... my son had NO interest in the beads. We own a large selection (but not quite all) of the golden bead materials, and it actually averted his interest for math. So, I sought to find another manipulative to use that would simulate the same idea, but would stay semi-true to the Montessori method.... and the Math-U-See blocks were what we found. There are a few aspects that I truly miss about the beads -- the lack of a representation of 1000 (or larger values) and the weight of the beads, which allowed the child to physically feel the difference in weight between 100 beads and 10 beads (a wonderful greater than/less than lesson!).