My criticisms

This isn't a game. There is no way to win or lose, only incorrect moves. Also, it's very boring. Within just a few moves you can tell it's going to have a checkerboard pattern, and the only difficulty is remembering what colors correspond to which place values. Terrible all around.

This is also not a game. There is no way to win or lose. This is just a math exercise that is being called a game.

Top Trumps might be a fine game to play, I don't know anything about how it is normally played. Regardless, this way of playing it is extremely boring. This way of playing also affords the player zero choice, and so I would not consider it a game at all.

I've noticed that many Montessori educators take their dear sweet time in teaching a concept. I'm not entirely sure if it's the educators or the lesson plans, but I would wager it's a bit of both. Here's an example of a 17 minute video, where the lesson could easily be given in half the time. When watching Montessori educators, I often feel that I'm witnessing a ritual. Montessori educators seem engrossed in particular materials, procedures, and terminology, much moreso than traditional educators. Here's another example. The kid clearly gets what's happening within the first minute. The arrangement of the pieces and counting the same thing twice is unnecessary.

I hate the Montessori addition snake game. It's very tedious. If I wanted to add many numbers, each 1-10, I would lay out the appropriate bead bars, count, and write down my answer. I would not do all of this exchanging, and I would not place a marker. I can't see a reason why we should do all this exchanging, and I have come across no good reason thus far.

The Montessori method for dividing one fraction by another, doesn't feel intuitive to me. Unless someone can prove to me that it's more effective than the traditional method, I won't be including it. You can see the method demonstrated here. It works because you're giving a/c wedges to each of the d skittle pieces. Each wedge has a value of 1/b, and so each of the d skittle pieces receives a value of (a/c) * (1/b) = a/(bc). And since the method considers the sum of the values given to the d pieces, the result is a/(bc) * d = (ad)/(bc) which agrees with the abstract method.

The Montessori activity "the short bead stair" is often seen with a piece of wood where a triangle has been cut out. Here, for example. There seems to be no reason for using this particular piece of wood. You could just as easily do the same activity without it. Nobody should buy this. Because many Montessori advocates emphasize procedure, it might be the case that companies are selling expensive pieces of wood to people who are too engrossed with procedure to ask "is this necessary?"