Leaving the laptop open is a great idea. Strewing with technology! My kids will come look when I ask to show them something, but anything that smacks of "teaching" and they turn off, eyes glazed. Watching short movies engages mine, too. Scale and comparisons are something they do naturally, but these movies and games help make them more conscious. Good idea with the orders of magnitude in food, which is much more real than Pluto and Texas. :-)
Good idea to do the chunks of different colors. Small kids just learning to count could easily help by assembling those chunks into little piles and then slide them on, where legos or computer programing might be too hard for them.
Beautiful! I went to a Montessori school for kindy, and I have a body memory of those beads. I do not use them with my kids, though, as I haven't seen their benefit over blocks (like cuisinaire rods or even legos). This gives a new spacial understanding of the towers that might click for a kid in a way that square blocks going up might not. Oh, and don't worry about the door. ;-)
I love this idea - I can see a whole room of kids with keyboards or boomwhackers. I shared it with my husband, who is a musician (I am not much of one) and he also liked it. Both of your answers using music are beautiful illustrations about how people are always saying that music teaches math, but yours takes it to a new level. People often don't take the music-and-math beyond fractions and basic rhythm.
My daughter plays Animal Jam, and so I started looking at the possible combinations for her character - 40 colors, 40 secondary colors, 8 eye shapes, 40 eye colors, and so on. I don't remember the equation for this kind of big combinations.