I really love the Montessori approach to large numbers.
This afternoon my son and I had a really good, long laugh when I tried to tell him that there are one hundred one hundreds in a thousand. He just looked at me like I was crazy and started laughing. I realized my mistake way too late. I'm not sure he will ever let me live that one down.
For him, it's very clear how many hundreds are in one thousand because he's touched them. He's moved them around. He's counted them all. It makes sense to him. While I'm still trying to remember how many zero's it's supposed to have and do some type of crazy mental math in my head.
This past week and the week before we have been going through some of the Golden Bead Materials. You can buy the real deal but it's probably a waste of money for a home environment. Although there are a TON of activities you can do with them, the price is a little steep.
We own a version of these that I found at a yard sale. Ours are yellow and don't snap together but these look reasonable. I wanted to see if a paper copy got the point across just as well and it did! I was able to use the ones from my manual from KHT Montessori (make sure to get the optional math support forms) but I looked around online to find some other options.
Our Montessori Home made a great DIY version
I'd recommend introducing after you have worked with the teen board and the ten board along with the hundred board. The idea is working numbers up to and over one thousand.
You can start by showing a large number (136) and placing one "hundred" three "Tens" and six "ones on the mat. Have fun coming up with different numbers!
We had a great time adding large numbers- I made up a quick plus and equal sign. You can also subtract easily. Once they have mastered those there isn't really a limit- adding with regrouping, multiplication, and division.