Montessori Math - Divisibility rule - A teacher's story - Part 1

I give them a really really huge number and ask them if it's possible just by looking at the number to tell me if it's exactly divisible by say 2 or 3 or whatever is the rule we are doing. Not to divide but to simply say if it's divisible,ie leaves no remainder. They are bummed by the sheer size of the number. 

Then we say let's take a number which is small n easier first to work with. They give me a thousands (4 digit) number


We use the Montessori dynamic material. 

We take a 1000 cube and ask if this can be given  equally to two people?

If 1 thousand can be given, any number of 1000s can be given hence 1000 and the digits above it don't matter as they are all divisible


Same we do with one hundred square and hence any number of hundreds


Same with ten bar.


So we are left with the ones. Only they matter


Now they check with the ones they have. And we keep reducing/ adding a one and seeing. They see the pattern of evens ad odds

Then we take a 1000 digit number and present and arrive at the rule. Now they look at the huuuge number and with a smile are able to check it. They then ask for more numbers


They do ask me what's the point of checking it, but not dividing. I tell them it'll help then solve work faster when they can first check