So we have abandoned the Schiller book a little bit for now. We continued building large quantities. It took a while for Dot to remember which category were the thousands and which were the hundreds. Today she knew that confidently, so we went on to addition with large quantities. We added two numbers, ensuring that they would not involve carrying. Dot already knows how to add with small quantities.
The way I learned to do it as a Montessori teacher is to build 2 quantities, put them together (using a scarf) and then count them up. We then tell the story something like this: Mom brought 1101, and Dot brought 2310. We put our quantities together, and we had 3401. Putting together is addition.
This whole procedure with the quantities up to the 1000's place seems very appealing to the age group (usually 5-6). And because it's done in such a concrete way, the larger quantities are not intimidating. In fact, that is kind of the point, that we work with the large quantities so that the children aren't intimidated by them later. I used to give my sons a few (or just one) addition problems in the millions or billions or trillions when they were in early elementary. They thought this was much more interesting than a whole bunch of smaller problems.
If children are clear on how place value works (which is why we use these manipulatives), then they see how easy it is to work with the larger numbers. It's nice to see children excited by the large quantities rather than intimidated.
Next time, we will do an addition with exchanges/carrying.
