borrowing -- bringing forth the calculation

This is the 2nd part of my post about borrowing, a continuation of my previous post entitled "borrowing -- the story".

To bring forth the calculation process of borrowing, I added actual counting boxes and jewels on top of my story drawings (above). Then (below), beginning on the right side of the page, I asked the kids how we could take 7 jewels from a wooden box that only had 6 in them. Right away they saw how they could "borrow" a china box's worth of jewels (10 of them) from the 10s column. So we took those jewels out and added them to the 6 that were already in there. (I did the same on the paper, changing the 4 to a 3 in the 10s column, and adding a 1 in front of the 6.) We then took 7 jewels from the wooden box and moved the remaining 9 to the wooden box at the bottom of the page (the solution line).

The kids totally (and easily) saw how this worked, so we did the same thing for the china boxes (borrowing a silver box's worth of china boxes) and the silver boxes (borrowing a golden box's worth of silver boxes), moving boxes as needed and changing numbers in the equation to correspond to what we were doing. Below is the final solution to our problem:

While we were all working the problem together on my drawing, the boys kept up as well with their own equations (which I'd provided for them at the start of the activity). Below is Zoo Boy's work. (By the way, I didn't even say anything to them about doing it on their own pages, they just naturally knew to follow along, it was obvious to them where we were headed by this point.)

The following day, we did some problems together using the base 10 blocks rather than the counting boxes and jewels. It was a very easy, obvious transition to the boys. This week, we dropped the manipulatives altogether (tho my drawing was still available as a reference if needed), and the boys have been doing long subtraction with carrying on their own without support from me or the manipulatives.

I'm VERY pleased with how this little math unit went, and am so glad I decided to broach the topic now by using the same characters and manipulatives they had used throughout their place value work. When we reawaken this work in the fall, it will be with a whole different story line, focusing on tribes rather than counting boxes.