This paper shows the progression of Kal-El's long division skills the past few weeks. The equation in color at the top left of the page is the very last equation he ever completed with the racks and tubes while only recording the quotient. It became clear that he could go, and needed to go, much more quickly through the racks and tubes work than he had been. So directly below that equation you will two more which he completed with the racks and tubes recording both the quotient and the intermediate remainders.
A little lower on the page and centered you'll find a few more equations he completed. In addition to a couple of random multiplication equations there are a couple of division equations. These were done without the racks and tubes, just on paper. Here again he was recording the quotient and intermediate remainders.
These equations were going so well that I decided he could move on to recording the quotient, the "number of beads used" (Does anyone know the name of this step? Intermediate products?), and the intermediate remainders. We did a couple on the racks and tubes but Kal-El immediately wanted OFF the racks and tubes. This was possible because his multiplication is so solid. Therefore, he doesn't need to to count beads to find the products. In fact, he really dislikes the carrying that you have to do to record the products with the bead. What is recorded on the bottom right-hand corner of the paper is his first equation purely on paper.
This is a close-up of the equation itself, but scattered around the larger piece of paper you'll find the multiplication equations he used to find the answer. This paper isn't organized in a way that could be used to turn in work at a school, but was fine for us at home because it's his work. It's not being turned in for assessment. However, when he started to add ANOTHER division equation to this paper I couldn't take it anymore and stepped in. I made him use another piece of paper. I'm all for conserving resources, but this was getting ridiculous.
In order to train him to record his work in a more teacher-friendly manner (in case I'm abducted by aliens and my husband sends him to school) I "invented" a new specialty paper for him to use for long division. I am attracted to specialty papers like raccoons to shiny objects. Now, I don't really think I "invented" this. I'm sure I've seen it somewhere at some point in my life. But, the fact stands that I don't know where or when and have no idea what to call it or how to find it.
He has been using 1/4 cm graph paper for most of his math, but at his developmental level the squares were fine for recording simple numbers but too small for recording regroupings. I bumped him up to the 1 cm squares. I have to figure out what I'm going to do for the really big equations with four-digit divisors and seven-digit dividends, but this will do for now. I was really happy to see that he had written "yay" (in cursive no less) after his quotient came out to match the back of his equation card.
Me Too has started the racks and tubes as well, but has been choosing to hold off work on them until he's finished the bingo board. I though he would be done last week but I forgot that we do all the extensions listed in the MRD math album for these. I had scanned the Montessori by Hand album to refresh my memory and she only lists one activity for this. Me Too remembered.
This reminds me that I made some much needed room on my iPad last week by DELETING all of my digital primary albums. I still have them on my desktop but no longer need them on my mobile device. That really felt like a landmark.
I have a couple of "big" posts in the works. Those of you who have been reading me for years probably guessed that already due to the slower rate of posting lately. That always happens to me when I'm putting together big ones. I have given the science area of our classroom a much needed makeover. I am working on putting together a post on our science equipment storage, chemical storage, and science experiment resources. I also have been slowly working on the posts that readers have requested regarding art and Spanish. I don't know how long it will take, but they are in the works.