One of the big things in Singapore Math is always following the concrete to pictorial to abstract trajectory, even for older and higher level students. In the presentation, we saw hundreds, tens and ones place value discs that had the value of each written on it (here is a video that takes you through the basics). My mentor teacher and I both liked them a lot, and I thought it would be great to incorporate into my lesson the next day. Sounds like a great idea, right? Well, it WOULD have been if I actually followed the great inspiration from the presentation right in that lesson. However, for some reason, neither my teacher nor I thought there would be anything wrong with skipping the concrete part of the lesson, and jumped straight to the pictorial! Big mistake.
I was so excited to go home and rewrite my lesson, and I spent a bunch of time updating it to include students solving addition regrouping problems through drawing an HTO (hundreds, tens, ones) chart and drawing place value discs. Well, let me tell you, when I taught that easy lesson, it was met with confused stares and loud exclamations of "huh?!?" I slogged through the lesson, trying to pull my poor kiddos along with me, but after seeing their less than desirable results on the worksheet, I admitted defeat and went back to the drawing board. After a discussion with my mentor teacher, I wrote another lesson that actually took the students from concrete to pictorial. I made an 11x17 HTO chart with a tens frame and used two-sided discs for ones and tens, and used unifix cubes for the hundreds. The manipulatives we McGyvered together I am sure are not as effective as the real thing, but they worked well enough for a last minute lesson!
The lesson the next day went so well, it was like night and day. Case in point that students actually DO learn better when they go from concrete to pictorial to abstract. Go figure! Both my mentor teacher and I felt pretty silly for not even thinking it would be an issue, and both experienced a big "DUH!!" moment. The students not only grasped the material quickly, but they also were really engaged in the lesson. They loved playing with the manipulatives, and understood what the discs stood for. Ms. G and I both felt that their number sense got stronger through this lesson, and will be much more prepared for later, more difficult concepts. One thing that really made me happy was to hear a student who had been struggling with the concept tell me that this made so much more sense to her, because it showed her how to do math the way she thinks. Yay!! I can't wait to learn more about Singapore Math and be fully trained, as I really believe in the power of this program to teach students to think flexibly about math.
I went on to teach a few different ways to regroup- base ten blocks (also starting with the concrete manipulatives), the break apart method, and the traditional method (carry the one). We talked about why it is important to learn different ways to solve problems, and how to figure out which method works best for them. We also worked a lot on explaining their answer and asking "does this make sense?"