A couple of weeks ago, I blogged about working with my firsties on 2-digit numbers. This is a follow-up to that post.
Let me reiterate that the idea of tens and ones is not an easy one for young children to understand. It is incredibly abstract. As I said in my previous post, students need lots of experience with 2-digit numbers before they can fully understand the concept of tens and ones. And as with any new experience, students need concrete and representational experiences to support the abstract understanding. My students had previously worked with linking cubes (building trains of ten) and ten frames and counters. These are both concrete methods of instruction. With both, however, I recorded equations corresponding to their models to connect the concrete experience with the abstract (symbolic) representation. That connection between concrete and abstract is often left out of instruction, but it’s so very important.
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Since the students had had a variety of concrete experiences, I decided to move on to representational instruction, so we used our individual student ten frame kits. I love these!! They are small plastic tiles that students can use to build numbers. Each student gets his own little ‘wallet’ with tiles. It’s a little faster than ten frames and counters. Now, you might think this is concrete instruction because students are manipulating the tiles, but it’s not, it’s representational. The dots on the tiles represent real counters on ten frames. You definitely don’t want to start your instruction with the tiles.