This week as part of my Guided Lead Teaching, one of my last lessons was introducing addition. First I used everyday language and relevant examples using my students' lives and our classroom culture to represent simple addition problems. Next, we developed problems together using a story board of a bunk bed and animal math manipulatives about "bears having a slumber party (the meanipulatives on the top bunk) who called their friends to come over (the manipulatives on the bottom bunk) and showing this "number story" as a math equation.
I then released my students into independent practice, so that they had their own bunk bed story board and animal manipulatives. Walking around, I noticed that some of my students weren't understanding that in for a simple addition equation, we need three numbers- the two numbers we're adding together and the sum. In particular, I noticed that Jamir was simply counting two groups of manipulatives- his animals on the top bunk, continuing onto his animals on the bottom bunk. Next week, when I teach number stories again, I want to think of a way to really show two distinct number entities and representations joining but also how numbers relate and decompose into each other.
It is good to see that you are thinking about how to use what you learned during one lesson to influence what you do in subsequent lessons. I would also encourage you to think about how what students are thinking might not be "incorrect", but simply a first stage to thinking about these number concepts. Could you ask them to explain their reasoning, to you and to one another? This sounds like a good example / task that might lead to a very fruitful whole-class discussion.
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