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Reply To: 3.1 – Progression Ah-ha’s and Wonders


The videos that resonated with me the most, since I (student) teach in a third grade classroom, were the videos on multiplication and division, since that’s essentially all we’ve been working on since the beginning of the school year. An “ah-ha” that I had with regards to multiplication was that multiplication learning really starts in second grade, when students are taught to partition a rectangle into no more than 5 rows/columns. This is interesting to me as I reflect on my own students’ knowledge when it came to arrays and finding the area of rectangles, both things we’ve covered this year, and I notice that there are a good chunk of my students who gravitate toward array when it comes to solving multiplication and division problems. A second “ah-ha” when it comes to multiplication and division is to let the context of the problem explain the equation. Lately, I’ve noticed that my students are able to look at an equation and come up with a strategy to solve, but when it comes to interpreting and tackling a word problem, they have a hard time creating a model and therefore an equation that aligns with the context of the problem. A final “ah-ha” that I had with regards to division, specifically, was that students should experience the difference between efficient and inefficient thinking. That way, they can recognize the need for a faster strategy for dividing with larger numbers and hopefully come up with some ways to mitigate that through their own exploration. A “wonder” I had with regards to third grade and the progression of multiplication and division, it how to get students to see the value of each and the difference between repeated subtraction strategies in which the groups are unknown and the fair share or partitioning strategy in which to objects are unknown. In my experience, too often the students get stuck on one of these and have a hard time differentiating which one makes the most sense in the context of the word problem they might be solving.