Are you thinking about how to address students’ unfinished learning? We are too! In this webinar, we will share our current thinking on how to leverage reasoning routines to assess and advance underdeveloped math concepts from the previous year. We will discuss how students’ capacities to reason quantitatively and think structurally hold the keys to building new mathematical understandings and connections. We will focus on critical concepts in middle school mathematics: ratio and proportional relationships, algebratizing arithmetic, rational number concepts, geometric relationships, and/or functions. Join us to explore this building-on-strengths approach to accelerating unfinished learning.
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I’m wondering about why this one has decimals rather than fractions. The strategies I came up with all relate to the notion of the 0.5 as 1/2, and I don’t see 325 / 5 as “obvious” of a shortcut. So I’m wondering what the goal is with this problem using decimals.
The goal here is for math doers to this structurally by chunking, changing the form, and connecting to math they know. So students who “change the form” of 32.5 and/or 0.5 to a fraction equivalent to make the numbers easier to work are thinking structurally. Some may also change the form of the numeric expression, as you mentioned, to 325 / 5. Another approach might be to change the form of 32.5 to 30 + 2.5, and then divide each “chunk” by 0.5. or…
I could also imagine students connecting to what they know about division and asking themselves, “how many 1/2s are in 32.5?”.