Are you worried about how your students will approach learning mathematics in a post-pandemic classroom? Structural thinking, a building-on-strengths approach, and reasoning routines are three critical ingredients to address unfinished learning. In this webinar, we will explore how to integrate all three as we develop students’ capacity to interpret mathematical content, including expressions, equations, graphs, and representations, with confidence. We will focus on structural thinking in critical concepts in middle school mathematics: ratio and proportional relationships, algebratizing arithmetic, rational number concepts, geometric relationships, and/or functions. Leave the webinar with concrete strategies to advance your students’ unfinished learning while teaching grade level content.
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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?”.