High-Leverage Microroutines: Maximizing Student Engagement
Description: During this preconference, participants will engage in and leave ready to apply two microroutines from the NCTM book High-Leverage Microroutines: Maximizing Student Engagement. These microroutines provide access and support for all learners and can be used with any curriculum. Participants will examine eight areas of cognition that students draw on when learning mathematics and identify students’ strengths in those areas. Participants will consider how the book’s ideas can be applied in their own contexts to ensure that all students think and reason mathematically.
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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?”.