Clip 3/8: Standard 8: Look for & Express Regularity in Repeated Reasoning Discussing Numbers
Overview
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts... They continually evaluate the reasonableness of their intermediate results.
In Elysha Passeggi’s 4th grade classroom, students work on a number talk asking them to evaluate the reasonableness of a two-digit problem and solution—to “see if they might be true or false without thinking.” As her students discuss their rationales for determining why 62 + 78 is or is not equal to 238, various students offer responses that the numbers are “too small” or “would have to be bigger.” Early on, a student observes that “to get 200 you’d need at least 100 and 100.” Later in the discussion, a student advances this idea, stating that “two 2-digit numbers cannot…no matter what… if it’s addition…cannot be more than 198.” Other students then affirm that they agree with this student’s rule.
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Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts... They continually evaluate the reasonableness of their intermediate results.
Passeggi works with her 4th grade students in a daily number talk routine called “Can This Be True?” In this number talk, Passeggi challenges her students to look at the relationships between numbers to determine whether or not a given answer can be correct, without calculating the result. In this clip, after initial discussion by the class, Passeggi asks the students to generate ideas for testing the reasonableness of their solutions with their "shoulder partners." One student then proposes that "if there's one number on one side, and another number on the other side, and this number is bigger, then this [other] number has to be bigger." Passeggi then challenges the class to test out "Maddy's way" to see if the strategy is effective. In so doing, the students generate and develop their understanding of general methods for strategic solving.