CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Implementing in the classroom:
This mathematical practice relates mostly to upper elementary grades and higher. This practice is not only about incorporating lessons where students have opportunities to recognize general methods and shortcuts, but mostly it requires teachers to listen for "teachable moments."
As math teachers we are no longer standing in front of the classroom and having our students take notes or follow along on their worksheet. Our role has changed. We are facilitators. We guide students to strategies, to talk with one another, to learn from each other. We also react to those "teachable moments," when a student discovers something new that can become beneficial for the entire class.
As math teachers we are no longer standing in front of the classroom and having our students take notes or follow along on their worksheet. Our role has changed. We are facilitators. We guide students to strategies, to talk with one another, to learn from each other. We also react to those "teachable moments," when a student discovers something new that can become beneficial for the entire class.
Classroom Connection
Click on the image above to view the lesson example.
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Stephanie Letson works with her 2nd grade students in a daily number talk routine called “Number of the Day.” In this number talk, Letson encourages her students to find multiple ways to arrive at the total of 170. In this clip, she engages the class in a discussion of one student’s approach, noting that several students have tried to extend and elaborate their equations by multiplying by 1 or adding 0. One student observes that these are functionally equivalent, leading to a group realization about the meaning of the identity property. Letson connects this student’s observation to work she had previously noted in her mathematics journal.
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