Clip 8/8: Standard 8: Look for & Express Regularity in Repeated Reasoning Using Numeric Patterning Part C
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Noticing the regularity…might lead them to the general formula…. 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.
In the closure section of a number talk, Fran Dickinson works with his 5th/6th grade students to identify many different ways of generating a rule to govern the inputs/outputs of a chart: various students offer x3 – 3, times 3 minus 3, 3x – 3. The students discuss the rule and the best way to represent it, making connections to their mathematics textbook in their conversations. They discuss the various ways of representing the rule and evaluate the reasonableness of the parameters of the problem. This clip is also indicative of standard 3 (construct viable arguments & critique the reasoning of others), standard 6 (attend to precision), and standard 7 (look for & make use of structure).