Clip 20/41: Standard 3: Construct Arguments & Critiques Using Numeric Patterning Part B

They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is... Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Fran Dickinson leads a number talk on an input/output table and graph, asking “What’s my rule?” In this clip, he continues a class conversation about input and output numbers. Dickinson notes that “It was interesting to hear all of the different opinions of how to state the rule. I think this illustrates where we were as a group as far as our familiarity with algebraic expression goes.” For example, the students discuss “3 groups of x versus x groups of 3.” Dickinson also models whole-group strategies for consensus and disagreement, which he explains as “silent signals.” This clip is also indicative of standard 1 (make sense of problems and persevere in solving them).

See this video in the context of an entire lesson.

(Parts B & C)