Clip 35/43: Standard 6: Attend to Precision Using Quadrilaterals Part A

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning... By the time they reach high school they have learned to examine claims and make explicit use of definitions.

Cathy Humphreys leads an extended exploration of a proof of the properties of quadrilaterals, helping students learn to investigate, formulate, conjecture, justify, and ultimately prove mathematical theorems. In these clips, students engage in the first of two block-length explorations of their proofs. The students are in groups of four. Each group has chosen a group member to perform these roles: a team captain, resource manager, recorder, and facilitator. The groups have access to the problem (one page per group), two packets of manipulatives, and other resources that they can retrieve, including a page of definitions of quadrilaterals. In some of the groups, students work individually for a while. In other groups, students work in pairs, and in still others, the entire group of four is collaborating. Humphreys’ commentary notes subtleties in the students’ discourse that either advance or impede the development of their thinking. This clip is also indicative of standard 1 (make sense of problems & persevere in solving them), standard 3 (construct viable arguments & critique the reasoning of others), and standard 7 (look for & make use of structure).

See this video in the context of an entire lesson.

See how SEL Competencies and Mathematical Practices work together in this classroom. 

(Describing an Ideal Classroom, Appendix)