Overview:  Aaliyah, Lee, Trey, and Carissa are working together on Part I of the problem.  Aaliyah and Lee are each using the paper folding operation.  Trey is drawing the right half of the leaf directly onto the worksheet.  He is not using any tools to reflect of measure the leaf; he draws it freehand.  Carissa is working based on the assumption that the students should create an artistic pattern.  She makes the leaves face different directions to make her pattern unique.

Prior knowledge:  The students seem to have some prior knowledge of the mathematical practice of paper folding, and they use that practice to trace copies of the leaf.  Aaliyah and Lee seem to value the practice of paper folding (because they are doing it).  Trey indicates that he may not value the practice, specifically when he says to Lee, “That’s because I’m not tracing it.  I’m actually drawing it myself.”  Trey seems to use prior knowledge of a different practice, visually estimating the reflection.  Carissa is working based on her prior knowledge of the context of the problem.  Specifically, because Carissa sees the problem as an opportunity to make an “artistic pattern,” she is not especially concerned with creating reflective symmetry.

Other points of interest:  In this version of Explore 1, the teacher does not intervene in students’ work.  The students in the group provoke conversation about the problem by asking questions to one another about what each person is doing (DeJarnette, Dao, & González, 2014).  Although Lee is using a practice that may make the perpendicular bisector explicit, Trey does not see value in Lee’s work because his pattern is “messed up.”  It seems that Trey finds the strategy of visually estimating the reflection more precise than using paper folding to find the reflection of the leaf.