Overview:  This block begins identically to Explore 1 Alternative 1.  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.  The teacher approaches the group and notes that there are many different strategies at play within the group.  By asking Lee how he might make the leaves evenly spaced out, the teacher provokes students to begin thinking about measuring distances with a perpendicular line.

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.  When the teacher approaches the group, he pushes students to recall the relevant knowledge from school mathematics.  The teacher tells students, for example, “think about how we talked about measuring the distance from a point to a line.”

Other points of interest:  In this version of the Explore, the teacher seems to note that the students are using a variety of strategies, and he attempts to find a way to make the perpendicular bisector relevant to each of those strategies.  For Aaliyah and Lee, the perpendicular bisector could be a way to more precisely fold the paper.  Because Carissa is not using reflections, she does not seem to see a need to incorporate perpendicular lines in her work.  With his comments to Carissa, the teachers seems to try to find a balance between valuing Carissa’s prior knowledge and solution and pushing Carissa to develop a more mathematical solution.