Overview:  On the second page of the problem, Nolen doubles the height of the back house.  Emily and Aditi use the same strategy as Nolen, and Alonso uses visual perception to draw different elements into the diagram.  Aditi asks whether they should have a vanishing point in their diagram, so Alonso draws line segments from the different elements in his diagram to a point.

Prior knowledge:  On the second page of the problem, students rely on the mathematical practice of the visual perception of perspective.  They recognize that objects that are farther away should look smaller, except in the case of the 2-story house.  In addition, Emily, Aditi, and Nolen use the school mathematics concept of scale factor again when they double the height of the back house to make it two stories.  Students draw upon knowledge of the context of the problem to note that there should be a vanishing point in the picture on the second page.  Alonso identifies a point that he calls the vanishing point, although it does not seem that all of the objects in Alonso’s picture follow perspective lines to the same vanishing point.

Other points of interest:  At the end of his work on the first page, Nolen determines that he must have made an error measuring, rather than considering whether his strategy may have been flawed.