Overview:  While working on the first page of the problem, Nolen comments that the two houses look to be the same width because they are situated in between the same pair of line segments.  Emily notes that the back house looks smaller than the front house, and Nolen comments that they need to determine whether the houses scale.  Nolen measures the front and back house and says they cannot be the same height because they do not scale by a factor of 2.  Emily, Alonso, and Aditi conclude that the houses and trees should be equal height, because the back house and tree look smaller than the front. 

Prior knowledge:  Nolen draws upon prior knowledge of the school mathematics concept of scale factor.  Nolen seems to misapply his knowledge of scale factor on the first part of the problem, when he says the back house is not the same size as the front house because it does not scale by a factor of 2.  Nolen seems to think that scaling can only occur by a factor of 2.  Alonso, Emily, and Aditi misapply the mathematical practice of deductive reasoning when they conclude the houses and trees must be the same height because the house and tree in the back look smaller. 

Other points of interest:  On the first page of the problem, Nolen is unable to reconcile his idea that the houses are not the same height (based upon the idea of scale factor) with Emily and Aditi’s idea that the houses must be the same height because houses farther away should look smaller.