Overview:  In Explore 2 Allen, Khalil, Paige, and Alejandra begin by comparing the heights of the two houses on the first page of the worksheet.  Khalil and Alejandra draw lines through the tops of the houses to the vanishing point, and they determine the houses are the same height.  Paige measures the base and height of each house to compute the ratio of base to height.  Alejandra points out that her solution did not require measuring or a calculator, but Allen says he will try both strategies.  The teacher asks students how they are doing on the problem, and Paige concludes the houses are the same height because the ratios are approximately the same.  Khalil tells the teacher he thinks the back tree is taller than the front tree, based on his drawing of a perspective line.  The teacher asks Khalil to share his method with Paige and points out that a line through the tops of the two trees does not go through the vanishing point.

Prior knowledge:  Paige draws upon prior knowledge of the school mathematics concept of ratio to compare heights of the houses.  Alejandra and Khalil use a mathematical practice of using the perspective lines of the picture to determine whether the objects in the diagram are the same height.  Alejandra and Khalil’s strategy also requires knowledge of the context of drawing in perspective, namely that objects which are the same height should follow the same perspective line back to a vanishing point. 

Other points of interest:  Allen acts as the novice throughout this launch, asking the other students how they are working on the problem.  Although Allen does contribute any of his own solution strategies, his questions provoke the students in the group to share their ideas back and forth.