Overview:  Elena, Olive, Jaipal and Patrick work together in this explore.  Jaipal first determines that the pair of houses and the pair of trees are, respectively the same height, because the bases of each are aligned horizontally.  Patrick agrees with Jaipal, but Olive suggests the strategy of drawing perspective lines through the tops of the houses to check that they are the same height.  Using Olive’s method of perspective lines, Elena concludes that the trees must not be the same height.  Jaipal is uncertain why his method of checking the horizontal alignment of the bases of the trees did not work.  Olive suggests that Jaipal’s method may not work, but Patrick points out that the trees are not exactly centered in between the pair of perspective lines.

Prior knowledge:   Olive and Elena rely on knowledge of the mathematical practice of drawing perspective lines through given objects to determine the vanishing point of each picture.  Again, the use of vanishing lines requires students to have some prior knowledge of the context of 1-point perspective drawing.  Jaipal seems to draw upon school mathematics knowledge of comparing the height of an object to its width, but he incorrectly concludes that the objects must be the same height because they look to have approximately the same width. 

Other points of interest:  Olive’s work, especially on the second page of the problem, illustrates the historical evolution of the concept of vanishing point in works of art.  When artists first began to use perspective in their work in the 15th century, they often identified multiple, contradictory vanishing points in a single drawing.  In Olive’s work we can see that she is using the idea of a vanishing point, but the point she identifies is different than the vanishing point that already exists in the drawing.