Perspective Problem Explore 2, Problems 3-5

Overview:  On the second page of the problem, Khalil continues the same strategy of extending perspective lines through the front house to identify a vanishing point.  Alejandra has also drawn perspective lines like Khalil, but Alejandra has also drawn horizontal lines through the vertices of the given tree in order to make a congruent copy of the tree on the other side of the street.  Paige again measures the heights of the givens on the second page of the problem, and Paige doubles the height of the back house to make it a 2-story house.  The teacher approaches the group and reminds Alejandra that she will need to find the height of the trees in real life, not simply the height of the diagram.  Paige decides to draw items into the diagram freehand, so she adds trees to the diagram that do not follow the perspective lines.

Prior knowledge:  On the second page of the problem Alejandra uses school mathematics knowledge of congruence to attempt to make a congruent copy of the tree.

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.  When the teacher approaches the group, she performs a similar function to what Allen has been doing by requiring the students to share their ideas with others.