Like other unit assessments, the Pythagorean Theorem Test has been broken down into two parts: Foundations and Application/Extension. In the foundations section, students work through several problems that target basic understanding of the Pythagorean Theorem, the distance formula, and special right triangles. In the application and extension part of the test, students apply their understanding of the Pythagorean Theorem in novel or more complicated ways (MP1). For example, problem #9 is a problem that really requires students to look for and make sense of structure by adding an auxiliary line while problem #11 demands that students integrate several geometric conventions in order to solve the problem (MP7).
This homework assignment is really a pre-assessment for the upcoming unit on triangle similarity and trigonometry. Similarity is an idea we have talked about throughout the year, but not in formal terms. For that reason, I wanted to create an opportunity for students to use their own language to describe how they know a figure is an exception to a given set by discussing commonalities and differences in what they observe.