High School Geometry Assignment

Students find the measures of unknown angles and arcs formed by circles, their chords and radii, and tangent segments or rays. Although the assignment aligns with the math content of the standards, it does not engage students in appropriate types of mathematical thinking.  

Focus
The assignment does address the mathematical concepts of standard HSG.C.A.2, as it deals with the relationships among inscribed (and circumscribed) angles, radii, and chords. Students identify the appropriate relationship(s) in order to set up equations and solve for unknown values.

Rigor
Although the mathematical content of the assignment is aligned to standard HSG.C.A.2, the assignment does not require students to engage with the content in ways required by the standards. Specifically, students are not asked to demonstrate their conceptual understanding of these relationships: It asks students to solve for unknown values, but it doesn’t ask them to explain how they arrived at their answers or describe the relationships between the angles formed by chords, radii, and segments tangent to the circles.

Practice Standards
High school geometry standards often require students to go beyond simple computations. For example, standard HSG.C.A.2 requires students to identify and describe the relationships among angles and segments in circles, which allows them to engage in Mathematical Practice Standard #3 (“Construct viable arguments and critique the reasoning of others”). A written explanation of the relationships between the angles formed by chords, radii, and segments tangent to the circles would allow students to exhibit their understanding of the relationships, as well as their ability to use accurate terminology, symbols, and definitions, as required by Mathematical Practice Standard #6 (“Attend to precision”).