High School Geometry Assignment

Focus
In eighth grade, students learn the volume formulas for cylinders and cones and begin reasoning about the formula for a pyramid (standard 8.G.C.9). In high school, they can explain how and why these formulas work, and apply the formulas to geometry relationships in the real world. Four of the five problems in this assignment involve a real-world context, and two of the problems also involve the concept of density, which is specifically referenced in standard HSG.MG.A.2. 

Rigor
This assignment focuses on all three aspects of rigor (conceptual understanding, procedural skill, and application), which is appropriate since standards HSG.MG.A.2 and HSG.GMD.A.3 target all three aspects of rigor. All five problems build students’ procedural skill in calculating values using the density and volume formulas. Four of the five problems are word problems grounded in authentic, real-world contexts, which builds students’ application skills. In addition to interpreting word problems and calculating the answers, students’ conceptual understanding of density and volume is also developed through questions that ask students to make judgments about their answers (for example, problem #1 asks students to explain how the density of the pyramid could let you know whether or not the pyramid is solid gold). 

Practice Standards
Problems #1-2 and 5 involve multiple steps and require students to make sense of the given information. This gives students a chance to engage with Mathematical Practice Standard #1 ("Make sense of problems and persevere in solving them") as they determine which information to use—and how to use it—to answer the problems. Problem #3 allows students to model the real world with geometry and state any assumptions made in the modeling process, required by Mathematical Practice Standard  #4 (“Model with mathematics”).