How do you address a standard that prompts students to "know" formulas? The word "know" is completely different from being prompted to "derive" formulas. 21st Century learning pushes us to ditch "know" being equated with "memorize" when a formula can quickly be obtained from Google. Perhaps a focus on the relationship within the structure of the formulas would best serve our students...thoughts?
The emphasis of volume as layered base area starts with cylinders. And since cylinders are critical for understanding volume of cones and spheres, be sure students are firmly rooted in this concept. The Oreo lab activity can confirm the level of student understanding. Then consider the following activities that use
View-Thru Large Geometric Solids from
Learning Resources for a hands-on investigation to determine the volume of cones and spheres from relational cylinders.
Short on time from the recent ice days? This animation is quick but powerful in showing the 3:1 volume ratio of cone to cylinder.
Similar extensions can be made to investigate the volume of a square pyramid from a relational cube. Note: Pyramids are included in Grade 7 standards (7.G.A.3) with respect to cross sections and High School Geometry standards (HSG-GMD.A.1 and HSG-GMD.A.3) with respect to volume.
These investigations highlight Common Core State Standard 8.G.C.9 included in MATH-8 and Accelerated MATH-7.
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