Lesson plan

7. Extend understanding of volume of cylinders to volume of spheres (C)

teaches Common Core State Standards CCSS.Math.Content.8.G.C.9 http://corestandards.org/Math/Content/8/G/C/9
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2
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Lesson objective: Extend understanding that finding the volume of spheres is similar to finding the volume of cylinders.

Students bring prior knowledge of finding the volume of cylinders from 8.G.9 earlier in this unit. This prior knowledge is extended to spheres as students watch a live-action video that illustrates the relationship between the volumes of cones and spheres that have equal radii and heights. A conceptual challenge students may encounter is that it is absolutely necessary to multiply the volume of a cylinder by \(\frac23\)to get the volume of a sphere.

The concept is developed through work with a hemisphere-shaped container that fills a cylinder-shaped container with the same radius and height since it illustrates the 1:3 relationship of their respective volumes. This then extends to the ratio of 2:3 that exists between the volumes of spheres and cylinders respectively.

This work helps students deepen their understanding of operations because it requires the product of constants and dimensions and also requires knowledge of simplification using the order of operations.

Students engage in Mathematical Practice 2: Reason abstractly and quantitatively as they work with different scenarios since they require students to determine what information is given, if the information needs to be modified before use (diameters cut in half to form radii), students then have to substitute the values into the volume formula correctly and simplify to find an answer. After getting an answer, in some cases, students will be asked to explain what the answer represents and the implications of that representation.

Key vocabulary:

  • area
  • base
  • cone
  • cylinder
  • diameter
  • height
  • radius
  • volume