Lesson plan

1. Extend understanding of volume of prisms to volume of cylinders (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 cylinders, by multiplying the area of their base by their height, is similar to finding the volume of prisms.

Students bring prior knowledge of finding the volume of prisms from 5.MD.C.5.A in fifth grade. This prior knowledge is extended to finding the volume of cylinders as students work to understand that in many cases, volume is the area of two-dimensional objects stacked upon each other until they reach the desired height. A conceptual challenge students may encounter is that increasing the size of the radius has a greater impact on the volume of a cylinder than increasing the height, since the radius is squared (used twice) and the height is not.

The concept is developed through work with stacks of crackers, which illustrate that the volume of a cylinder is really the area of many congruent circles stacked upon each other.

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 in 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
  • cylinder
  • diameter
  • height
  • prism
  • radius
  • volume