November 11, 2016

In this lesson for grades 6-12, learners explore the relationship between dimension and volume. Using colored paper, students create two rectangular prisms and two cylinders to determine which holds more popcorn. They then justify their conclusions by analyzing the formulas and identifying dimensions with the largest impact on volume. Editor's Note: This activity presents an excellent opportunity for students to gain real insight into why increasing the radius of a cylinder has more impact on volume than increased height. It will also promote understanding of why the formulas for calculating volume work. This resource includes lesson objectives, teaching tips, and student worksheets with answer keys provided. It is part of a larger collection of activities developed by the National Council of Teachers of Mathematics (NCTM).

- Mathematics > General

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- Grade 12

Reason abstractly and quantitatively.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.