November 11, 2016

This simple Java applet for grades 5-8 lets users explore how volume is calculated in a box-shaped object. The user fills the box, layer upon layer, with small cubes to see why volume is a cubic function in a rectangular prism. Dimensions of the object can be easily changed by adjusting the width, depth, or height. This resource is part of a larger collection of lessons, labs, and activities developed by the National Council of Teachers of Mathematics (NCTM).

- Mathematics > General

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Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

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.

Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.