Illuminations: Cubes

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published by the National Council of Teachers of Mathematics

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.

See Related Items for a more complex simulation that explores volume in both rectangular prisms and triangular prisms.

This resource is part of a larger collection of lessons, labs, and activities developed by the National Council of Teachers of Mathematics (NCTM).

Please note that this resource requires Java Applet Plug-in.

https://www.nctm.org/Classroom-Resources/Illuminations/Interactive...

Subjects	Levels	Resource Types
General Physics - Measurement/Units = Units and Dimensional Analysis Other Sciences - Mathematics	- Middle School - Elementary School	- Instructional Material = Activity = Interactive Simulation

Appropriate Courses	Categories	Ratings
- Physical Science - Physics First	- Lesson Plan - Activity - New teachers	Currently 0.0/5 Want to rate this material? Login here!

Intended Users:: Learner
General Public
Formats:: application/java
text/html
Access Rights:: Free access
Restriction:: © 2003 National Council of Teachers of Mathematics; http://illuminations.nctm.org/TermsOfUse.aspx
Keywords:: geometry, measurement, rectangular prism, volume, volume simulation
Record Cloner:: Metadata instance created February 1, 2011 by Caroline Hall
Record Updated:: February 22, 2025 by Lyle Barbato
Last Update when Cataloged:: July 15, 2008

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AAAS Benchmark Alignments (2008 Version)

9. The Mathematical World

9C. Shapes

6-8: 9C/M7. For regularly shaped objects, relationships exist between the linear dimensions, surface area, and volume.
6-8: 9C/M10. Geometric relationships can be described using symbolic equations.
9-12: 9C/H3a. Geometric shapes and relationships can be described in terms of symbols and numbers—and vice versa.

12. Habits of Mind

12B. Computation and Estimation

6-8: 12B/M3. Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids.

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<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=10640">National Council of Teachers of Mathematics. Illuminations: Cubes. Reston: National Council of Teachers of Mathematics, July 15, 2008.</a>

AIP Format

(National Council of Teachers of Mathematics, Reston, 2003), WWW Document, (https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/).

AJP/PRST-PER

Illuminations: Cubes (National Council of Teachers of Mathematics, Reston, 2003), <https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/>.

APA Format

Illuminations: Cubes. (2008, July 15). Retrieved March 16, 2025, from National Council of Teachers of Mathematics: https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/

Chicago Format

National Council of Teachers of Mathematics. Illuminations: Cubes. Reston: National Council of Teachers of Mathematics, July 15, 2008. https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/ (accessed 16 March 2025).

MLA Format

Illuminations: Cubes. Reston: National Council of Teachers of Mathematics, 2003. 15 July 2008. 16 Mar. 2025 <https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/>.

BibTeX Export Format

@misc{ Title = {Illuminations: Cubes}, Publisher = {National Council of Teachers of Mathematics}, Volume = {2025}, Number = {16 March 2025}, Month = {July 15, 2008}, Year = {2003} }

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%T Illuminations: Cubes %D July 15, 2008 %I National Council of Teachers of Mathematics %C Reston %U https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/ %O application/java

EndNote Export Format

%0 Electronic Source %D July 15, 2008 %T Illuminations: Cubes %I National Council of Teachers of Mathematics %V 2025 %N 16 March 2025 %8 July 15, 2008 %9 application/java %U https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Cubes/

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The AIP Style presented is based on information from the AIP Style Manual.

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Illuminations: Cubes:

Covers the Same Topic As CSERD Interactivate: Surface Area and Volume

This is a somewhat more complex simulation that allows students to compare volume calculations for rectangular prisms and triangular prisms. Includes lesson and tips for teachers.

relation by Caroline Hall

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