published by
the National Council of Teachers of Mathematics

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 is aligned to NCTM standards and includes lesson objectives, teaching tips, and printable student worksheets with answer keys provided. It is part of a larger collection of lessons, labs, and activities developed by the National Council of Teachers of Mathematics (NCTM).

3-5: 1A/E2. Science is a process of trying to figure out how the world works by making careful observations and trying to make sense of those observations.

6-8: 1A/M3. Some scientific knowledge is very old and yet is still applicable today.

1B. Scientific Inquiry

6-8: 1B/M1b. Scientific investigations usually involve the collection of relevant data, the use of logical reasoning, and the application of imagination in devising hypotheses and explanations to make sense of the collected data.

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 numbersâ€”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.

6-8: 12B/M7b. Convert quantities expressed in one unit of measurement into another unit of measurement when necessary to solve a real-world problem.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.2 Reason abstractly and quantitatively.

Measurement and Data (K-5)

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. (5)

5.MD.3.b 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.

5.MD.5.b 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.

Geometry (K-8)

Graph points on the coordinate plane to solve real-world and
mathematical problems. (5)

5.G.2 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. (7)

7.G.6 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. (8)

8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

This resource is part of a Physics Front Topical Unit.

Topic: Measurement and the Language of Physics Unit Title: Applying Measurement in Physics

One of the best lessons we've found to help students get the connection between dimension and volume. They conduct an experiment to create two rectangular prisms and two cylinders, then determine which design holds the most popcorn. They will test ideas, graph outcomes, and present findings. Includes printable worksheets with answer keys.

<a href="http://www.compadre.org/precollege/items/detail.cfm?ID=10641">National Council of Teachers of Mathematics. Illuminations: Popcorn, Anyone?. Reston: National Council of Teachers of Mathematics, July 15, 2008.</a>

Illuminations: Popcorn, Anyone?, (National Council of Teachers of Mathematics, Reston, 2005), <http://illuminations.nctm.org/LessonDetail.aspx?id=L797>.

Illuminations: Popcorn, Anyone?. (2008, July 15). Retrieved March 30, 2015, from National Council of Teachers of Mathematics: http://illuminations.nctm.org/LessonDetail.aspx?id=L797

National Council of Teachers of Mathematics. Illuminations: Popcorn, Anyone?. Reston: National Council of Teachers of Mathematics, July 15, 2008. http://illuminations.nctm.org/LessonDetail.aspx?id=L797 (accessed 30 March 2015).

Illuminations: Popcorn, Anyone?. Reston: National Council of Teachers of Mathematics, 2005. 15 July 2008. 30 Mar. 2015 <http://illuminations.nctm.org/LessonDetail.aspx?id=L797>.

@misc{
Title = {Illuminations: Popcorn, Anyone?},
Publisher = {National Council of Teachers of Mathematics},
Volume = {2015},
Number = {30 March 2015},
Month = {July 15, 2008},
Year = {2005}
}

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%0 Electronic Source %D July 15, 2008 %T Illuminations: Popcorn, Anyone? %I National Council of Teachers of Mathematics %V 2015 %N 30 March 2015 %8 July 15, 2008 %9 text/html %U http://illuminations.nctm.org/LessonDetail.aspx?id=L797

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