published by
the National Council of Teachers of Mathematics

In this lesson for grades 6-8, learners calculate and compare volumes of cylinders and rectangular prisms, using bales of hay as the common unit. Students must use mathematics to explain why one shape of hay bale may be preferable economically to the other. But wait.....the round bales don't fit in a barn as well. Storing bales outside results in loss of product due to mold, which students must consider.

The activity was developed to promote understanding of volume through real-life scenarios. The resource is aligned to NCTM standards and includes lesson objectives, teaching tips, and a printable student worksheet.

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

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.1 Make sense of problems and persevere in solving them.

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)

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

This fun lesson lets students explore a real-life scenario as they compare volume for a cylinder (round hay bale) and a rectangular prism (box-shaped hay bale). They will use math to decide why one shape of hay bale is preferable economically to the other. But wait.....the round bales don't fit in a barn as well, which could affect the outcome of the problem!

<a href="http://www.thephysicsfront.org/items/detail.cfm?ID=10639">National Council of Teachers of Mathematics. Illuminations: Hay Bale Farmer. Reston: National Council of Teachers of Mathematics, July 15, 2008.</a>

Illuminations: Hay Bale Farmer, (National Council of Teachers of Mathematics, Reston, 2005), <http://illuminations.nctm.org/LessonDetail.aspx?id=L783>.

Illuminations: Hay Bale Farmer. (2008, July 15). Retrieved March 4, 2015, from National Council of Teachers of Mathematics: http://illuminations.nctm.org/LessonDetail.aspx?id=L783

National Council of Teachers of Mathematics. Illuminations: Hay Bale Farmer. Reston: National Council of Teachers of Mathematics, July 15, 2008. http://illuminations.nctm.org/LessonDetail.aspx?id=L783 (accessed 4 March 2015).

Illuminations: Hay Bale Farmer. Reston: National Council of Teachers of Mathematics, 2005. 15 July 2008. 4 Mar. 2015 <http://illuminations.nctm.org/LessonDetail.aspx?id=L783>.

@misc{
Title = {Illuminations: Hay Bale Farmer},
Publisher = {National Council of Teachers of Mathematics},
Volume = {2015},
Number = {4 March 2015},
Month = {July 15, 2008},
Year = {2005}
}

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This 3-D Java applet by the respected CSERD group lets students interactively explore two types of polyhedrons and see how volume/surface area are calculated.