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Volume of Regular Solids

Name of Corresponding Unit Plan: Archaeological Documentation

Grade Level: 5-8

Common Core Standards:
RS9-10. 3. Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

M 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.

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

Content Areas: Math, Science

Recommended Length/Duration: 45-60 minute period

Learning Goals: Students will learn to measure and calculate the volumes of various regularly shaped solids.

Description/Sequence:

  1. Discuss the definition of volume.  Include that all forms of matter take up three dimensional space.  The amount of space they take up is volume. 
  2. Define regular versus irregular objects.  Describe how regular solids have shapes that form consistent prisms, cylinders, and spheres.  Show some examples of regular objects.  Have students identify other regular objects they can see around the room (e.g. books, pencils, cups, papers, boxes, globe).
  3. Point out that the dimensions of regular objects can be measured in linier units (length, width, depth/hight, radius, diameter, circumference)
  4. Once measured, the volume of a regular object can be calculated by formula.  Common formulas can calculate the volume of triangular prisms, rectangular prisms, cylinders, circles.
  5. Introduce each formula one at a time and have students do the practice exercise on their worksheet. 
  6. Provide students with a collection of objects, or have them find objects around the room to measure and calculate their volume.  Dimensions and volumes should be recorded on their worksheet.
  7. After students have had a chance to calculate the volumes of a variety of objects, explain that more complex regular objects can be calculated by breaking them into their component parts and adding the individual volumes together.  Have students do the two examples on the worksheet.

Assessments: Check worksheets for accuracy. Informally quiz students on retention of the formulas for calculating the volume of various solids.

Materials/Resources: Worksheets, Rulers, Calculators, Collection of various regular solids

Special Considerations: Weaker math students could be partnered with stronger students.

Scientific measurements are generally easier to take and calculate in metric than in English units.  Additional work may be needed if students are not familiar with metric measurements, or if the teacher chooses to use English units.

Extensions:
Additional measurements and calculations of volume can be taken at home.  This would enable students to choose larger objects (their whole home) or more unusual and interesting objects.

Students may want to try and break a very complicated object into regular solids to compute the total volume.

Students might want to research the history of one or more of the formulas for calculating volume.