Type of Class:
           High School Geometry Class (all levels)

Related VA SOL: G.13 and G.14b

 Time Frame:
           90 minute block period

 Objectives:

  • Students will know and use the formulas for surface area and volume of three dimensional figures.

  • Students will be able to use the formulas for volume and surface area to solve practical problems. 

  • Students will understand the differences between surface area and volume.

 Materials:

  • Food or other items packaged in boxes and cylindrical shapes (such as cereal, crackers, Pringles, oatmeal—in cylindrical containers, soda cans, box drinks, rolled candy/mints, etc.)

  • Rulers

  • Water or sand or beans

  •  Measuring cups or beakers

  • Record Sheet

  • Project Sheet

 Procedures:

  1. Give each student a copy of the record sheet.  Instruct them to record everything asked for on the sheet.  Put students into groups and have them discuss the differences between surface area and volume.  Have them come up with a definition for each.  Then, have each group share with the class and have the class come up with a complete definition of volume and surface area.  This may take some prompting and questioning, depending on the level of the students and their prior knowledge.

  2. Ask students why it is important to know volume and surface area when packaging foods.  Some possible answers include:  to know how much food is in the package, to know how much material you need to make the package, to find the best way to package food so that the costs are minimal, etc.  

  3. Next as a class, discuss (in general terms) how to find surface areas and volumes of objects.  To help students with the concept of volume, choose an example object to find the surface area and volume as a class.  Hopefully this will help the students be able to find the volume of their group’s objects, even if they cannot figure out the formulas.  This may be done using water or sand or possibly other things like beans.

  4. Give each group a rectangular object that you have brought in.  They will be finding (and describing how they find) the surface area and volume of their object.  Remind them to pay attention to their record sheet so they record all of their information.  As students finish, ask them to share their finding for the formulas for surface area and volume.

  5. Next give students a cylindrical object.  They will be doing the same type of tasks they did for the rectangular object.  Have students share their results with each other and make sure that all students have come up with the correct formulas.  At the end of class, be sure to collect all Record sheets to look at the students’ progress and make sure that all students have the correct information.

  6.  Give students the Project Sheet to work on together.  There may be enough time that you want them to turn this in at the end of class.  However, they may need more time, depending on how much work the class has previously done with surface area and volume.

Assessment:
          Students will be given the project sheet to be turned in at a time determined by the teacher.  Students should be graded on their accuracy for using the formulas, the accuracy of  their results and for their creativity in solving the problem.