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In this exploration, students will apply their knowledge of finding volume and surface area of cylinders and rectangular prisms. Students will make recommendations to the local movie theater after determining which package is cost effective. Students will support their decision through a presentation.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
NCTM Measurement Standards: Understand measurable attributes of objects and the units, systems, and processes of measurement
NCTM Measurement Expectations: Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume
Apply appropriate techniques, tools, and formulas to determine measurements -develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders;
Primary Learning Objective(s):
Students will compare a cylinder to a rectangular prism to see which holds more volume and which is more cost effective to manufacture.
Additional Learning Objective(s):
Students will make presentations of cost effectiveness of the packaging chosen.
61 to 90 Minutes
Materials and Resources:
Technology Resources Needed:
Computer with Internet access
Teacher can review surface area and volume of cylinders and rectangular prisms using the surface area and volume tutorial.
Tell the story of a local movie theater trying to decide on serving popcorn in a bucket or in a box. Emphasize that the two types of packages will contain the same volume. Show an example of a popcorn bucket (cylinder) and a popcorn box (rectangular prism) if you have them available. If you don't have these resources available, you may view pictures on popcorn packaging website. Question students as to how a decision would be made concerning which package to choose.
Give students dimensions of cylinder (radius = 2 inches and height = 7 inches) and rectangular prism (length = 4 inches, width = 2 inches, and height = 11 inches). Provide student with Popcorn Worksheet. You may also want to provide graph paper and calculators. Have students recall how to determine surface area and volume of cylinders and rectangular prisms. Have students to round values to the nearest tenth.
Remind students that they must show work. They will also have to explain their conclusion during presentation.
Give students dimensions of another cylinder and rectangular prism that will not have the same volume. Ask students how they might compare the cost effectiveness of the two types of packages. Students may also want to construct cylinders and rectangular prisms with the specified dimensions. Students still struggling on the concept of finding surface area and volume may want to practice on interactive surface area and volume website.
Students will be evaluated on presentations. Use Popcorn Rubric for evaluation.
Teacher may want to do individual assessment while working on projects. Students will be assessed on presentation of material using the Popcorn Rubric.
Give students a specific volume and see if they can come up with possible surface areas. For example, a rectangular prism with a volume of 180 cubic units might have dimensions of 6 by 5 by 3 or 30 by 3 by 2. How would these two different possibilities of dimension affect the surface area?
Some students may want to continue applying knowledge of surface area and volume to other types of solids such as cones, triangular prism, triangular pyramids, and rectangular pyramids.
Each area below is a direct link to general teaching strategies/classroom
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.