Calculating Area and Volume

Topic: Breakfast Cereal Boxes (Surface Area and Volume)
Expectations:

  • develop the formula for finding the surface area of a rectangular prism
  • develop the formula for finding the volume of a rectangular prism
  • understand the relationship between the dimensions and the volume of a rectangular prism
  • calculate the surface area and the volume of a rectangular prism in a problem solving context
  • sketch a rectangular prism given its volume
Materials:
  • Have students bring in an assortment of cereal boxes (various types, sizes)
Activity 1 -- Develop Formula for Surface Area of a Rectangular Prism using Nets
  • Group Work
  • Each group draws (traces) the net of their cereal box
  • Develop a formula for finding the surface area of the box
  • Group share to ensure each group has developed the formula correctly
Activity 2 -- Calculating Surface Area
  • Using the net and the developed formula, students calculate the surface area of their box
  • When groups have completed the task, they can estimate the surface area of all cereal boxes in order from least to greatest.
  • Groups can now share surface area to confirm predictions
Activity 3 -- Develop Formula for Volume of a Rectangular Prism
  • Group Work
  • Develop the formula for finding the volume of a rectangular prism using concrete materials (cereal box)
  • Each group uses their cereal box to develop the formula for finding the volume of the box
  • Group share to ensure each group has developed the formula correctly
Activity 4 -- Calculating Volume
  • Using the developed formula, students calculate the volume of their box
  • When groups have completed the task, they can estimate the volume of all cereal boxes in order from least to greatest.
  • Groups can now share volume to confirm predictions.
Activity 5 -- Real World Problem Application (Enrichment)

The producer needs to change distribution companies. The new company wants to have their shipping crates to be approximately 1m3. Calculate the greatest number of cereal boxes which could be packaged in the crate? How do the cereal boxes have to be configured to allow the greatest number of boxes packaged in each shipping crate? Justify your response.

Back