Download Cubic Cereal

GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Cubic Cereal
In this activity, students design a cubic box with
the same volume as a rectangular prism.
Materials
• Transparency/Page: Puzzle Crunchies
• Transparency/Page: Cubic Cereal Problem
• Transparency/Page: Cubic Cereal Problem Answer Key
• Transparency/Page: Cubes Work Sheet
• calculators (1 per pair)
Vocabulary
• volume
• surface area
Time:
Puzzle Crunchies
15 minutes
Introduce
•Explain to students that their assignment is a
problem-solving assessment that simulates a real-life
situation.
•Display Transparency: Puzzle Crunchies.
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Puzzle Crunchies
•Explain that they will take on the role of package
designers for an advertising company. The client,
Puzzle Cereals, wants to introduce a new cereal in a
box that resembles a famous mathematical cube
puzzle. The box must hold the same volume of cereal
as the standard cereal box so that when the
promotion is over, the company can switch back to
standard packaging.
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Cubic Cereal Problem
Discuss and Do
Dimensions of original box: 16 in. � 8 in. � 4 in.
Volume of original box:
•Have students work in pairs to solve the problem.
•Display Transparency: Cubic Cereal Problem.
Dimensions of new box:
Volume of new box:
Surface area of original box:
Surface area of new box:
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Cubic Cereal Problem
Cubes Work Sheet
•Ask students to take out their Puzzle Crunchies, Cubic
Cereal Problem, and Cubes Work Sheet pages.
•Have one person from each pair come up and take
a calculator.
•Suggest to students that they find the volume of the
original box first and then use the calculators to find
the volumes of various-sized cubes.
•Remind them that cubes have the same dimensions
on all sides.
•Suggest that students use the cubes on their Cube
Work Sheet pages to record the numbers that they test.
•Give students time minutes to complete the exercise.
Conclude
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Cubes Work Sheet
Cubic Cereal Problem
Answer Key
Dimensions of original box: 16 in. � 8 in. � 4 in.
•Review the list of questions and solicit student
responses.
•Display Transparency: Cubic Cereal Problem Answer Key
and ask students to verify their work.
Volume of original box: 512 cubic inches
16 � 8 � 4 = 512 cubic inches
Key Questions
Dimensions of new box: 8 in. � 8 in. � 8 in.
Volume of new box: 512 cubic inches
8 � 8 � 8 = 512 cubic inches
Surface area of original box: 448 square inches
2 � 16 � 8
2 � 16 � 4
2�8�4
256 + 128 + 64
= 256 sq in. (2 large sides)
= 128 sq in. (2 narrow sides)
= 64 sq in. (top and bottom)
= 448 sq in. total
Surface area of new box: 384 square inches
6 � 8 � 8 = 384 sq inches
(6 congruent sides)
•What skills were needed to complete this activity
besides a knowledge of surface area and volume?
(how to multiply decimal values, ability to use a
calculator, number of inches in 1 square foot)
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development
Transparency: Cubic Cereal Problem
Answer Key
End of Cubic Cereal
GEOMETRY AND MEASUREMENT OF SOLID FIGURES
Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development