CYLINDERS V’ PRISMS,
ARE YOU BEING RIPPED OFF?
Geometry & Measurement
(image site: http://www.usatoday.com/money/industries/food/2008-06-11-shrinking-sizes_N.htm )
Authors: Linda Burrington and Bonnie McCormick
June 18 – 23, 2008
Written as part of the BITL IV grant which was funded by the Office of Commissioner of
Higher Education of Montana.
ABSTRACT:
This lesson will use surface area, and volume to investigate rectangular prisms and
cylinders. The students will predict which container has more volume. They will also
predict the number possible ice scoops to fill their rectangular prism and cylindrical
containers. Students’ prior knowledge should consist of being able to use measurement
correctly and how to find the area of a two-dimensional figure. An extension to this
lesson may be to have the students explore the minimum surface area needed to hold one
gallon of ice cream.
GRADE LEVEL: 8
MATH STRAND: Geometry – Analyzing two and three-dimensional space and figures
using circumference, area, and volume.
MONTANA STANDARDS FOR MATHEMATICS:
.
Mathematics Content Standard 4 – Demonstrate an understanding of shape and
an ability to use geometry.
 4:1 Identify, describe, construct, and compare plane and solid
geometric figures.
 4:5 Use geometry as a means of describing the physical world.
Mathematics Content Standard 5 – Demonstrate an understanding of
measurable attributes and an ability to use measurement processes.
 5:1 Estimate, make and use measurements to describe,
compare, and/or contrast objects in real-world situations.
 5:3 Apply the concepts of perimeter, area, volume and
capacity, weight and mass, angle measure, time, and
temperature.
 5:6 Demonstrate relationships between formulas and
procedures for determining area and volume.
CLASS TIME REQUIRED:
The objectives for this focal point will be approximately covered over three 50 minute
periods.
MATERIALS:
Each group of two students will use the following supplies:
- Two copies of grid paper
- One pair of scissors
- Two rulers
- Two calculators
- A rectangular prism (possible choice may be a check blanks container)
- Tape (teacher will circulate the room and distribute)
- One empty soda can
- How Many Scoops Can You Get? worksheet
The teacher will need the following supplies:
Copy of nets for cylinder and rectangular prism (see below)
OBJECTIVES:
- Students will make predictions pertaining to surface area and volume.
- Students will create nets for a rectangular prism and a cylinder.
- Students will calculate lateral area, surface area and volume of a cylinder and
a rectangular prism.
TECHNOLOGY:
Websites used:
http://routingbyrumor.wordpress.com/2007/12/06/deceptionengineering/ (article about consumer deception June, 2008)
http://argyll.epsb.ca/jreed/math14/strand3/images/cylinder_net
2.gif (image of cylinder net)
http://images.google.com/imgres?imgurl=http (image of
rectangular prism net)
Calculators
: http://www.usatoday.com/money/industries/food/2008-06-11-shrinking-sizes_N.htm
LESSON PLAN
DAY ONE: Each class is fifty minutes in length.
INTRODUCTION: To engage the students’ interests, the teacher may open by
discussing manufacturing packaging deception. The teacher may begin with the question
“Are manufacturers deceiving shoppers?” This would lead into a class discussion about
how consumer product manufacturers are using every trick that they can conceive to hide
the fact that we are paying more for less. Give several examples of the shrinking
amounts in packages for the same or higher price. (See hyperlink)
http://routingbyrumor.wordpress.com/2007/12/06/deception-engineering/
After discussion, ask the question, “Would changing the shape of the package be another
way to deceive the shopper?” The teacher could display two different ice cream
containers, a cylinder and a rectangular prism, that appear to be the approximately the
same size. At this point, the teacher may ask, “Which container do you think would
contain more ice cream?” The students will give their predictions and justify by
explaining why they made their choice.
Hand out the grid paper, scissors, and ruler to each group. The teacher will be assuming
that all students will have a pencil (Ha, Ha!). Write the dimensions (Height = 6 inches,
Length = 8.2 inches, Width = 6 inches) on the board. Hand each group one example of a
rectangular prism. Instruct the students to create a net of a rectangular prism and label
dimensions on their net which was created on the grid paper. Then have the students
draw a three-dimensional picture of the prism and label the sides. The teacher will
circulate, dispensing tape, and assisting as necessary. Upon completion, the class will
discuss their successes and failures and why.
Next, the teacher will hand out a second sheet of grid paper and an empty soda can to
each group. Write the dimensions (Diameter = 6 inches, Height = 8.2 inches) on the
board. Instruct the students to make a net of a cylinder using the grid paper and label the
dimensions. Have the students draw a three-dimensional picture of the cylinder and label
the dimensions. The teacher will circulate the room, dispensing tape, and assisting as
necessary. Again upon completion, the class will discuss their successes and failures and
why. Students will put their names on their nets, and the teacher will collect them.
Assign students to go home and discuss deception of packaging by manufacturers with
their parents. The next day, the students will share any information that they received
from their parents.
DAY TWO:
Begin class with students sharing information about packaging deception after parent
discussions. Hand out the students’ prisms and cylinders from the previous day’s lesson
and calculators. The previous day’s measurements will remain on the board. Instruct
students to find the surface area of the rectangular prism. Ask the students to round to the
nearest tenth if needed. Prompt students as to what they know about area and how many
areas are in a rectangular prism. Note: The answer to the surface area of the
rectangular prism is 268.8 sq. inches. The teacher will circulate and assist groups as
necessary. The groups will share their results with the class. Ask a volunteer to go to the
board and show how he or she determined the answer to the surface area. Check for
understanding before proceeding. Repeat procedure implementing the cylinder. Note:
The answer to the surface area of the cylinder is 211.0 sq. inches.
The teacher may say, “Now that we have discovered the surface area of our prisms and
cylinders, let’s determine the amount of space which is in our container. Ask students
what the name for the amount of space is in a container. More than likely, a student will
know the answer and will tell the class. Students will calculate the volume of the
rectangular prism and share. Discuss results and check for understanding by circulating
and looking at the students’ work. Repeat the procedure implementing the cylinder.
Note: The answer to the volume of the rectangular prism is 295.2 cubic inches. The
answer for the cylinder is 231.8 cubic inches.
Follow up with a discussion about which containers holds more, the rectangular prism or
the cylinder. Does the class feel that consumers are being ripped off by the
manufacturers? Collect all prisms and cylinders for use the next day.
DAY THREE:
Review previous day’s lesson. Now that the students know the surface area and volume
of each of their containers, the students will determine the number of ice cream scoops
that they can place in each container using an ice cream scoop with the diameter of three
inches. Hand out How Many Scoops Can You Get? activity worksheet to the groups.
(See activity worksheet) Let the groups work on the worksheet following the
instructions. The teacher will circulate and assist as needed while the students complete
the worksheet. After the students complete the worksheet, discuss the outcome. Collect
worksheets.
Finish project with an ice cream party rewarding the students for their participation and
good work.