WALTER AND JUANITA’S WATER TROUGHS
Enduring Understanding: Develop a better understanding of how to use the properties of special
right triangles and special triangles. Develop a better understanding of how the change in a linear
dimension will affect the volume of a figure.
Essential Questions:
Original Lesson Design
 How does a change in one linear
dimension affect the volume?
 How are units of measure converted
within the US system?
 What properties of special triangles such
as equilateral, isosceles and right triangles
assist in determining solutions to
problems?
 How can a conclusion be supported using
mathematical information and
calculations?
Suggestions for English Language Learners
Enhance Vocabulary:
Linear dimension
Volume
Equilateral triangle
Isosceles triangle
Right triangle
Triangular prism
Lesson Overview:
Original Lesson Design
Suggestions for English Language Learners
Prerequisite skills that students need to have
 Before allowing the students the
to be successful with this problem:
opportunity to start the activity: access
their prior knowledge regarding how to
 Area of a triangle
find the volume of a triangular prism,
 Area of a rectangle
equilateral triangles and how the special
 Area of a circle
properties of an equilateral can be used to
 Surface area
assist in solving a problem. Allow for
 Lateral surface area
collaborative time for the students,
 Volume of a prism
possibly activities around the room,
 Volume of a cylinder
discuss with the students.
 Special properties of a 30-60-90 right
 What would happen if one linear
triangle
dimension of a triangular prism changes?
 What are the relationships that exist
among the units of measure for linear
dimensions and volume?
 What is known about special triangles and
special right triangles?
 How is a problem situation decoded so
that a person understands what is being
asked?
 What mathematical information should be
used to support a particular conclusion?



7.48 gallons = 1 cubic foot
How will the students make their thinking
visible?
Use resources from your building.
EALRs/GLEs:
1.2.1
1.2.5
1.2.3
1.3.1
2.2.2
3.1.1
5.1.1
Item Specifications: ME01; ME02; ME03; GS01; SR05; MC01
Assessment:


Use WASL format items that link to what is being covered by the classroom activity
Include Multiple Choice items
Walter and Juanita’s Water Troughs
Adapted from The Charles A. Dana Center at the University of Texas at Austin, © 2002
You have been hired as chief mathematician by a company named Walter and Juanita’s Water
Troughs. This company builds water troughs for various agricultural uses. The company has one
design (figure 1). Your job is to perform mathematical analysis for the owners.
1 cubic foot holds 7.48 gallons
1. A customer would like to know the depth of the water (in inches) when the trough has 32
gallons in it. Show work using words, numbers or diagrams to support your answer.
2. The interior of the troughs must be coated with a sealant in order to hold water. One
container of sealant covers 400 square feet. Will one container of sealant be enough to seal
ten troughs? Why or why not? Show the work that supports your answer.
3. Walter and Juanita would like to explore some minor modifications of their original design.
They would like to know which change will produce a water trough that would hold more
water—adding one foot to the length of the trough, making it 11 feet long, or adding three
inches to each side of the triangular bases, making them 2 feet 3 inches on each side (see
figures 2 and 3). Justify your answer.
4. A new tank is designed in the shape of a cylinder with a radius of 2 feet to hold the same
volume of water as the tank in Figure 1. What is the height of the tank?
Support your answer using words, numbers or diagrams.
5. While calculating the lateral surface area of the right circular cylinder represented in the drawing
below, Sharon misread the ruler and used 3.5 inches as the height.
Which of the following is closest to the difference between Sharon’s result for the lateral surface area
and the actual lateral surface area of the right circular cylinder?
A
B
C
D
1.5 square inches too much
3.75 square inches too much
5.25 square inches too much
9.5 square inches too much
6. Gene has a cylinder with radius 4 inches and height 2 inches. He cut the cylinder in half along the
length of the diameter, as shown in the diagram below.
What is the area of the shaded cross-section?
A
B
C
D
1
square inches
2
24  square inches
16 square inches
8 square inches
48 1