Stage-Storage Relationships
PBL
Objectives
Engagement
Day 1 (5 to 30 minutes):



Ask students to discuss the different
shapes of plastic and glass beverage
containers
Give students containers of various
shapes and ask them to fill half the
volume of the container with water by
estimation
Discuss natural occurrence of
irregular-shaped depressions that hold
water (puddles, ditches, lakes). How
would you estimate water volume in
those settings?
Exploration
Day 1 (30 to 45 minutes):



Mathematics Concepts/Objectives
Have students find data of the stage of
local lakes
Have students research how the stage
of a lake relate to the volume of water
it holds
Develop a plan to collect stage-storage
data for various containers
Day 2 (45 to 90 minutes):




Have students collect data on storage
volume as a function of stage (water
depth) in both the straight-sided and
slope- (or irregular-) sided containers
Ask students to plot their data
Compare graphs for similar containers.
Is there data variability? If so, where
might it have come from?
Develop non-linear relationships
describing the data
Explanation
Stage-storage relationships are
frequently used to describe the relationship
511 Harrington 4226 TAMU
College Station, TX 77843-4226
Materials
 Tap water in large containers
 Large-mouth containers with straight,
vertical sides (e.g. beakers or clean
food cans)
 Large-mouth containers with sloped or
irregular sides (e.g. drinking glasses or
vases)
 Rulers
 Graduated cylinders or measuring cups
 Pencils and paper for recording data
 Graph paper
Grade 10
TAKS Objective 8 – Measurement
TAKS Objective 10 – Mathematical Tools
and Processes
Grade 11
TAKS Objective 6 – Geometric Relationships
and Spatial Reasoning
TAKS Objective 8 - Measurement
(Note: These objectives were determined to be
high stakes for North Dallas campus based on
TAKS item analysis data provided for 9-10th
grade 2006-2007 results).
Safety Notes

Perform experiments in an area with a
non-skid surface
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between water volume and water depth. In
situations in which very large volumes of
water are stored, such as in lakes and
reservoirs, these relationships are essential
in predicting water volume available for
use. Because these lakes and reservoirs are
very large, we need a method to estimate
water from a measurement that is easily
obtained. Water depth provides this easy
measure and can be recorded by comparing
the water surface to a scale mounted to a
fixed surface or by using float-type
devices. Stage-storage relationships for
large areas are often developed using
topographic maps and the “average-endarea” method of volume estimation.
Extension 1
Estimate Volume of a Ditch
Ask students to research the “average-endarea” method for estimating volume of
irregularly shaped objects. Take
measurements of a ditch or other
depression in the school yard. Use the
average-end-area method to estimate the
volume of storage in the ditch.
Extension 2
Estimate Volume from a Topographic
Map
Apply the average-end-area method to
develop a stage-storage relationship for a
valley or other natural depression using
topographic maps.
Evaluation
 PBL Rubrics
 Teacher-created TAKS formatted
questions related to high stakes
objectives/TEKS-TAKS
presentation
 TI Navigator – technology
demonstrating teacher formatted
511 Harrington 4226 TAMU
College Station, TX 77843-4226



Use caution handling glass containers
Use caution handling the cut edge of
cleaned food cans
Work over a shallow tray to contain spills
Website:
Access powerpoint for this lesson plan at
ntstem.tamu.edu
Tel - 979-820-3409
Fax - 979-862-4347
aggie-stem@tamu.edu
http://aggie-stem.tamu.edu
questions as application for
classroom immediate assessment
511 Harrington 4226 TAMU
College Station, TX 77843-4226
Tel - 979-820-3409
Fax - 979-862-4347
aggie-stem@tamu.edu
http://aggie-stem.tamu.edu
Social Interaction Rubric
CATEGORY
Communication
Advanced
Proficient
Basic
Minimal
Routinely
communicates useful
ideas. Rarely
dominates discussion.
Usually
communicates
useful ideas.
Occasionally
dominates
discussion.
Usually appears to
listen attentively to
other group
members through
eye contact and
body language.
Occasionally
interrupts others.
Usually is publicly
positive of the
project and the work
of others. Usually
has a positive
attitude toward the
project and others.
Usually draws on
other group
members’ ideas
when participating.
Usually addresses
others’ ideas and
responds
accordingly.
Usually gives
explanations of
communication with
clear reasoning and
logical thought
processes. Usually
speaks coherently
and cohesively.
Sometimes
communicates useful
ideas. Often dominates
discussion.
Rarely provides useful
ideas.
Always tries to dominate
discussion or not engaged
in discussion enough to
dominate.
Rarely appears to listen
attentively to other group
members through eye
contact and body
language. Always tries to
interrupt others or does
not listen enough to
engage at all.
Rarely is publicly
positive of the project and
the work of others. Rarely
has a positive attitude
toward the project and
others.
Listening
Routinely appears to
listen attentively to
other group members
through eye contact
and body language.
Rarely interrupts
others.
Attitude
Routinely is publicly
positive of the project
and the work of
others. Often has a
positive attitude
toward the project and
others.
Routinely draws on
other group members’
ideas when
participating. Often
addresses others’ ideas
and responds
accordingly.
Consideration
Explanation
Routinely gives
explanations of
communication with
clear reasoning and
logical thought
processes. Speaks
coherently and
cohesively.
511 Harrington 4226 TAMU
College Station, TX 77843-4226
Tel - 979-820-3409
Fax - 979-862-4347
Sometimes appears to
listen attentively to
other group members
through eye contact
and body language.
Often interrupts others.
Sometimes is publicly
positive of the project
and the work of others.
Sometimes has a
positive attitude
toward the project and
others.
Sometimes draws on
other group members’
ideas when
participating.
Sometimes addresses
others’ ideas and
responds accordingly.
Sometimes gives
explanations of
communication with
clear reasoning and
logical thought
processes. Sometimes
speaks coherently and
cohesively.
Rarely draws on other
group members’ ideas
when participating.
Rarely addresses others
ideas and responds
accordingly.
Often tries to work alone.
Rarely gives explanations
of communication with
clear reasoning and
logical thought processes.
Rarely speaks coherently
and cohesively.
Communication often
seems disconnected.
aggie-stem@tamu.edu
http://aggie-stem.tamu.edu
Individual Accountability Rubric
CATEGORY
Preparedness
Advanced
Proficient
Basic
I routinely bring
needed materials. I am
always ready to work.
I usually bring
needed materials. I
am usually ready to
work.
I sometimes bring
needed materials. I am
sometimes ready to
work.
I rarely bring needed
materials. I am rarely
ready to work.
Focus
I routinely stay
focused on tasks that
need to get done. I
routinely use my time
well. The group does
not have to adjust
deadlines or
responsibilities due to
my participation.
I routinely produce
work of the highest
quality. I routinely
produce work that
shows my best effort.
Collaboration
I routinely listen,
share, and support the
efforts of others. I
routinely keep people
working together well.
I usually listen,
share, and support
the efforts of others.
I do not cause
tension in the group.
I sometimes stay
focused on tasks that
need to get done. I
sometimes use my
time well. The group
has had to adjust
deadlines or
responsibilities twice
due to my
participation.
I sometimes produce
work that has to be
checked or redone by
other group members
to ensure quality. I
usually produce work
that shows some effort.
I sometimes listen,
share, and support the
efforts of others.
Occasionally, I do not
work well with the
group.
I rarely stay focused on
the tasks that need to get
done. I rarely use my
time well. The group has
had to adjust deadlines or
responsibilities three or
more times due to my
participation.
Quality
I usually stay
focused on tasks
that need to get
done. I usually use
my time well. The
group has had to
adjust deadlines or
responsibilities once
due to my
participation.
I usually produce
work of high
quality. I usually
produce work that
shows strong effort.
Problem-solving
I routinely look for
and suggest solutions
to problems.
I usually look for
and suggest
solutions to
problems. However,
most of the time, I
refine solutions
suggested by others.
I sometimes look for
and suggest solutions
to problems as well as
try to refine the
solutions of others.
However, most of the
time, I simply go along
with the solutions of
others.
I rarely look for and
suggest solutions to
problems or try to refine
the solutions of others. In
fact, most of the time, I
let others do the work.
511 Harrington 4226 TAMU
College Station, TX 77843-4226
Tel - 979-820-3409
Fax - 979-862-4347
Minimal
I usually produce work
that has to be checked or
redone by other group
members to ensure
quality. I usually produce
work that shows very
little effort.
I rarely listen, share, and
support the efforts of
others. I often do not
work well with the group.
aggie-stem@tamu.edu
http://aggie-stem.tamu.edu
Mathematics/Science Rubric
CATEGORY
Knowledge and
Understanding
Reasoning
Communication
8-7
Demonstrates complete
understanding of the
concepts and principles. Is
able to apply knowledge to
challenging problems in
unfamiliar situations.
Executes algorithms
completely and in a correct
manner.
Identifies the elements of the
problem and shows
understanding of the
relationship between them.
Selects and applies problemsolving techniques to
recognize patterns. Draws
conclusions consistent with
findings. Provides
justifications or proofs were
appropriate.
Successfully follows correct
mathematical and scientific
notation. Moves effectively
between different forms of
mathematical representation.
Reasoning is concise, logical,
and complete. Supports his
findings by effective use of
diagrams, charts, and other
visual tools.
511 Harrington 4226 TAMU
College Station, TX 77843-4226
6-5
4-3
2-1
0
Demonstrates nearly
complete understanding of
the problem’s concepts and
principles. Is able to apply
knowledge to challenging
problems in familiar
situations. Executes
algorithms completely, but
computations may contain
minor mistakes.
Identifies the important
elements of the problem and
shows general understanding
of the relationship between
them. Selects and applies
problem-solving techniques
to recognize patterns. Draws
conclusions consistent with
findings. Fails to provide
justifications.
Demonstrates
understanding of some of
the problem’s concepts
and principles. Is able to
apply knowledge to
simple, familiar problems.
Executes algorithms with
some mistakes, and
computations contain
major errors.
Identifies some important
elements of the problem
and shows general
understanding of the
relationship between them.
Selects and applies
problem-solving
techniques to recognize
patterns.
Demonstrates very limited
understanding of the
problem’s concepts and
principles. Is not able but
still attempts to solve
simple, familiar problems.
Executes algorithms with
major mistakes, and
computations contain
serious errors.
Identifies only the
unimportant elements of
the problem and shows
very limited understanding
of the relationship between
them. Applies, with
guidance, mathematical
problem-solving
techniques to recognize
patterns.
Does not understand
the problem. Does
not solve the
problem. Does not
execute algorithms
or computations.
Follows nearly correct
mathematical and scientific
notation. Moves between
different forms of
mathematical representation
with some success.
Reasoning is clear, but not
always logical or complete.
Supports findings by using
some visual tools.
Follows mathematical and
scientific notation with
some errors. Shows good
use of mathematical
language and/or forms of
mathematical
representation, but unable
to move between them.
Reasoning is not clear.
Attempts to follow
mathematical and
scientific notation. Shows
basic use of mathematical
language and/or forms of
mathematical
representation. Reasoning
is difficult to follow.
Tel - 979-820-3409
Fax - 979-862-4347
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Does not identify
elements of the
problem and does
not understand
relationships
between them. Does
not apply
mathematical
problem-solving
techniques. Does not
recognize patterns.
Does not follow
mathematical and
scientific notation.
Does not use
mathematical
language or
representation.
Reasoning does not
exist.
511 Harrington 4226 TAMU
College Station, TX 77843-4226
Tel - 979-820-3409
Fax - 979-862-4347
aggie-stem@tamu.edu
http://aggie-stem.tamu.edu