University of Arizona College of Education/MASTER-IP 1
your name, unit title
Ping's Pools & Pads
Cassandra Ping
TTE 596C/Dr. Olsen
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Stage 1 – Desired Results
Established Goals
What content standards and program
goals will the unit address?
6.M.G.04
Standard: Represent threedimensional figures using nets made
up of rectangles and triangles, and use
the nets to find the surface area of
these figures. Apply these techniques
in the context of solving real-world
and mathematical problems.
Cluster: Solve real-world and
mathematical problems involving area,
surface area and volume.
Student Friendly: I can calculate the
surface area of a 3-D solid by creating a
net.
7.M.G.06
Standard: Solve real-world and
mathematical problems involving area,
volume and surface area of two-and
three-dimensional objects composed
of triangles, quadrilaterals, polygons,
cubes and right prisms.
Cluster: Draw, construct and describe
geometrical figures and describe the
relationships between them.
Student Friendly: I can solve realworld problems by calculating volume
of 3-D objects including cubes and
right prisms.
Transfer
Mathematical principles can be used along with technology
tools to make real-world decisions.
Understandings
Meaning
Essential Questions
Nets are a useful aid to the
study of polyhedra and in
general, as they allow for
models of polyhedra to be
constructed (Wikipedia)
What is the purpose of finding
surface area?
A net is a two-dimensional
representation, or pattern, of a
three-dimensional figure that
can be folded to form the
figure.
Why is it necessary to
understand volume?
Surface area and volume can
be computed for all 3Dimensional figures.
Every 3-dimensional figure
has a unique set of faces,
edges, and vertices.
Many different nets can exist
for a given polyhedron,
depending on the choices of
which edges are joined and
which are separated
7.Technology.Strand6.Concept2.PO3 (Wikipedia)
Students will select and use
applications effectively and
Mathematics is a language that
productively.
can be used for
Students will enter data using simple
communication, constructing
formulas while using spreadsheets to
arguments, and critiquing the
perform calculations.
work of others.
Technology tools, such as
Excel, can assist in the work of
doing mathematics.
How can you construct a net of
a 3-D solid?
How is Excel useful in solving
mathematical problems?
University of Arizona College of Education/MASTER-IP 3
your name, unit title
Students will know …
Acquisition
Students will be skilled at
6.M.G.04
6.M.G.04
 3-D shapes are solids
 Constructing a
that have 3 dimensions
height, width, & length.
mathematical model
 Rectangular prism is a
 Describing 3D figures
solid (3-dimentional)
using edges, vertices
object, which has six
and faces
faces that are
 Testing mathematical
rectangles.
conjectures
 Triangular prism is
composed of two
7.M.G.06b
triangular bases and
 Calculating surface area
three rectangular sides.
and volume of a 3 Pyramid is a
Dimensional shape
polyhedron that has
 Using Excel to calculate
three or more
formulas for surface
triangular faces that
area and volume of
share a common vertex.
figures
 Edge is a line where
two surfaces meet.
7.T.Strand 6. Concept 2.PO3
 Vertex (vertices) is a
 Using basic functions of
point where two or
a computer
more straight lines
 Opening and closing
meet. A corner.
documents
 Face is any of the
 Entering data into cells
individual surfaces of a
in Excel
solid object.
 Creating formulas in
 Base is the lowest part
Excel
on a solid object.
 Net is a pattern that
you can cut and fold to
make into a shape.
 Surface area is the total
area of each surface on
a 3-D object.
7.M.G.06b
 Area is the size of the
surface. (Square,
Triangle, Circle,
Trapezoid)
 Square units is the
measurement used to
determine the area of a
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





two-dimensional
object.
Volume is the amount
of space a threedimensional object
occupies (sphere,
pyramid, prism,
cylinder, cone)
Cubed units are the
measurement used to
determine the volume
of a three-dimensional
object. .
Polygons a twodimensional shape with
straight sides.
Quadrilateral is a flat
surface with four
straight sides.
Height is the vertical
distance from top to
bottom (the highest
point)
Formulas of Area for:
Square, Triangle, Circle,
Trapezoid and Volume
of : sphere, pyramid,
prism, cylinder, cone
University of Arizona College of Education/MASTER-IP 5
your name, unit title
Stage 2 - Assessments
Performance Task (in GRASPS format)
(R)You are a designer working for Ping’s Pools & Pads. You have been promoted to “Head Designer” and
have been asked to design unique pools of specific shapes along with yards that are attractive to the
customers’ eyes. The housing market was on a decline putting pool installment and landscaping
at a halt, but with the economy recovering people are back on the market purchasing houses and
making them entertaining and beautiful. But we have to remember cost is still an issue. There
has been a spark of interest with having uniquely shaped pools and yards while keeping cost at a
minimum. It is your job to design backyards with pools (of specific shapes) and find all of the
necessary measurements for the builders along with the costs for the customers. You have
backup designers that will assist you with recording and accounting for each pool project. It is
your job to work as a team to ensure you are ready to present to Ping’s Pools & Pads construction and
clients who are eagerly ready to enjoy their new backyard. During the presentation you will need to
1) Present a theory of what shape of pool will be the most desired and why. 2) Calculate the surface
area of the yard and the volume of the pool. 3) Propose a budget to show the least expensive route
with the desired pool design. 4) Create an Excel document with the formulas that calculate
volume, surface area, and cost for the backyard of their dreams.
Goal: You are to work with your team on designing desired pools, yards, and calculate the cost in
Excel. In doing this you will need to calculate surface area and volume by inserting formulas into
Excel and using the dimensions to calculate the total cost.
Role: A designer working for a pool company that has been asked to design backyards (pools and
yards).
Audience: Customers purchasing pools and landscaping (sod).
Situation: You find yourself and your team having to collaborate to determine the best pool and yard
design that has the least amount of cost, but is still appealing to the customer. You will be using
surface area and volume formulas to help complete these calculations.
Product, Performance, & Purpose: You will create a presentation that consists of a theory of the best
pool/backyard design for the cost. You will then develop an Excel sheet that calculates these
formulas according to design and propose a budget to show the least expensive route.
Standards & Criteria for Success: It is your job to work as a team to ensure you are ready to present to
Ping’s Pools & Pads construction and clients who are eagerly ready to enjoy their new backyard. During
the presentation you will need to 1) Present a theory of what shape of pool will be the most desired
and why. 2) Calculate the surface area of the yard and the volume of the pool. 3) Propose a budget
to show the least expensive route with the desired pool design. 4) Create an Excel document with
the formulas that calculate volume, surface area, and cost for the backyard of their dreams.
Other Evidence: (quizzes, tests, prompts, work samples, labs, etc.)
* Mini Presentation using PowerPoint
During the presentation you will need to 1) Present a theory of what shape of pool will be the most
desired and why. 2) Calculate the surface area of the yard and the volume of the pool. 3) Propose a
budget to show the least expensive route with the desired pool design. 4) Create an Excel
document with the formulas that calculate volume, surface area, and cost for the backyard of their
dreams.
Customer Requests (3 Scenarios)
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*Back ground information on pools, construction, and landscaping--give the students ideas of pool
designs and backyards http://www.houzz.com/Hot-Tub-and-Pool-Connected
*Cost of Materials (Spreadsheet)
*Quiz--Short answer quiz calculating surface area and volume. Students will be expected to solve
the real-life problem as well as explain their steps and reasoning why they took the route they
did.
Student Self-Assessment and Reflection
Project Information: Excel printout consisting the total surface area, total volume, shapes, formulas,
and cost calculation. Work Habits (scale grading): survey on productivity in the group. Specific
questions pertaining to collaboration, initiative, and project outcome. Overall Project (open-ended
questions): Survey on the project and reflection of how it took place. Rubric for students to circle about
the project process.
University of Arizona College of Education/MASTER-IP 7
your name, unit title
Stage 3 – Learning Plan
1) Begin with an entry question (What pool and yard design is the
least expensive?) to hook students into considering the volume
and area of real-life scenarios for example: "Julia just purchased a
new home and has budgeted in $30,000 for a pool and
landscaping. She defiantly can't go over that budget and
would like to use any left over money for some new living
room furniture. Can you help her design a great pool and
lovely lawn all while keeping her costs under control?" H
2) Introduce the essential question and scenario and discuss the
surface area and volume unit and the performance tasks (Ping’s
Pools & Pads Action Plan). W
3) Key vocabulary words are introduced as needed by the various
learning activities and performance tasks. E
4) Present lessons of surface area with cereal boxes, nets, rooms, etc.
Then have students practice calculating surface areas of
manipulatives, book picture examples, as well as word problems
without pictures. E
5) Have students work in cooperative groups to develop formulas for
specific surface area polyhedrons as well as 2-D shapes. Students
will create a poster to display their findings. Display the
posters in the classroom. E
6) Present lessons of volume with water and different sizes and
shapes of containers. (Cylindrical, spherical, rectangular prism) E
7) Have students work in cooperative groups making predictions of
new containers’ capacities, collaborate and test out predictions.
Use formulas to calculate exact capacities and test out
calculations. Students will create a handwritten spreadsheet
of data collected. E
8) Have groups share their predictions and finding and have a
classroom discussion. R, T
9) Give a quiz on surface area and volume (open response). E-2
10)Partner students (2) and present them with a hands-on Excel
lesson; teaching them the basics. Allow them to have to time
experiment and collaborate with each other. E
11)Teacher models Excel expectations and desired functions. E
12) Give cooperative groups (4 members) the tasks, roles, and
scenarios of Ping’s Pools & Pads. H, E, O
13) Students work collaboratively in their groups designing the best
backyard and pool remembering the cost factor. Evaluate and give
feedback on the design and measurements. Students self and
peer assess their projects using rubrics. E-2, T
14) At the conclusion of the unit students will present their projects
to the class using PowerPoint (presentation criteria is listed).
Pre-Assessments
Students will need to know
fractions, squared & cubed
values, measurement,
application of data
(calculation of costs)—
adding/multiplication
Misconceptions: Longer the
pool the more volume it will
contain.
Progress Monitoring
Students will keep a daily log
of measurements and costs on
Excel, which will include
dimensions (surface area and
volume), materials (sod, pool
cost with specific range
dimensions) Students will
have mini presentations to
ensure they are
comprehending and sharing
information, many class
discussions and predictions,
along with a short quiz, and a
final pool and landscaping
package including a
PowerPoing presentation. (I
will have groups check-in 3
times with me: after pool
design, yard design, and cost
calculations.)
• What
are potential rough
spots and student
misunderstandings?
Technology--Using Excel
and becoming familiar with
operations. Group
collaboration--becoming
frustrated with others and
lack of communication.
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E-2, T
Formulas--not using them or
inserting them in Excel
correctly.
• How will students get the
feedback they need
Student Self-Evaluation
Peer Feedback Survey
Participation points,
presentation comments,
teacher walk
around/questioning to steer
them in the right direction,
group collaboration with other
groups
University of Arizona College of Education/MASTER-IP 9
your name, unit title
APPENDICES
Ping's Pools & Pads is an excellent 7th grade Geometry unit that includes business skills as well as 7th
grade content. A math teacher can easily blend this unit into his or her classroom and bring many more
elements such as writing, research, science, etc. into it as well. As it is set up right now it includes content such
as: surface area, volume and technology. The cooperative learning environments enable skills to develop such
as: communication, problem solving, essential questioning, deeper-level thinking, creativeness, innovation and
many more.
In my internship I was able to see how content, skills, and practices were used daily within many
different departments. The main department I focused on at Tucson Electric Power was the Engineering
Department. It was a great experience that was very different than what I was use to in the school setting.
Engineers were at a constant collaboration process when designing, developing, and implementing new material
into the plant. Formal and informal meetings were being held on a regular basis where problem solving,
questioning, inventiveness, data collection, as well as uses of technology were always present. As I saw these
practices taking place and I thought of how I could make my classroom successful within the math department
as well as preparing the students for the business world.
I believe this unit goes hand-in-hand with the classroom as well as my internship observations. There
are many 21st Century Learner skills being taught and used as well as the use of Excel, which are all excellent
business skills. This will open many new windows for the students being able to use Excel with their school
projects and home use. This is the first time many have ever even opened this program so it will be a great
introduction into the business world with this specific technology as well as all the other benefits from
cooperative learning environments.
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Appendix A1: Instrument #1 [Cooperative Environment Survey]
Questions
1. I enter my group with
a positive feeling.
2. I take initiative to start
group collaboration.
3. I know my role in my
group.
4. I use essential
questioning skills to start
discussions within my
group.
5. I like receiving peers'
feedback.
6. I feel comfortable with
group discussions.
7. I feel confident asking
my peers for their
opinion.
8. I find multiple ways of
solving problems.
9. I use other materials
(internet, book,
manipulatives, etc) as
resources in
collaborative learning.
10. I feel confident using
the knowledge from my
group in real-life
situations.
Almost Always
Usually
Sometimes
Rarely Almost Never
University of Arizona College of Education/MASTER-IP 11
your name, unit title
Appendix A2: Instrument #2 [Surface Area Quiz]
Name____________________________________ Date______________
Teacher_____________________________________
6.M.G.04
Represent three-dimensional figures using nets made up of rectangles
and triangles, and use the nets to find the surface area of these figures. Apply these
techniques in the context of solving real-world and mathematical problems.
1. The following net represents which type of solid?
a. rectangular prism
b. rectangular pyramid
c. cube
d. triangular prism
2. Using the net below, how many vertices does this solid contain?
a. 10 vertices
b. 6 vertices
c. 3 vertices
d. 5 vertices
3. What is the surface area of the solid represented in the net below?
a. 14 in2
b. 64 in2
c. 40 in2
d. 72 in2
2 in
2in
8 in
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4. Create a net for the given prism, then use the net to calculate the surface area of the solid.
5. Create a net for the given pyramid, then use the net to calculate the surface area of the solid.
4 cm
4 cm
3 cm
University of Arizona College of Education/MASTER-IP 13
your name, unit title
Appendix A3: Instrument #3 [Volume Quiz]
Name_________________________________ Date______________________
Teacher_______________________________
7.M.G.06
Solve real-world problems by calculating volume of 3-D objects
including cubes, right prisms and cylinders.
1) Ariel bought a large cube of bird feed to put out in her backyard for all the beautiful birds. One side of
the cube has an area of 9 square inches. What is the volume of the cube?
A) 27 cubic inches
B) 729 cubic inches
C) 81 cubic inches
D) 12 cubic inches
2) Garfield needs to buy some cat litter. His litter box has a base area of 216 square inches. The height is 6
inches. How many cubic inches of litter does he need to fill the box?
A) 648 cubic inches
B) 432 cubic inches
C) 1,296 cubic inches
D) 1,296 square inches
3) Bella received a large cube of chocolate as a wedding gift. The cube is 12 centimeters in height. She
wants to share it with Edward equally, so she cuts the cube in half to make two congruent triangular
prisms. What is the volume of one of the triangular prisms?
A) 1728 cubic centimeters
B) 144 cubic centimeters
C) 72 cubic centimeters
D) 864 cubic centimeters
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4) Sammy wants to fill his rectangular pool with vanilla pudding for a “sweet” wrestling match with his
friends. His pool has a square base with a width of 5 meters. The height is 6 meters. How many cubic
meters of vanilla pudding will he need to fill the pool?
5) Anna’s favorite snack is Crunch and Munch. Her mom buys her a big box for a special treat, and Anna
wants to figure out exactly how much of her sweet and salty snack is in the box. The box has a base area
of 18 square inches, and the height is 2 feet. How many cubic inches of snack fills the box
University of Arizona College of Education/MASTER-IP 15
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Appendix A4: Instrument #4 [Extended Response Rubric #4 & 5]
Math - Problem Solving : Ping\'s Pools & Pads
Teacher Name: Mrs. Ping
Student Name:
________________________________________
CATEGORY 4
Mathematical Concepts
3
2
1
Explanation shows
Explanation shows
Explanation shows
complete substantial understanding of some understanding of
understanding of the
the mathematical concepts
the mathematical
mathematical
used to solve the
concepts needed to
concepts used to solve
problem(s).
solve the problem(s).
the problem(s).
Explanation shows very
limited understanding of
the underlying concepts
needed to solve the
problem(s) OR is not
written.
Mathematical Reasoning
Uses complex and
refined mathematical
reasoning.
Uses effective mathematical
reasoning
Some evidence of
mathematical
reasoning.
Little evidence of
mathematical reasoning.
Explanation
Explanation is
detailed and clear.
Explanation is clear.
Explanation is a little
difficult to understand,
but includes critical
components.
Explanation is difficult to
understand and is
missing several
components OR was not
included.
Mathematical Terminology
and Notation
Correct terminology
and notation are
always used, making
it easy to understand
what was done.
Completion
All problems are
completed.
Correct terminology and
Correct terminology There is little use, or a lot
notation are usually used, and notation are used,
of inappropriate use, of
making it fairly easy to but it is sometimes not terminology and notation.
understand what was done.
easy to understand
what was done.
All but one of the problems
are completed.
All but two of the
problems are
completed.
Several of the problems
are not completed.
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Appendix A5: Instrument #5 [Surface Area & Volume Key]
6.M.G.04
1. c) cube
2. b) vertices
3. d) 72 in2
4.
5.
7.M.G.06
1. a) 27 cubic inches
2. c) 1,296 cubic inches
3. d) 864 cubic centimeters
4. 150 cubic meters
5. 432 cubic inches
University of Arizona College of Education/MASTER-IP 17
your name, unit title
Appendix A6: Instrument #6 [Cooperative Group Rubric]
Math - Problem Solving : Ping's Pools & Pads
Teacher Name: Mrs. Ping
Student Name:
________________________________________
CATEGORY 4
3
2
1
Working with
Others
Student was an engaged
partner, listening to
suggestions of others and
working cooperatively
throughout lesson.
Student was an engaged
partner but had trouble
listening to others
and/or working
cooperatively.
Student cooperated with Student did not
others, but needed
work effectively
prompting to stay onwith others.
task.
Use of
Manipulatives
Student always listens
and follows directions
and only uses
manipulatives as
instructed.
Student typically listens
and follows directions
and uses manipulatives
as instructed most of the
time.
Student sometimes
listens and follows
directions and uses
manipulatives
appropriately when
reminded.
Student rarely
listens and often
\"plays\" with the
manipulatives
instead of using
them as instructed.
Neatness and
Organization
The work is presented in
a neat, clear, organized
fashion that is easy to
read.
The work is presented in
a neat and organized
fashion that is usually
easy to read.
The work is presented in
an organized fashion but
may be hard to read at
times.
The work appears
sloppy and
unorganized. It is
hard to know what
information goes
together.
Checking
The work has been
checked by two
classmates and all
appropriate corrections
made.
The work has been
checked by one
classmate and all
appropriate corrections
made.
Work has been checked
by one classmate but
some corrections were
not made.
Work was not
checked by
classmate OR no
corrections were
made based on
feedback.
Diagrams and
Sketches
Diagrams and/or
sketches are clear and
greatly add to the
reader\'s understanding
of the procedure(s).
Diagrams and/or
sketches are clear and
easy to understand.
Diagrams and/or
sketches are somewhat
difficult to understand.
Diagrams and/or
sketches are
difficult to
understand or are
not used.
Explanation
Explanation is detailed
and clear.
Explanation is clear.
Explanation is a little
difficult to understand,
but includes critical
components.
Explanation is
difficult to
understand and is
missing several
components OR was
not included.
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Appendix A7: Instrument #7 [Spreadsheet of Pool and Yard Costs]
Pool Shapes
Cylindrical
Spherical
Rectangular
Prism
Rectangular
Pyramid
Cost
Pool
Length
$11,585.98 5-7 feet
$11,221.82 8-10 feet
$13,5879.71 11-13 feet
Cost
$10,7325.95 14-16 feet
Pool Width
Cost
Pool Depth
Cost
$358.40 5-7 feet
$578.23 8-10 feet
$786.14 11-13 feet
$358.40
$578.23
$786.14
3-5 feet
6-8 feet
9-11 feet
$358.40
$578.23
$786.14
$982.75 14-16 feet
$982.75
13-15 feet
$982.75
There are 748 gallons of water in 100 cubic feet.
1 gallon of water costs $.07. or 7 cents
Chemicals needed are $35.78 per gallon-- every 500 gallons of water needs 1 gallon of chemical
Pool Extras
Diving Board
Water Fall
Hot tub
Pool Chairs
Slide
Cost
$494.98
$695.75
$6,785.94
$120.00 each
$982.98
Sales Tax is 10.1%
Sod
Evergreen Turf
Green Valley Sod
Cost
$.18 per square foot
$ .22 per square foot
Rock
Red Rock
Pea Gravel
Crushed Granite
Cost
$. 23 per square foot (3 in. deep)
$. 28 per square foot (3 in. deep)
$. 35 per square foot (3 in. deep)