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University of Arizona College of Education/MASTER-IPUbD Workshop for AAPT your name, unit title

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Ping's Pools & Pads

Cassandra Ping

TTE 596C/Dr. Olsen

2 UBD WORKSHOP FOR AAPT

Stage 1 – Desired ResultsEstablished Goals

What content standards and program goals will the unit address?

6.M.G.04Standard: 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.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.06Standard: 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 real-world problems by calculating volume of 3-D objects including cubes and right prisms.

7.Technology.Strand6.Concept2.PO3Students will select and use applications effectively andproductively.Students will enter data using simple formulas while using spreadsheets to perform calculations.

Transfer

Mathematical principles can be used along with technology tools to make real-world decisions.

MeaningUnderstandings

Nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for models of polyhedra to be constructed (Wikipedia)

A net is a two-dimensional representation, or pattern, of a three-dimensional figure that can be folded to form the figure.

Surface area and volume can be computed for all 3-Dimensional 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 (Wikipedia)

Mathematics is a language that can be used for communication, constructing arguments, and critiquing the work of others.

Technology tools, such as Excel, can assist in the work of doing mathematics.

Essential Questions

What is the purpose of finding surface area?

How can you construct a net of a 3-D solid?

Why is it necessary to understand volume?

How is Excel useful in solving mathematical problems?

AcquisitionStudents will know …

6.M.G.04 3-D shapes are solids that

have 3 dimensions height, width, & length.

Rectangular prism is a solid (3-dimentional) object, which has six faces that are rectangles.

Triangular prism is composed of two triangular

Students will be skilled at

6.M.G.04

Constructing a mathematical model

Describing 3D figures using edges, vertices and faces

Testing mathematical conjectures

7.M.G.06b

Julia Olsen, 08/15/13,

This is a lot, but ok


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bases and three rectangular sides.

Pyramid is a polyhedron that has three or more triangular faces that share a common vertex.

Edge is a line where two surfaces meet.

Vertex (vertices) is a point where two or more straight lines meet. A corner.

Face is any of the individual surfaces of a solid object.

Base is the lowest part 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 two-dimensional object.

Volume is the amount of space a three-dimensional object occupies (sphere, pyramid, prism, cylinder, cone)

Cubed units are the measurement used to determine the volume of a three-dimensional object. .

Polygons a two-dimensional 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

Calculating surface area and volume of a 3-Dimensional shape

Using Excel to calculate formulas for surface area and volume of figures

7.T.Strand 6. Concept 2.PO3 Using basic functions of a

computer Opening and closing

documents Entering data into cells in

Excel Creating formulas in Excel


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Stage 2 - AssessmentsPerformance 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 PowerPointDuring 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)*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.


Ok you specified each section hre


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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-210)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. E12) Give cooperative groups (4 members) the tasks, roles, and

scenarios of Ping’s Pools & Pads. H, E, O13) 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

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. Formulas--not using them or inserting them in Excel correctly.

• How will students get the feedback they need

Student Self-EvaluationPeer Feedback Survey

Participation points, presentation comments, teacher walk around/questioning to steer them in the right direction, group collaboration with other groups


Word choice? Absolutely, perhaps


listed). E-2, T


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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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UBD WORKSHOP FOR AAPT

Appendix A1: Instrument #1 [Cooperative Environment Survey]

Questions Almost Always Usually Sometimes Rarely Almost Never1. 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.


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Appendix A2: Instrument #2 [Surface Area Quiz]

Name____________________________________ Date______________Teacher_____________________________________

6.M.G.04Represent three-dimensional figures using nets made up of rectanglesand triangles, and use the nets to find the surface area of these figures. Apply thesetechniques in the context of solving real-world and mathematical problems.

1. The following net represents which type of solid?

a. rectangular prism b. rectangular pyramidc. cubed. triangular prism

2. Using the net below, how many vertices does this solid contain?

a. 10 verticesb. 6 verticesc. 3 verticesd. 5 vertices

3. What is the surface area of the solid represented in the net below?

a. 14 in2b. 64 in2c. 40 in2d. 72 in2

2in

8 in

2 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


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Appendix A3: Instrument #3 [Volume Quiz]

Name_________________________________ Date______________________Teacher_______________________________

7.M.G.06 Solve real-world problems by calculating volume of 3-D objectsincluding 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 inchesB) 729 cubic inchesC) 81 cubic inchesD) 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 inchesB) 432 cubic inchesC) 1,296 cubic inchesD) 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 centimetersB) 144 cubic centimetersC) 72 cubic centimetersD) 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


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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 3 2 1

Mathematical Concepts Explanation shows complete

understanding of the mathematical

concepts used to solve the problem(s).

Explanation shows substantial understanding of

the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of

the mathematical concepts needed to

solve 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 Terminologyand Notation

Correct terminology and notation are

always used, making it easy to understand

what was done.

Correct terminology and notation are usually used,

making it fairly easy to understand what was done.

Correct terminology and notation are used, but it is sometimes not

easy to understand what was done.

There is little use, or a lot of inappropriate use, of

terminology and notation.

Completion All problems are completed.

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) cube2. b) vertices3. d) 72 in24.

5.

7.M.G.06

1. a) 27 cubic inches2. c) 1,296 cubic inches3. d) 864 cubic centimeters4. 150 cubic meters5. 432 cubic inches


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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 others, but needed prompting to stay on-task.

Student did not work effectively with others.

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 Cost Pool Length Cost Pool Width Cost Pool Depth CostCylindrical $11,585.98 5-7 feet $358.40 5-7 feet $358.40 3-5 feet $358.40Spherical $11,221.82 8-10 feet $578.23 8-10 feet $578.23 6-8 feet $578.23Rectangular Prism

$13,5879.71 11-13 feet $786.14 11-13 feet $786.14 9-11 feet $786.14

Rectangular Pyramid

$10,7325.95 14-16 feet $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 CostDiving Board $494.98Water Fall $695.75Hot tub $6,785.94Pool Chairs $120.00 eachSlide $982.98

Sales Tax is 10.1%

Sod CostEvergreen Turf $.18 per square footGreen Valley Sod $ .22 per square foot

Rock CostRed Rock $. 23 per square foot (3 in. deep)Pea Gravel $. 28 per square foot (3 in. deep)Crushed Granite $. 35 per square foot (3 in. deep)

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