StealingFromTheSun.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and 1 Science Partnership Grant Program NCLB Title II Part B Revised 8/13/12

Mathematics Senior Level Capstone Course Unit Overview

Title of Unit: Stealing from the Sun Unit Designers:

Kristin Vaughn, Page County Lisa Rosazza, Page County Tiffany Comer, Page County Pam Walker, Page County Laura Hansen, Culpeper County Context:

Summary of the issue, challenge, investigation, or problem.

Your school superintendent wants to know if using solar energy will help meet budget requirements. Your class has been requested to research, analyze, and recommend whether or not to invest in solar panels as an energy source for your school.

Number of Class Hours: 11

11 hours Unit

Design: ___Task Based __X_Project Based Other Subject

Areas/Disciplines Addressed:

Economics, science, vocational education

Driving Question: Would solar panels be a worthwhile investment for your school? Mathematics Content

Addressed:

Interpret graphs and data, write mathematical models such as a quadratic equation to predict future energy production, generate and interpret statistical tests, calculate area and cost per square foot.

MPE Addressed:

Problem Solving, Decision Making and Integration; Understanding and Applying Functions; Procedure and Calculation Assumption of Prior

Knowledge:

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College and Career Readiness/21st Century Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37

Collaboration E and A Research E

Communication (Oral and/or Written) E and A Technology E

Critical Thinking/Decision Making T and A Other: (Describe)

Major Products and/or Performances:

Group: Each group will present their final mathematically sound argument to a mock school board panel, regarding the viability of using solar energy to power the school.

Presentation Audience:

x Class

School

Individual Expert

Community

x Other: Mock Local School Board

Launch: Event or experience used to engage the students interest and inquiry:

http://community.myvoa.com/_Teens-Raise-Funds-for-Solar-Power-on-School-Roof/VIDEO/734079/45137.html

This video (Teens Raise Funds for Solar Power) shows how students from

another Virginia high school have studied solar energy and generated funds to purchase solar panels for their

high school.

Evaluation: Formative Assessments (During the Unit)

Interview Practice Presentations x

Mathematicians Journal x Notes

Preliminary

Plans/Outlines/Prototypes

Checklists

Rough Drafts x Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Presentation materials and diagrams with a rubric

x Peer Evaluation, with a rubric

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Oral Presentation with a rubric x Self Evaluation, with a rubric

x

Other Product(s) or

Performance(s), with a rubric

Other:

Resources Needed: On-site people, facilities:

Equipment/Technology: Graphing calculator and computer with Excel, internet access Materials: Graph paper, poster board

Community Resources:

Reflection Methods: Individual, Group, and/or Whole Class

Mathematicians Journal x Small/Focus Groups x

Whole Class Discussions x Fishbowl Discussions

Survey Other:

Material Adapted From:

http://www.sunrisesunset.com/calendar.asp?comb_city_info=Luray%2C%20Virginia;78.4553;38.6647;-5;1&month=7&year=2011&time_type=0&want_mphase=1&wadj=1

http://www.thehousedesigners.com/plan/7726/

http://www.sunviewer.net/portals/NYSERDA/

Shenandoah Valley Electric Coop. for sample electric bill included as HO#3b

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Virginia’s Senior Level Capstone Course Instructional Plan

Unit Title: Stealing from the Sun

Driving Question: Would solar panels be worthwhile for our school? Project: Students are challenged to investigate solar energy as a supplemental energy source for their high school. The final product is to create a convincing presentation of their findings to a mock school board.

ENGAGE How will student’s interested be peaked so they want to engage in the inquiry in this unit?

Number of hours 0.25

Begin this project viewing the video : Teens Raise Funds for

Solar Power

http://community.myvoa.com/_Teens-Raise-Funds-for-Solar-Power-on-School-Roof/VIDEO/734079/45137.html

This video (Teens Raise Funds for Solar Power) shows how

students from another Virginia high school have studied solar

energy and generated funds to purchase solar panels for their

high school.

To launch this activity, initiate a discussion with the class about different energy sources and their impressions of the need to seek alternative energy sources. Begin to focus the discussion on solar energy. Would the use of solar energy be possible in their region? What are some the advantages of solar energy for their area? Disadvantages?

Mathematician Journal Prompts What things would we need to know in order to decide if solar power is worthwhile for our school? EXPLORE Teacher provides guidance for the explorations to prepare students with the

knowledge and skills to engage in the task.

Exploration 1: Graphs of Solar Panels

Following this discussion, students work in small groups to analyze the shape of a graph that represents time of day and power produced from 18 solar panels currently being used by a local county building. They can use the graphs to predict the amount of energy that could be produced in different scenarios per panel. They are to complete the Graphs of Solar Panels worksheet, HO #1. The teacher should see students recognize the type of function each graph represents and use the labeled axes to get a quantitative idea of the amount of energy produced by the panels. After

completing the worksheet, each group elects a spokesperson to share their predictions with the entire class. The teacher should summarize their findings if necessary and encourage students to consider factors such as weather, and local topography. Students are to record their individual reflections in a journal (see journal prompts).

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Students will self-assess on the prior knowledge and skills assumed for the unit

Number of hours: 4

Tutorial: Additional resources for interpreting graphs, scatterplots and curve of best fit are attached. See Sites for Assessing and Remediating Skill Areas HO #7

Exploration 2: Analyzing Data

To transition to this exploration, ask students what key elements can be derived from graphical displays. Look for comments on the shape, center and spread of the data. To get a closer analysis, it is helpful to see the data in a table. In this exploration students continue to work in groups to compare data from two different locations using Analyzing Data from 2010 HO #2. Students decide what is typical for the amount of power that is produced in one year per panel. Student groups share their results on poster board for the class, this time asking each person in the group to explain a part of the summary.

Note: As a result of the journal prompt we are hoping that students will answer questions such as: “What trends do you see during the year? Which months appear to be more productive? Which months are less productive? What factors may contribute to productivity? How much energy might be produced in a given year? How much energy is produced per panel? “ If students do not generate these items, the teacher can prompt them with questions.

The teacher should look for the calculation of summary statistics such as mean, median, range, standard deviation.

Tutorial: Additional resources for measures of central tendency are attached. See Sites for Assessing and Remediating Skill Areas HO #7

Exploration 3: How much Energy do you need?

To recognize the amount of energy required to operate a high school, students examine a smaller, more familiar space, an average size home. Ask students to brainstorm the amount of energy they think would be required for their individual home. After that discussion, show them Sample Ranch Style House HO#3a and HO#3b.

Students continue to work in small groups. Give each student a floor plan of a ranch style house and the sample energy bill for that house. They are to determine the square footage of the house, average energy use, and average yearly power needed. They can then use this information to determine a ratio of power to square footage. The teacher should see students calculating area, ratios and proportions.

After completing the journal topic (see journal prompt), students elect a spokesperson for their group and share their ideas to the class.

What trends did you observe during the year? What might have explained some of these trends?

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Additional resources for area are attached. See Sites for Assessing and Remediating Skill Areas HO #7

Exploration 4: Materials To Get the Job Done

As an extension to Exploration 3, students use Sample Ranch Style House (HO #4) to determine the amount of solar panels needed to power the sample house, and if it is possible to fully power the house with solar energy. Students calculate the area of the roof and the area of each solar panel, and then determine the number of solar panels that could be used. (The Pythagorean Theorem can be used to determine the height of the roof.) A spokesperson for each group shares their conclusions to the class. The teacher should lead the class to a consensus based on the individual groups’ calculations. A discussion of cost versus benefit should be included and options such as adding solar energy as a supplement to the existing energy source should be considered.

What steps must be taken to determine the amount of solar panels needed for a given structure?

EXPLAIN Teacher introduces the main task of the unit and prepares students to work independently in small groups…

Number of Hours: 0.5

The teacher assigns students to groups of 3–4 students. The teacher launches the project with the following statement to the students;

“You have been asked by your local school district to determine if solar power is worthwhile for your school. You have found the power produced, cost, and necessary space needed for solar energy. Your job is to create a mathematically sound argument that would persuade the school board to use or not to use solar energy. This argument must include a cost-benefit analysis using calculations similar to what you have done in the previous explorations.”

The students are directed to create a presentation with visual aids, such as graphs, data tables and calculations that will be presented orally to a mock school board. Documentation of any reference materials or websites must be included in the written portion of the presentation.

Students should be encouraged to use technology software such as PowerPoint or video if available, but other presentation devices are acceptable. A rough draft of the presentation will be reviewed by the teacher with the students.

Use of the school’s library or technology center for additional reference materials should be made available during class time. The teacher gives out Stealing from the Sun Student Project Overview and Expectations HO#8a and HO#8b to the class to clearly explain the project’s goals and scope.

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A reminder of effective group dynamics should be reviewed. Each group member should be designated a task. Show the rubric, Peer/Self-Evaluation Form: Stealing from the Sun HO#6, to clearly state how students will evaluate each other.

The grade for this project is based on both the Summative Assessment and the Peer/Self-Evaluation forms.

After groups have had a chance to make some initial decisions, it is suggested that students be given a chance to visit other groups to learn from their arguments.

Student groups must submit a presentation outline to the teacher for review and approval before completing the project.

ELABORATE The student groups are working independently with teacher consultations. Number of Hours: 4.5

As student groups work, the teacher can assist by checking calculations, grammar, spelling and developing a logical, coherent argument. Using the formative assessment rubric as their guide, students know what needs to be included in order for the

presentation to be complete. Students are encouraged to practice their presentations to friends and family members prior to their final presentation to the mock school board.

Mathematician Journal Prompts Think about the tasks that you have completed so far in this unit. What do you think would be the best decision for the school board to make? Support your stand.

EVALUATE Working groups submit products or make

presentations

Number of Hours: 1.5

The final presentation is graded using the attached rubrics. The rubrics measure their presentation skills, analysis, mathematical data and calculations, ability to make a sound argument, use of visuals, and group work.

Rubric for teacher and/or audience for presentation (HO #5) Rubric for student/peer evaluation (HO #6)

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Map the Unit

What do students need to know and be able to do to complete the task/project/problem successfully? How and when will they assess their own necessary knowledge and skills? How will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major task for the unit and analyze the tasks necessary to produce a high-quality product.

Task:

You have been asked by your local school district to determine if solar power is worthwhile for your school. Your job is to create a mathematically sound argument that would persuade the school board to use or not to use solar energy.

KNOWLEDGE AND SKILLS NEEDED Assumed already learned

Students will self-assess

Will be taught during the unit 1. Interpreting graphs (including domain,

range, continuous, discontinuous)

x x

2. Measures of central tendency x x

3. Ratios and Proportions x x

4. Area x x

5. Pythagorean Theorem x x

6.

7.

8.

9.

10.

11.

What project tools will student’s use?  Know/need to know lists  Daily goal sheet

X Mathematician’s Journals  Briefs/Memos

 Task lists

 Planning Calendar

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HO #1 Solar Panel Graphs

To complete this activity you can use the following website to determine the length of a day: http://www.sunrisesunset.com/calendar.asp?comb_city_info=Luray%2C%20Virginia;78.4553;38 .6647;-5;1&month=7&year=2011&time_type=0&want_mphase=1&wadj=1

July 21, 2011 (power produced by 18 panels)

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1. What is the domain of each function? Explain what the domain stands for. Label it on the graph.

2. What is the range of each function? Explain the range. Label it on the graph.

3. Would you say these graphs are continuous or discontinuous?

4. Both graphs show output from the same solar panels on different days, what do

you think would explain the differences in the graphs?

5. Both of these graphs are taken in July, predict what a graph in December on a

sunny day would look like. Predict what a blizzard in March would look like.

6. How would these graphs be used to help someone decide if solar energy is right

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HO #2 Analyzing Data for 2010 The tables below indicate power generated by solar panels at two different sites. Each table

shows monthly output for 2010 in KWH. Both sites contain 8 solar panels. Analyze the data given to help us learn more about solar power generated. Depict your findings on a poster display to share with other groups.

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HO #3a

Sample Ranch Style House

In this activity, your job is to determine the average yearly power (in kilowatt hours) needed to power this house. You have been given the floor plan and an electric bill that details electrical usage. Determine the amount of power being used per square foot. Note: The porch measures 12’ x 6’-6”.

21 ft

10 ft

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HO #3b

Sample Electric Bill

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HO #4

Sample Ranch Style House

The typical installation of solar panels is on roofs of buildings. Solar panels must face south. Using information from the previous activity:

Determine how many solar panels are needed to power this house. Is it possible for this house to be fully

powered by solar energy? If not, will there be any month(s) where this is possible?

21 ft

10 ft

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HO #5

Stealing from the Sun: Summative Assessment (End of Project)

Teacher Name: _______________ _______________

Student Name: ________________________________________

CATEGORY 4 3 2 1

Mathematical Concepts Explanation shows complete understanding of the mathematical concepts used to determine most economical use of solar energy.

Explanation shows substantial

understanding of the mathematical concepts used to determine most economical use of solar energy

Explanation shows some

Explanation shows very limited understanding of the mathematical concepts used to determine most economical use of solar energy Mathematical

Reasoning

Uses complex and refined

mathematical reasoning to choose the best energy source.

Uses effective mathematical reasoning to choose the best energy source.

Some evidence of mathematical reasoning to choose the best energy source.

Little evidence of mathematical reasoning to choose the best energy source.

Explanation Explanation is detailed and clear to justify their conclusion mathematically.

Explanation is clear to justify their conclusion

mathematically.

Explanation is a little difficult to understand, but includes critical components to justify conclusion. Explanation is difficult to understand and is missing several components OR was not included. Strategy/Procedures Uses an efficient

and effective strategy to solve the problem(s).

Typically, uses an effective strategy to solve the problem(s).

Sometimes uses an effective strategy to solve problems, but does not do it consistently.

Rarely uses an effective strategy to solve problems.

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.

Diagrams and Sketches

Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s).

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HO #6

Peer/Self-Evaluation form: Stealing from the Sun

The following is a list of statements to be answered by you and about each of your group

members. Think carefully about assigning rating values for each of the statements.

1- Strongly Agree

2- Agree

3- Neutral

4- Disagree

5- Strongly Disagree

Self:

Teammate:

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HO #7

Sites for assessing and remediating skill areas Interpreting graphs:

Domain and range remediate:

http://www.mathdemos.org/mathdemos/domainrange/domainrange.html

http://www.intmath.com/functions-and-graphs/2a-domain-and-range.php

Continuous or discontinuous remediate:

http://www.intmath.com/functions-and-graphs/7-continuous-discontinuous-functions.php

http://www.bbc.co.uk/schools/ks3bitesize/science/organisms_behaviour_health/variation_classifi cation/revise3.shtml

Measures of central tendency: Assess:

http://onlinestatbook.com/chapter3/measuresq.html Remediate:

http://cnx.org/content/m11061/latest/

Scatter plots: Remediate:

http://www.corvallis.k12.mt.us/high/staff/brockh/IntSciWorksheets/how%20to%20graph.pdf http://mste.illinois.edu/courses/ci330ms/youtsey/scatterinfo.html

Curve of best fit: Remediate:

http://fym.la.asu.edu/~tturner/MAT_117_online/Regression/Linear%20Regression%20Using%20 the%20TI-83%20Calculator.htm

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Area:

Assess and remediate: http://www.mathsisfun.com/area.html

Remediate:

http://www.helpingwithmath.com/by_subject/geometry/geo_area.htm

Pythagorean Theorem:

Assess:

http://www.crctlessons.com/Pythagorean-theorem-test.html

Remediate:

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HO #8a

Stealing from the Sun Student Project Overview and Expectations

Project Overview and Expectations:

You have been asked by your local school district to determine if solar power is

worthwhile for your school. Your class has been requested to research, analyze, and

recommend whether or not to invest in solar panels as an energy source for your school.

You will need to determine power and spatial requirements and associated costs needed

for solar energy. Your job is to create a mathematically sound argument that would

persuade the school board to use or not to use solar energy.

This argument must include a cost-benefit analysis using calculations you find in your

research. You are required create a presentation with visual aids, such as graphs, data

tables and calculations that will be presented orally to a mock school board.

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HO #8b