Is This the Best.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B Revised 12/11/12

1 Mathematics Senior Level Capstone Course

Unit Overview

Title of Unit: Is This the Best? Unit Designers:

Frederick County Schools Erin Hopple

Judy Cain Meredith Zirkle Joe Hamaker Context:

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

Students will select between buying a car, choosing a college or choosing a career path. Students will identify criteria, research the information for the criteria and analyze their criteria using a decision-making matrix. Students will make and justify their decision based on their analysis.

Number of Class

Hours: 10.5 hours

Unit

Design: ___Task Based _X Project Based Other Subject

Areas/Disciplines Addressed:

Career and technical education, economics, statistics

Driving Question: When you are faced with an important decision, how do you decide what to do? How do you know you made the right choice?

Mathematics Content Addressed:

Matrices, statistical experimental design MPE

Addressed:

Problem solving, Decision making and Integration Assumption of Prior

Knowledge:

Matrices

College and Career Readiness/21st Century

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2 Skills to be taught (T)

during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37

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

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

Major Products and/or Performances:

Group: Power Point, oral presentation Presentation Audience:

X Class

School

Individual: Mathematician’s journal Expert

Community Other:

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

Debate over what is the best sports team.

ESPN site espn.go.com/sportsnation/teamrankings

Evaluation: Formative Assessments (During the Unit)

Interview Practice Presentations

Mathematicians Journal X Notes

Preliminary

Plans/Outlines/Prototypes X

Checklists

Rough Drafts Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Written Products, with a rubric Peer Evaluation, with a rubric

Oral Presentation with a rubric

X Self Evaluation, with a rubric

Other Product(s) or

Performance(s), with a rubric X

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3 Resources Needed: On-site people, facilities: Facilitator/Teacher

Equipment/Technology: Computers with presentation and spreadsheet software; Internet access

Materials:

Community Resources:

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

Mathematicians Journal X Small/Focus Groups Whole Class Discussions X Fishbowl Discussions

Survey Other:

Material Adapted From:

“Decision Matrices Projects”, Diane Leighty

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4 Virginia’s Senior Level Capstone Course

Instructional Plan Unit Title: Is This the Best?

Driving Question: When you are faced with an important decision, how do you decide what to do? How do you know you made the right choice?

Task/Project/Problem: Project

ENGAGE How will student’s interested be peaked so they want to engage in the inquiry in this unit? Number of hours: 30 minutes

Students will be asked which is the best professional sports team in North America. The class will debate the suggestions offered.

Directions for Instructor:

 Focus the discussion on the criteria used to make the students’ choices.

 Discuss similarities and differences in the criteria students used.

 After debate, show example from ESPN, the Magazine’s rankings of the top professional sports franchises

Materials and/or Resources Needed:

 ESPN site espn.go.com/sportsnation/teamrankings

No HO for this activity.

Anticipated products and artifacts if any: journal prompt

Mathematician Journal Prompts What criteria would you use to justify your choice for the best professional sports team in North America? EXPLORE Teacher provides guidance for the explorations to prepare students with the knowledge and skills to engage in the task. Students will self-assess on the prior knowledge and skills assumed for the unit

Explore Task 1: Choosing a Fast Food Restaurant: Introduction to a Decision Matrix (HO#1) Goal of activity:

 To introduce a decision matrix

 To transition to a spreadsheet decision matrix

Description of activity:

 Teacher should work through the handout with students.

 Students will choose their own restaurants and criteria so answers are open-ended.

Materials/Equipment/Resources Needed:  Copies of HO#1

 Computer access with spreadsheet software

Student self-assessment of skills required for unit and

Mathematician Journal Prompts Describe the difficulties you had in the

completion of this task and how you overcame them

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5 Number of

hours: 5 total (3 for Part 1 and 2 for Part 2)

recommendations for tutorial and/or practice:

 Excel tutorial: www.free-training-tutorial.com  PowerPoint tutorial : www.free-training-tutorial.com

 Help students through the worksheet, modeling and assisting as needed.

 Students’ answers will vary based on their restaurants and criteria.

Teachers questions, anticipated reactions and results:  Students may have difficulty with Part 2 of HO#1.

Difficulties will include reciprocal values and location within the matrix.

 Students may not have had experience with spreadsheets, specifically inserting formulas Student Direction(s) Sheet Attached: HO#1

Anticipated products and artifacts:  Completed handout  Completed spreadsheet

__________________________________________________ Explore Task 2: Choosing the Best Cell Phone Plan(HO#2) Goal of activity:

 Reinforce students’ ability to create a decision matrix with minimal teacher assistance.

Description of activity:

 Students will create their own decision matrix on the topic of choosing a cell phone provider and plan.  Students will access the Internet to research cell phone

providers and plans.

Materials/Equipment/Resources Needed:  Copies of HO#2

 Internet access

 Computer access with spreadsheet software

Student self-assessment of skills required for unit and recommendations for tutorial and/or practice: none Directions for Instructor:

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6 create their decision matrix.

 Teacher should provide minimal assistance.  Students’ answers will vary based on their research

and criteria.

 Differentiation: Teacher can provide students with different cell phone plans, so they have data to work with, rather than finding the data themselves, or teachers can have students research the topic on their own.

o Websites that teachers can use for data collection:

o http://www.verizonwireless.com/b2c/explore/ ?page=choosing-a-plan

o http://www.wireless.att.com/cell-phone- service/cell-phone-plans/?wtSlotClick=1-0060AN-0-5

o http://www.sprint.com/index_p.html o

http://www.bestbuy.com/site/Mobile-Cell-

Phones/No-Contract-Phones/abcat0801002.c?id=abcat0801002 o

http://www.t-mobile.com/shop/plans/cell-phone-plans-overview.aspx

Student Direction(s) Sheet Attached: HO#2 Anticipated products and artifacts:

 Completed handout  Completed spreadsheet

EXPLAIN Teacher introduces the main task of the unit and

prepares students to in small group independent work... Number of Hours: 30 minutes

“Is This the Best?”

Students will choose a topic for their final project. Teacher will provide some options for the topic, but students may choose their own topic with teacher approval. Teacher topics include choosing a car, a college, or a career.

Students will work in groups to create a presentation, using presentation software, explaining their decision matrix and results for their topic.

Describe the expectations for how students will work in their group:

 Students will reach consensus on the criteria to be used in the decision matrix.

Task/Project/Problem: Student HO #3

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7 Skills or knowledge needed:

 How to make and use a decision matrix  How to research the chosen topic  How to use spreadsheet software  How to use presentation software

Materials/Equipment/Resources Needed:  copies of HO#3

 Internet access

 Computer access and spreadsheet software

 Meet with each group to approve the chosen topic.

ELABORATE The student groups are working independently with teacher consultations. Number of Hours: 4

Describe what the teacher will be doing during this time:  Monitor group progress

 Address technical difficulties

Formative Assessments: none

Anticipated Products and Artifacts Described: HO#3 Rubric(s) for self-evaluation of product: none Tools for Students to Use in Planning: HO #3

Mathematician Journal Prompts At this point in your project, what difficulties have you encountered? What could I, as the teacher, or you, as the student have done to ease these difficulties? EVALUATE Working groups submit products or make presentations Number of Hours: 1.5

Directions for Instructor regarding final evaluation: Each group will create a presentation, using presentation software that will be presented to the class.

Rubric for teacher for final project: HO#4 Rubric for teacher for presentation: HO#5

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8 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:

KNOWLEDGE AND SKILLS NEEDED Assumed already learned Students will self-assess Will be taught during the unit 1. Create a decision matrix on paper.

X 2. Create a decision matrix using spreadsheet

software. X

3. Conduct research on the Internet.

X 4. Create a presentation, using presentation

software. X

5. Basic functionality skills for spreadsheet

software X

6. Basic functionality skills for electronic

presentation software. X

7. Interpreting and organizing information

that is retrieved from the Internet. X X

8.

9.

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

 Mathematician’s Journals  Briefs/Memos

 Task lists

 Planning Calendar

□ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ Attachments:

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9 HO #1

Choosing a Fast Food Restaurant: Introduction to a Decision Matrix

In the following problem you will be deciding the best fast food restaurant. There is no right answer as different people like different foods. What you will be finding is the best fast food restaurant for you. Part 1: Developing the restaurant matrix

1. Choose 5 fast food restaurants to compare.

2. Identify some criteria to use to compare these restaurants. Examples: cost, variety, quality, etc.

3. Make a table (matrix) ranking each restaurant from 5 (this restaurant is the best on that criteria) to 1 (this restaurant is the worst on that criteria). Note: you may not need all the columns on the table. Restaurant

Name

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10 Part 2: Developing the weighting matrix

4. People differ in what they consider the most important criteria to choose a restaurant. Cost may be more important than the quality of food if you don’t have much money. Distance to the restaurant may be the most important criteria of you have a limited amount of time to eat. In the following matrix, you will be comparing the restaurant rating criteria according to what is most important to you. Put the criteria across the top then repeat the criteria in the same order down the side.

Criteria Cost Variety

Cost 1

Variety 1

1

Total

5. Fill in the matrix using this rating system:

1 Top criteria and side criteria are equally important

2 Top criteria is very slightly more important than side criteria 3 Top criteria is somewhat more important than side criteria 4 Top criteria is definitely more important than side criteria 5 Top criteria is absolutely more important than side criteria Notes:

 Since the diagonal compares the same criteria, it will be filled with 1’s.

 If the top criteria is less important then use the reciprocal of the rating (½, 1/3, ¼, or 1/5).  If you fill in one side of the diagonal of the matrix first, the other side can easily be filled in

with the reciprocals.

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11 6. Convert the table to percentages by dividing each cell by its column total. Leave your answers in

decimal form and record them here.

Criteria Cost Variety

Cost Variety

7. To calculate the weighting for each criteria, average each row in the preceding matrix. Record your answers here.

Criteria Weight

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12 Part 3: Deciding the best restaurant for you

8. Refer back to your first matrix containing the 5 fast food restaurants and the ranked criteria. If you multiply each row by your weights from above, you will give each restaurant a final score that can be used to decide the restaurant that best meets your needs. Record your results here.

Restaurant Name Final Score

9. What is the best restaurant for you? Do you agree with this result? Why or why not?

Part 4: Using EXCEL to make a decision matrix spreadsheet.

Note: The screen shots are examples and will not be the same information as your matrix. Be sure to note the fx line to see formulas.

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13 11. Enter your fast food restaurant matrix into SHEET 1. Include all row and column headings. Change

the sheet name to FAST FOOD RESTAURANTS.

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14 13. Copy the criteria matrix into another location on CRITERIA WEIGHTING (SHEET 2). Change each

cell to a percentage by using the appropriate formula. Add a column to the matrix to average each row. Be sure to use AVG to do the calculation. Title the column of averages WEIGHT.

14. Copy your fast food restaurant matrix and weight matrix into SHEET 3. In a different section of SHEET 3, make row and column headings for restaurant names and final scores. Multiply your matrices together using formulas and store the results under these headings. Change the sheet name to

FINAL SCORES.

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15 HO #1 (Teacher Guide)

Note: These restaurants, criteria, and weightings are examples of what you may get in class. They are based on the opinions of the teacher who made the worksheet. They may be modified to fit the needs of your students.

Choosing a Fast Food Restaurant: Introduction to a Decision Matrix

In the following problem you will be deciding the best fast food restaurant. There is no right answer as different people like different foods. What you will be finding is the best fast food restaurant for you. Part 1: Developing the restaurant matrix

1. Choose 5 fast food restaurants to compare.

Chick-Fil-A McDonalds Taco Bell Burger King Hardee’s

2. Identify some criteria to use to compare these restaurants. Examples: cost, variety, quality, etc.

Cost Variety Quality Setting Type Food Delivery Time

3. Make a table (matrix) ranking each restaurant from 5 (this restaurant is the best on that criteria) to 1 (this restaurant is the worst on that criteria). Note: you may not need all the columns on the table. Restaurant

Name

Criteria

Cost Variety Quality Setting Type Food Delivery

Time

Chick-Fil-A 1 3 5 5 3 0

McDonalds 5 1 1 2 1 0

Taco Bell 4 4 3 3 4 0

Burger King 3 2 2 1 2 0

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4. People differ in what they consider the most important criteria to choose a restaurant. Cost may be more important than the quality of food if you don’t have much money. Distance to the restaurant may be the most important criteria of you have a limited amount of time to eat. In the following matrix, you will be comparing the restaurant rating criteria according to what is most important to you. Put the criteria across the top then repeat the criteria in the same order down the side.

Criteria Cost Variety Quality Setting Type Food Delivery

Time

Cost Variety Quality

Setting

Type Food

Delivery Time

Total

2 Top criteria is very slightly more important than side criteria 3 Top criteria is somewhat more important than side criteria 4 Top criteria is definitely more important than side criteria 5 Top criteria is absolutely more important than side criteria Notes:

 Since the diagonal compares the same criteria, it will be filled with 1’s.

 If the top criteria is less important then use the reciprocal of the rating (½, 1/3, ¼, or 1/5).  If you fill in one side of the diagonal of the matrix first, the other side can easily be filled in

with the reciprocals.

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17 Reciprocals are color-coded to show the pattern. It is suggested that the table be completed with a row and reciprocal column at the same time to help students see the reciprocal locations. The completed example can be seen in the spreadsheet on Problem 13.

Criteria Cost Variety Quality Setting Type Food Delivery

Time

Cost 1 3 4 3 3 1

Variety 1/3 1 4 2 1/2 1/5

Quality 1/4 1/4 1

Setting 1/3 1/2 2 1

Type Food 1/3 2 1

Delivery

Time 1 5 1

Total 3.25 11.75

6. Convert the table to percentages be dividing each cell by its column total. Leave your answers in decimal form and record them here. All columns should total to 1.00 if calculations are correct.

Criteria Cost Variety Quality Setting Type

Food

Delivery Time

Cost 1 3.25 0.31 3 11.75 0.26 4 20.00 0.20 0.26 0.22 0.36 Variety 1 _3.25 _0.10

3  0.09 0.20 0.17 0.04 0.07

Quality 0.08 0.02 0.05 0.04 0.02 0.07

Setting 0.10 0.04 0.10 0.09 0.29 0.07

Type Food 0.10 0.17 0.20 0.02 0.07 0.07

Delivery

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18 7. To calculate the weighting for each criteria, average each row in the preceding matrix. Record your

answers here.

Criteria Weight

Cost (0.31 0.26 0.20 0.26 0.22 0.36) / 6     0.27

Variety



_{0.10 0.09 0.20 0.17}_ _ _ __{0.04 0.07 / 6}_



__0.11

Quality 0.05

Setting 0.12

Type Food 0.11

Delivery

Time 0.35

Part 3: Deciding the best restaurant for you

8. Refer back to your first matrix containing the 5 fast food restaurants and the ranked criteria. If you multiply each row by your weights from above, you will give each restaurant a final score that can be used to decide the restaurant that best meets your needs. Record your results here.

Restaurant Name Final Score

Chick-Fil-A 1 0.27



 

3 0.11

 

5 0.05

 

5 0.12

 

3 0.11

 

0 0.35



1.78

McDonalds 5 0.27



 

1 0.11

 

1 0.05

 

2 0.12

 

1 0.11

 

0 0.35



1.75

Taco Bell 2.47

Burger King 1.25

Hardee’s 2.32

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19 Part 4: Using technology to make a decision matrix spreadsheet.

Note: The screen shots are examples and will not be the same information as your matrix. Be sure to note the fx line to see formulas. The screenshots are from EXCEL.

10. Open your spreadsheet software and start a new spreadsheet.

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20 12. Enter your criteria matrix into SHEET 2. Include all row and column headings and change the sheet

name to CRITERIA WEIGHTING. Be sure to use SUM to total each column. Extra credit will be given if your spreadsheet calculates the reciprocals for you. Extra credit requires that reciprocal cell shows the formula =1/cell where cell is the original value of which we want the reciprocal. Example: C2 is Variety versus Cost. It equals 3. B3 is cost versus Variety so for extra credit B3=1/C2. The spreadsheet should fill B3 with 0.33.

13. Copy the criteria matrix into another location on CRITERIA WEIGHTING (SHEET 2). Change each cell to a percentage by using the appropriate formula. Add a column to the matrix to average each row. Be sure to use AVG to do the calculation. Title the column of averages WEIGHT.

 The formula for percentage is =cell/total of column. Example: The total of the Cost column is in B8. Quality is located in B4. To calculate the percentage for Quality in that column, B13=B4/B8.

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21 14. Copy your fast food restaurant matrix and weight matrix into SHEET 3. In a different section of

SHEET 3, make row and column headings for restaurant names and final scores. Multiply your matrices together using formulas and store the results under these headings. Change the sheet name to FINAL SCORES.

 Each restaurant row needs to be multiplied by the weight column so that like categories are multiplied together, Cost*Cost Weight + Variety*Variety Weight + …+ Delivery Time*Delivery Weight. Example: For Chick-Fil-A, B17=B2*B10 + C2*B11 + D2*B12 + E2*B13 + F2*B14 + G2*B15.

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22 HO #2

Choosing a Cell Carrier and Cell Plan

In the following problem you will be discovering what the best cell phone plan and carrier is for you. There is no right answer as different people have different preferences when it comes to chatting, texting, or e-mailing. What you will be finding is the best phone and plan for you.

Part 1: Developing the Cell Carrier and Plan matrix 1. Choose 5 Cell carriers with plans to compare.

2. Identify some criteria to use to compare these plans and carriers.

3. Make a table (matrix) ranking each carrier/plan from 5 (is the best) to 1 (is the worst). Note: you may not need all the columns on the table.

Carriers and plans Name

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Criteria

Total

2 Top criteria is very slightly more important than side criteria 3 Top criteria is somewhat more important than side criteria 4 Top criteria is definitely more important than side criteria 5 Top criteria is absolutely more important than side criteria

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24 6. Calculate the weighting for each criteria. Record your answers here.

Criteria Weight

Part 3: Deciding the best carriers and plans for you

7. Refer back to your first matrix and rank your five carriers and plans. Carriers and plans Name Final Score

8. What is the best carriers and phone for you? Do you agree with this result? Why or why not?

Part 4: Using EXCEL to make a decision matrix spreadsheet

Use EXCEL to make a decision matrix spreadsheet for the cell carriers and plan. Answer the question below based on the EXCEL sheet and decision matrix.

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25 HO #3

Is this the Best?

I. Select one topic that you would like to focus on for your final project. After making your selection, you will be grouped with other students that have chosen the same topic. Some ideas for topics are listed below. You are not limited to these topics. Any topic is acceptable, with teacher approval.

A. Purchasing a car

B. Selecting a college/university to attend C. Choosing a career path to follow

The following will be completed in groups:

II. Select 5 categories within your topic to compare. Make sure your choices are realistic, but varied.

(10 points)

III. Select your criteria for comparing your choices. You must have a minimum of 6. The group must agree on the criteria. Develop a matrix of weights for these criteria based on their importance to you.

(20 points) IV. Research your five selections (from part II) on each criteria listed in part III. Record your

findings.

(30 points) V. Create a spreadsheet using EXCEL.

1. All charts are to be on the same spreadsheet file. (Each of the criteria can be on a different worksheet of the same file if desired.)

2. Formulas used where appropriate: Sums of columns, incorporation of weights. 3. Selections and criteria clearly displayed in each chart.

4. Weights used must be exactly as created in class.

(40 points)

VI. Analyze your results in several ways. Examine all of the factors that went into this determination, including the weights. Create a PowerPoint presentation explaining your final selection based on the results of your data analysis. Be sure to include specific reasons for your selection over the other four based on your research. Your discussion must include a comparison of all five selections and not focus on just the one that “wins” in the final analysis. Support your findings with facts, graphs, and spreadsheets as needed.

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26 Grading

Each group will receive 2 grades for the “Is this the Best?” Project.

1. Matrix Creation on Excel (100 points)

a. See requirements and specific point values in Sections I through V above.

2. Presentation of Product (50 points)

a. Rubric for Grading Presentation is attached.

Grading Scale (out of 150 total points) *

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27 HO#4

Is this the Best? Final Project Rubric

4 3 2 1

Research of Choices and Criteria

Five categories were selected and at least 6 criteria were chosen. Research was fact-based and

unbiased. Each criterion and category was researched equally.

Five categories were selected and at least 6 criteria were chosen. Research was mainly fact-based and unbiased. Each criterion and category was mainly researched equally.

Five categories were selected and at least 4 criteria were chosen. Research was somewhat fact-based and unbiased. Each criterion and category was somewhat researched.

Five (or less) categories were selected and at least 2 criteria were chosen. Research was barely fact-based and unbiased. Each criterion and category was barely researched.

Creation of Spreadsheet

All charts are on the same

spreadsheet file. Each chart is clear and concise, following the weights established in class. All

formulas are used appropriately and correct.

All charts are on the same

spreadsheet file. Most charts are clear and concise, following the weights established in class. Most formulas are used appropriately and correct.

Most charts are on the same

spreadsheet file. Some of the charts are clear and concise, somewhat following the weights established in class. Some formulas are used appropriately and correct.

Charts are on different

spreadsheet files. Charts are not clear and concise and/or weights are not the weights established in class. Formulas are not used, or are not used correctly.

Analysis of Results

Results are

analyzed in at least three ways. Connections are made between original thoughts and spreadsheet findings. Results are

analyzed in at least two ways. Connections are made between original thoughts and spreadsheet findings. Results are

analyzed in at least one way. Connections are somewhat made between original thoughts and spreadsheet findings.

Results are barely analyzed.

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