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 Skills to be taught (T) during this unit or
Collaboration E Research E
student use during this unit and assessed (A): BIE Page 35-37
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
Other:
Resources Needed: On-site people, facilities: Facilitator/Teacher
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
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
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
Directions for Instructor:
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
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
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 Directions for Instructor:
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
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:
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
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
1
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.
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 Cost
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.
11. Enter your fast food restaurant matrix into SHEET 1. Include all row and column headings. Change the sheet name to FAST FOOD RESTAURANTS.
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.
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
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 Quality Setting Type Food Delivery
Time
Cost Variety Quality
Setting
Type Food
Delivery Time
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.
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 0.26 0.22 0.36
Variety 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
7. To calculate the weighting for each criteria, average each row in the preceding matrix. Record your answers here.
Criteria Weight
Cost
Variety
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
McDonalds
Taco Bell 2.47
Burger King 1.25
Hardee’s 2.32
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.
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. To average each row, use AVG with the first cell and last cell to be averaged. Cells can be
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.
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
Part 2: Developing the weighting matrix Criteria
Total
4. Fill in the matrix using this rating system:
6 Top criteria and side criteria are equally important
7 Top criteria is very slightly more important than side criteria 8 Top criteria is somewhat more important than side criteria 9 Top criteria is definitely more important than side criteria 10 Top criteria is absolutely more important than side criteria
17. Calculate the weighting for each criteria. Record your answers here. Criteria Weight
Part 3: Deciding the best carriers and plans for you
18. Refer back to your first matrix and rank your five carriers and plans. Carriers and plans Name Final Score
19. 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.
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
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) *
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
Results are barely analyzed.
