GettingThere.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 10/23/12 1

Mathematics Senior Level Capstone Course

Unit Overview

Title of Unit:

Getting There

Unit Designers:

Mirela Geagla: Arlington

Kiera Poplawski: Loudoun

Debora Strickler: Loudoun

Editor: Su Chuang, Loudoun

County Public Schools

Context:

Summary of the issue,

challenge,

investigation, or

problem.

You decide to go on a vacation but there are limitations on various

factors such as time and available resources. Your task is to determine

the destinations that are attainable and to design a vacation plan that

meets your travel restrictions.

Number of Class

Hours:

5 hours

Unit

Design:

__X

Task Based

___Project Based

Other Subject

Areas/Disciplines

Addressed:

Writing, Geography

Driving Question:

Where do you plan to go on vacation and do you have the resources to get there?

Mathematics Content

Addressed:

Solving real world problems using univariate data analysis; ratio and

proportion, collecting and analyzing data; Using paired data analysis;

MPE

Addressed:

Problem Solving

and Decision

Making;

Understanding and

applying Functions

Assumption of Prior

Knowledge:

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Revised 10/23/12 2

College and Career

Readiness/21

st

Century Skills to be

taught (T) during this

unit or expected (E)

for student use

during this unit and

assessed (A):

Collaboration-Students work in

pairs(or a group of three if needed)

E

Research: Distances, speed limits, and

map reading

E

Communication (Oral and/or Written)

Written paper

E & A

Technology:

Internet for collecting data

E

Critical Thinking/Decision Making

Careful consideration of given

resources

T & A

Other: (Describe)

Major Products

and/or Performances:

Group- Submit a written paper identifying and justifying

the possible destinations. The report should include cost

analysis and justification that travel restrictions were met.

Presentation Audience: None for this task

Class

School

Individual- Mathematician’s Journal entries

Expert

Community

Other:

Launch: Event or

experience used to

engage the students

interest and inquiry:

Top 10 Most Visited U.S. Tourist Sites - http://www.youtube.com/watch?v=PftGLj-53nU - 2 minutes

Go-Go's Vacation Music Video - http://www.youtube.com/watch?v=sLXlwKbLjDM - 3 minutes

Evaluation:

Formative Assessments

(During the Unit)

Interview

Practice Presentations

Mathematicians Journal

X

Notes

Preliminary

Plans/Outlines/Prototypes

Checklists

Rough Drafts

X

Concept maps

Field Tests

Other:

Summative Assessment

(End of Project)

Written Products, with a rubric

X

Peer Evaluation, with

a rubric

X

Oral Presentation with a rubric

Self Evaluation, with

a rubric

X

Other Product(s) or

Performance(s), with a rubric

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Revised 10/23/12 3

Resources Needed:

On-site people,

facilities:

Facilitator/Teacher

Equipment/Technology:

Computers with internet access, access to online maps (i.e. www.mapquest.com)

and graphing calculators

Materials:

Hardcopies of maps

Community Resources:

Access to travel information centers or visitor centers

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:

(Provide credit for any materials or activities adapted from other sources.)

Appalachian Trail Problem: www.exeter.edu/academics/72_6539.aspx

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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 10/23/12 4

Virginia’s Senior Level Capstone Course Instructional Plan

Unit Title:

Getting There

Driving Question:

Where do you plan to go on vacation and do you have the resources to get

there?

Task/Project/Problem:

You decide to go on a vacation but there are limitations on various

factors such as time and available resources. Your task is to determine the destinations are

attainable and to design a vacation plan that meets your travel restrictions.

ENGAGE Teacher provides an experience to engage students. Number of hours : Video – 1-3 Minutes Journal – 10 minutes Discussion 10-15 minutes

Show a video clip to peak students’ interest in going on vacation.

You decide to go on summer vacation. Your task is to determine which of the

possible destinations are attainable.

KNOWLEDGE AND SKILLS NEEDED Assumed already learned

Students will self-assess

Will be taught during the unit

1. Ratios and Proportion X

2. Reading Maps/Using Mapquest X

3. Use of Internet for Research X

4. Collaboration X

5. Written Communication X

6. Critical Thinking/Decision Making X

7.

8.

9.

10.

11.

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

 Mathematician’s Journals  Briefs/Memos

 Task lists

 Planning Calendar

□ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ___________________________ ____

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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 10/23/12 9 HO #1

Exploration 1 – Appalachian Trail Problem

The Appalachian Trail is a hiking trail that stretches 2158 miles from Georgia to Maine. The record for completing this hike in the shortest time is 52 days. The record-setting hikers averaged 3 miles per hour.

1. How many hours a day did they average?

2. What factor(s) could you change in order to complete the hike in a shorter time?

3. How fast would the hikers travel if they want to complete the trail in 60 days and they are traveling 12 hours a day?

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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 10/23/12 10 HO #1b

Possible Solutions : Exploration 1 – Appalachian Trail Problem

The Appalachian Trail is a hiking trail that stretches 2158 miles from Georgia to Maine. The record for completing this hike in the shortest time is 52 days. The record-setting hikers averaged 3 miles per hour.

1. How many hours a day did they average?

2158 miles

1 hour

13 hours/day

5 52 days



3 miles



6

2. What factor(s) could you change in order to complete the hike in a shorter time?

The pace of the hiker or the number of hours hiked per day are two factors that would shorten

the number of days to complete the hike.

3. How fast would the hikers travel if they want to complete the trail in 60 days and they are traveling 12 hours a day?

2158 miles

1 day

3 miles/hr

60 days



12 hours



4. If you are averaging 4 miles per hour and traveling 12 hours per day, will you break the record for completion time?

2158 miles

45 days, a record

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Exploration 2 – Choosing the Route

You have decided that you want to visit Virginia Tech. There are three possible routes you can take. Which one would you choose?

Option 1: I-66 West to I-81 South – Distance: 270 miles, Average Speed Limit: 65 miles per hour

Option 2: I-95 South to Route 29 South to I-64 West to I-81 South – Distance 263 miles, Average Speed Limit: 63 miles per hour

Option 3: Route 29 South to I-64 West to I-81 South – Distance 266 miles, Average Speed Limit: 55 miles per hour

Option 1

Option 2

Option 3

What factors attributed to your decision?

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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 10/23/12 12 HO #2b

Possible Solutions : Exploration 2 – Choosing the Route

You have decided that you want to visit Virginia Tech. There are three possible routes you can take. Which one would you choose?

Option 1: I-66 West to I-81 South – Distance: 270 miles, Average Speed Limit: 65 miles per hour

Option 2: I-95 South to Route 29 South to I-64 West to I-81 South – Distance 263 miles, Average Speed Limit: 63 miles per hour

Option 3: Route 29 South to I-64 West to I-81 South – Distance 266 miles, Average Speed Limit: 55 miles per hour

A Possible Scenario is: [ Rate from 1 – 3 with 1 being the best and 3 the worst. ]

Shortest Time Traveled Shortest Distance Preferred Route – personal choice

Option 1 (4.154 hrs) 1 3 2

Option 2 (4.175 hrs) 2 1 1

Option 3 (4.836 hrs) 3 2 3

What factors attributed to your decision?

Answers will vary…..

Are there factors not given that could affect your travel time?

Possible construction on one of the roads listed could hinder travel.

Need to stop at an intermediary point.

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Getting There

You are planning a four day round-trip from Washington, D.C. Possible destinations include: Cedar Point, The Major League Baseball Hall of Fame in Cooperstown, NY, Yellowstone Park, The Indianapolis Speedway, and Disney World. You have a budget of $500 for gas and lodging. The average cost of gas is $3.50 and your car averages 25 miles per gallon. The average lodging cost is $70.

Which destinations are attainable? Create an explanation justifying your answers. Be sure to include the following:

 Describe the route you chose  Describe the use of your budget

 If a destination was not attainable, why and what factors could you change to make it attainable?

Rubric

CATEGORY 4 3 2 1

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.

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.

Completion All problems are completed.

All but one of the problems are completed.

All but two of the problems are completed.

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Name____________________________

Partner Name_____________________

Peer Evaluation

The following is a list of statements to be answered by you about your partner. Think carefully about assigning values for each of the following statements.

Directions: Put an ‘X’ in the box that applies.

My partner… Strongly

Agree Agree Neutral Disagree

Strongly Disagree

Contributed constructively to discussions

Did an equal portion of the workload

Helped to keep me focused on the task

Was respectful of my ideas and opinions

Is someone I would work with again

Self Evaluation

The following is a list of statements to be answered by you about yourself. Think carefully about assigning values for each of the following statements.

Directions: Put an ‘X’ in the box that applies.

I …. Strongly

Agree Agree Neutral Disagree

Strongly Disagree

Contributed constructively to discussions

Did an equal portion of the workload

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Student Name ___________________________

CATEGORY 4 3 2 1

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.

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.

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.