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Mathematics Governor’s Institute 2003

Problem-in-a-bag Template

 

(Download as Microsoft Word documents: Ready for a Road Trip?, Assignment Sheet, Calculations Sheet, My Road Trip Log, State Attractions, Summer Attractions, Trip Summary, Rubric, Special Education)

 

Title of Project:     “Ready for a Road Trip”?

 

 

 

Team Members:     Jeanine Miller

                               Susi Hamilton

                               Norm Ellis

                               Barbara Batts

 

 

 

Grade Level and/or Course:     7th and 8th Grade/ Pre-Algebra, Algebra

 

 

 

Concept(s) used:      The students will be computing with decimals and without, reading maps, measuring, working with rates and proportions and converting map scale to miles traveled.  

 

 

 

Pennsylvania Standards Addressed:

            2.1.8D  Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles.    

 

            2.2.8B  Add, subtract, multiply and divide different kinds of rational numbers including decimals.

 

             2.3.8A  Develop formulas and procedures for determining measurements.

 

             2.3.8B  Solve rate problems.

 

             2.3.8F  Use scale measurements to interpret maps or draw.

 

             2.5.8A  Invent, select, use and justify the appropriate methods, materials, and strategies to solve problems.

 

             2.5.8B  Verify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagrams.

 

             2.6.5A  Organize and display data using pictures, tallies, tables, charts, bar graphs and circle graphs.

 

 

 

NCTM Standards Addressed:     -Compute fluently and make reasonable estimates.

 

                                                     -Use mathematical models to represent and understand quantitative relationships.

 

                                                     -Understand measurable attributes of objects and the units, systems, and processes of measurement.

 

                                                     -Apply appropriate techniques, tools, and formulas to determine measurements.

 

                                                      -Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

 

                                                     -Problem Solving

 

                                                     -Communication

 

                                                     -Representation

 

 

 

Introduction/Application:     In this quest, each team of students will plan an itinerary of travel on the East Coast.  They will choose four attractions in various east coast states that they wish to visit.  The trip will begin in Philadelphia, Pennsylvania and end wherever they choose to travel.  When the quest is finished, the students will write a fictional, narrative account of a place of interest to which they traveled.

 

 

Question:    What is the total mileage, fuel cost, and driving time that was incurred on the “Road Trip”?

 

 

Model:     The students will: 

1)     use scale to convert map measure to distance

                         1 in.  =  pipe cleaner in.

                     63 miles            x miles

 

2)     determine the number of gallons of fuel needed

                        distance                                to determine cost of fuel:

                     (23.4) gas mileage                      gallons * cost ($1.39)

 

3)     determine the distance traveled in 1 day

                        65 * 9 =

 

4)     total days to travel

              total distance

           distance in 1 day

 

 

Resources and Materials (estimated cost):    

1)     U.S. Map = $5.00

2)     Display Board = $5.00

3)     Pipe Cleaners = $1.50

4)     Push Pins = $0.99

5)     Ruler = $0.99

 

Total Estimated Cost = $13.00

 

 

 

 

Procedures and Activities:     The students will first receive a student packet (Assignment Sheet, Calculations Sheet, My Road Trip Log, State Attractions, Summer Attractions, Trip Summary) with all of the necessary forms.  The team will receive pipe cleaners, push pins, ruler and a calculator.

1)     The team will choose which four attractions they wish to visit based on a list/descriptions that are provided.

2)     They will then locate all of these destinations on the U.S. map that is provided.

3)     The students will begin their road trip in Philadelphia, Pennsylvania.

4)     The team will measure the distance from Philadelphia to the first, closest attraction.  This pattern will continue until all of the attractions have been visited.

5)     Using the map scale, the team will convert inches measured to miles traveled.

6)     The team will then calculate the total cost of gas spent, and the days needed to travel to all of the four locations.

7)     Finally, the teams will reflect upon their journey and select one attraction to write about.  This writing will be fictional and may consist of the unusual and/or interesting facts learned from visiting the location.

 

 

 

Answers/ Rubric:

 

                   “see attached rubric”

 

 

 

 

Accommodations/ Adaptations

 

                   ESL:   - task read aloud

-         pair children with more advanced students

-         more support will be given by the teacher

-         visual clues will be given to complete computations

-         scrapbook/ digital portfolio

 

 

                  

Special Ed.:   -“same as above, plus…”

                      -visit only two attractions instead of four

                      -a pre-made computation sheet will be supplied

 

 

 

 

 

                    Enrichment:   -the children could go on the Internet to                                                          compare and contrast actual mileage found on Mapquest to the mileage found in class

                                           -the children will reflect on what factors could have contributed to any inaccuracies in their responses

                                           -graph a representation of the cost of travel                                      according to miles

                                          -predict costs for other road trip attractions                                                 

 

 

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