ALCA Members PLC Domains Data Standards Map Plan Curriculum Assessment Strategies

What is the distance and displacement between two selected points in you?

The difference between distance and displacement may be a difficult concept for students to grasp.  Students will learn the difference in this activity by obtaining data from a topographical map of the community and region, detailed road/street map of the school district, protractor and a ruler. Students will measure distances. Students will construct a straight-line elevation profile to calculate horizontal and vertical displacement.

Engaging Questions

  • What is the difference between a scalar measurement and a vector measurement?

  • How would a straight-line elevation profile be useful in city planning?

  • Which occupations or fields would one use vector measurements daily?Why?

  • What is the definition of displacement?

  • What is defintion of distance?

Teacher Goals

  • Determine the angle of displacement - Students will use trigonometric functions to calculate the angle of displacement

  • Interpret map scale - Students will observe the relationship between the distances on a map and the actual distances on the Earth's surface as map scale

  • Determine displacement - Students will use Pythagorean Theorem to calculate the displacement.

  • Research concepts of distance and displacement - Students will use resource books to compare and contrast the concepts of distance and displacement.

  • Read topographical map - Students will read contour lines and obtain data about changes in elevation. Students will calculate distance between points on a map.

  • Construct a Straight-line Elevation Profile - Students will construct a straight-line profile map to model the contour line data along the line between the points of home and school.

  • Dimensional Analysis - Students will use the factor-label method with appropiate unit conversion factors and convert the distance and displacement measurements to kilometers.

Required Resources

  • Metric ruler, protractor, coordinate grid, unlined white paper, calculator

    Metric ruler for measurements in distance and displacement.Coordinate grid and protractor to determine bearing.Unlined white paper to construct elevation profile.Scientific calculator

  • Physics or Physical Science Text , Trigonometry Text

    Students will use text books to find information to aid in answering questions

  • Topograhical maps of community and region, Digital Atlas of Oklahoma

    Maps can be obtained from Oklahoma Geological SurveyMain Office: 100 E. Boyd, Rm. N-131, Norman, OK 73019phone: 800/330-3996, FAX 405/325-7069Publications Sales Office: 1218-B W. Rock Creek Rd.Norman, OK 73069phone: 405-360-2886Web Address: http://www.ou.edu/special/ogs-pttc

Steps

  1. Select two fixed points

    Select two locations (points) that you will determine the distance and horizontal and vertical displacement between the two fixed points.

  2. Locate

    Locate the two selected fixed points on a topographical map.

  3. Measure and record

    Measure and record the horizontal length of the line from the first fixed point to the next fixed point.

  4. Determine scale of map

    Using the mile section of the map, determine the scale of the mile section .  Measure the length of the map mile section and record the length in centimeters.

  5. Convert horizontal length to scale

    Convert the horizontal length to scale using the map scale ratio from procedure 4.Use the correct conversion factors and convert the horizontal displacement to feet.

  6. Determine horizontal displacement line vector

    Overlay a coordinate grid atop the topographic map and determine the horizontal line vector or bearing.  Place (0,0) atop first fixed point location on map.Reference: 0 degrees=North, 45 degrees=Northeast, 90 degrees=East, 135 degrees=Southeast, 180 degrees=South,225 degrees=Southwest, 270 degrees=West, 315 degrees=Northwest.

  7. Construct straight-line elevation profile

    Construct a straight-line elevation profile of topography between the two points on the map.

  8. Determine the elevation difference between the two fixed points.

    Using the elevation profile, determine and record the elevation difference.

  9. Determine the angle of vertical displacement

    Using the tangent function, determine the angle of vertical displacement.  Angle of vertical displacement is equal to the change in elevation divided by the horizontal displacement.The angle of vertical displacement can be changed to a percent slope by multiplying the vertical displacement by 100.

  10. Determine displacement using the Pythagoreum equation

    Determine the total displacement between the two locations by using the equation steps:  A=horizontal displacement                              B=vertical displacement A squared plus B squared =sum Take square root of sum = total displacement

  11. Convert displacement unit to miles

    Using the proper conversion factor, convert the feet measurement unit to miles for each : horizontal displacement, vertical displacement and total displacement.

  12. Determine the distance between the two fixed points.

    Using a road/street map and ruler, determine the actual distance that one must travel by marked road to get from the first fixed point location to the final fixed point location.  Convert the distance to scale according to your map.  Convert the final distance measurement to miles using the proper conversion factor.

Teacher Notes

  • The Digital Atlas of Oklahoma can provide the topographical maps and city maps.If the Digital Atlas of Oklahoma is not available, topographical maps may be obtained through the Oklahoma Geologic Survey (OGS). Web address http://www.ou.edu/special/ogs-pttc/OGS Publication Sales1218-B W. Rock Creek RoadNorman, OK 73069

  • Duration: The duration of this activity is approximately two fifty minute class periods.

Learner Notes

  • Refer to procedure

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