AUTHENTIC TASKS IN A STANDARDS BASED-WORLD

Curriculum standards is guide instruction but not represent the be-all anda end-all of school mathematics.

The Meeting for Lunch problem is stated as follows : Three friends – one from Hamilton, one from Marrietta, and one from Fostoria – are making plans to meet for lunch. Each wishes to drive the same distance. Whera should they meet? Justify your solution mathematically.

The students surmised that Colombus, Ohio but with interactive geometry software (IGS), the sketch suggest that Parkersburg, West Virginia, is equidistant from these three city.

Students began to select different combinations of cities and document curious results. For instance, suppose three friends drove from Lorain, Hamilton, and Cleveland (marked as points A, B, and C in fig. 4).

Clearly, a lunch meeting in West Virginia is a less-than-optimal plan for friends living in Lorain, Hamilton, and Cleveland, Ohio.

We encouraged students to use the sketch to look for a point minimizing the total distance trav- eled from Hamilton, Lorain, and Cleveland.

When an angle of a given triangle ABC is greater than or equal to 120 degrees, the point that minimizes the total distance is the vertex of the obtuse angle.

Although the femat point was not included in the Ohio Academic Content Standards, it is important and usefulness in aplications such as the Meeting for Lunch problem. As students confronted the Meeting for Lunch problem, they explored a plethora of mathematics topics from triangle centers, angle measures, and types of angles and triangles to maps, distance, and scale factor. Mathematics can be engaging and creative for students. The use of Interactive Geometry Software afforded students opportunities to make and test conjectures in ways that would be impractical, if not impossible with paper and pencil. Our responsibility as educators is supporting students as we learn mathematics together, whether on or off the map.

Sumber: Mathematics Teacher. Vol. 106, No 5 ° December 2012/January 2013