Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all your work. Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions.
Radio waves travel from each radio station through the air, as represented below.
On the next page, draw a diagram that shows the following. The part of Highway 7 where both radio stations can be received Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. In this example, students must use logic and diagrams to communicate the reasoning behind their solution to this task. Hence, several key elements of mathematical power are being measured here. Extended open-ended items in mathematics should be evaluated according to an established grading scale developed from a sample of actual student responses.