Furthermore, these problems require students to use various forms of reasoning to arrive at a solution. You have been assigned for the first time to a trans-Pacific flight from New York to Hong Kong. You are curious about the shortest route between the two cities, but all you have is a regular globe and a piece of string. The task requires students to interpret the shortest distance between two points on a sphere, find a way of measuring that distance, and use proportional reasoning inventively and creatively. The task is suitable for junior high school students.
Students can work individually or in small groups while the teacher observes their interactions.
These observations can yield information about the students' ability to apply their knowledge in solving the problem. This task illustrates how mathematics can be integrated into other areas of the school curriculum. The assessment of students' mathematical power is appropriate at all grade levels and should not be delayed on the grounds that students must know a great deal of mathematics before they can integrate this knowledge. Group tasks are particularly useful in the lower grades for assessing the integration of students' mathematical knowledge. Use any of the materials to make a better estimate.