It is a good idea to let students create their own problems from a given context once they have had some experience in problem solving. This gives students a great deal of insight into the problem-solving process. It is empowering for students to realize they can create problems. Theirs will be tougher than common textbook problems in many cases. When given the following problem situation, students often generate problems involving inequalities or questions about domain and range of functions.
Problem situation. Janet is making a rectangular end table for her living room. She has decided the tabletop should have a surface area of 625 sq. in.
Task. Write three different types of questions that could be asked about this problem situation. Solve two of them.
Some students responses:
Table 1. Areas for tables of various dimensions, if the table is twice as long as it is wide
Length | Width (in.) | Area (in.2) | ||
(in.) | Process | Result | Process | Result |
40 30 34 36 35 35.4 35.3 | 40/2 30/2 34/2 36/2 35/2 35.4/2 35.3/2 | 20 15 17 18 17.5 17.7 ---- | 40 x 20 30 x 15 34 x 20 36 x 20 35 x 17.5 35.4 x 17.7 ---- | 800 450 578 648 612.5 626.58 ---- |