Title: Moving Problem
Problem: A circular table is pushed into the corner of a square room so that a point P on the edge of the table is 8 inches from one wall and 9 inches from the other wall. Find the radius of the table in inches.
Math Topic/Concept: Pythagorean Theorem, Circles
Materials: Handout
Classroom Use: Developmental
Classroom use comments: This problem helps develop the use of the Pythagorean Theorem and helps the student with problem solving skills because hopefully they will come up with the idea of using the Pythagorean Theorem on their own.
Grade: 9th or 10th
Grade Cluster: Early high school
Illinois Goal: 7 and 9
Standard: 9.D.4
Applied? (1-4): 2
Source: Mathematics Teacher
Answer: r = 29
Strategies Listed:
Solution: Construct a diagram with the corner of the room in the upper right hand corner. Construct a triangle with the hypotenuse starting at the center of the table and extending to the point P on the edge of the table. The legs of the right triangle go down from P and to the right from the circle’s center (or left from P and up from the center). One leg is equal to (r – 9) and the other leg is equal to (r – 8). Use the Pythagorean Theorem to solve for r.
Other solution methods (if any):
Extensions or related problems:
Intended rubric or assessment method: This is a developmental problem on the Pythagorean Theorem. I wouldn’t expect all the students to correctly set this problem up because not everyone can visualize what is going on. Therefore, a problem like this can be done in groups or as a sponge activity and should be graded on effort. However, if the students are struggling, I can provide the given information on the diagram. Then the students should be able to solve the problem. A general rubric can be used with 0 given for no effort, 1 given for effort and partial understanding, 2 given for effort and complete understanding.
Notes (if any):
Write-up submitted by: Dana Kimberley
James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated:
December 16, 2001