Why is it that we jump with elation when we discover math errors? For example, I recently waited patiently in a pita-sandwich shop while the staff filled in all the decimal points (using appriopriate colors) in their special signs...i.e. changing .95¢ to 95¢. Not sure they appreciated my business!
Another source of ready errors is on standardized tests. For example, consider this question taken from a sample test in the review manual for the PSAT:
A board 7 feet 9 inches long is divided into three equal parts. What is the length of each part?
Now, I realize that you (and I) know the right "obvious" answer...but that is not my point (or my jump for elation).
- 2 ft. 7 in.
- 2 ft. 6 1/3 in.
- 2 ft. 8 1/3 in.
- 2 ft. 8 in.
- 2 ft. 9 in.
Your Task: Think creatively...Can you think of other correct answers not displayed as options? For example, how could 7 ft. 9 in. be a correct answer...in multiple ways? How many new unique answers can you create?
Your New Task: Is it possible for for each of given answers in the problem to be correct?
Note 1: One difficulty is the meaning of the word "equal" in the problem as stated. Does it mean congruent in shape...or equal in area...or?
Note 2: Another difficulty is the interpretation of the word "board." Must we assume that all boards are rectangular parallelpipeds?
Perhaps this question should be discarded...
Source: E. Steinberg's PSAT-NMSQT, 1985, p. 239
Hint: Think of different ways (directions?) one can sawe a "board"? Do the cuts have to be straight?
Solution Commentary: Sorry, I will let you evaluate your own creative solutions.