Rounding Pi

Math Content: Rounding, Estimation and Number Sense in Evaluating Solutions

Distressingly, student selection of answer A or B from the original CAHSEE problem depends on how pi is rounded. If p is rounded to its nearest whole number (3), a reasonable assumption given that the answers are also in whole numbers, then the remaining answer gets rounded to 30 (answer choice B). Which is, unfortunately, not the answer we're looking for. Check it out:
 

A = s2 - Πr2, or

A = 102 - 3(5)2 = 100 - 75 = 25 (rounded to 30)


Mathematically, however, since p is a bit larger than 3, that would make the subtracted (the quantity being subtracted) in the equations above slightly more than 75, giving a final answer that was slightly less than 25, which would then round down to 20. However, as you can see, this is a pretty sophisticated "twist" that most students in this class (and some of us teachers) wouldn't be able to follow.

Alternatively, those students who used 3.14 for p and saved the rounding until the very end found it worked well, and again, gave them a procedure that would always work.

In this clip, Ms. Scott polls students for their solution to the CAHSEE problem. Without calling attention to incorrect solutions, Ms. Scott helps her students work through the steps of the problem to find the correct solution to this problem.

Classroom Clip Reflection:

  • What strategies does Ms. Scott use to make this problem accessible to her students?
  • What are the implications for your own work with students?