Math A Activity for  Error in Measurement

In this activity, students will encounter how error in measurement affects actual measurements and calculations.

Students will need rulers and calculators.

Lab Sheet:  Error in Measurement

1.  Measure the length and width of a large rectangular object in the classroom (such as a table, the blackboard, or the teacher's desk).  Take these measurements to the nearest 1/16th of an inch.   Express these answers as fractions.
                           Length = __________  Width = ___________ 

2.  Measure the length and width of a small rectangular object in the classroom (such as an eraser, a box of chalk, or a small memo pad).  Take these measurements to the nearest 1/16th of an inch.  Express these answers as fractions.
                          Length = ___________  Width = ____________

3.  Determine the precision of your measuring instrument.  Find the smallest scale division on your ruler (is it 1/16th, or 1/32nd, or .....?)  Take one-half of this value and add it to (and subtract it from) the measurements made above to establish the tolerance intervals.

Large object tolerance interval (length)  __________________
Large object tolerance interval (width) ___________________

Small object tolerance interval (length) __________________
Small object tolerance interval (width) ___________________

4.  Calculate the smallest possible area for each object.
Smallest possible area (large object) = _________________
Smallest possible area (small object) = _________________

5.  Calculate the largest possible area for each object.
Largest possible area (large object) = _________________
Largest possible area (small object) = _________________

6.  Examine the ranges between the largest and smallest possible areas for each object.  Does the size of the object seem to have an influence upon these ranges?  State your findings in the form of an hypothesis.
   _______________________________________________________
   _______________________________________________________
   _______________________________________________________
   _______________________________________________________

7.  Test your hypothesis by taking one additional set of measurements.  What size object should be used to test your hypothesis?_______________________
Record your results below.
Length = ______________   Tolerance interval for length: _______________
Width = ______________    Tolerance interval for width: _______________
Smallest possible area = __________________
Largest possible area = ___________________
Range between smallest and largest possible areas: ____________________
Is your hypothesis supported?_____________  If NO, how would you reformulate your hypothesis?___________________________________
   _______________________________________________________

(This activity is a modification of an activity appearing in CORD Applied Mathematics.)