Solution:
The measurements aren't the same because the students may have used different measuring tools and techniques. Also, physically measuring an object is likely to produce some degree of measurement error. The measurement process is, by its nature, never exact. Precision is affected by the measuring tool. The smaller the unit on a measuring tool, the more precise it is.


Answers to Questions:
a.  The measurement content of this lesson is the idea that measurements are approximations and that differences in units affect precision. 
b.  The idea of measurement error forms the basis for the study of standard deviation. This problem builds on students' prior experiences with measurement units, measuring tools, and decimals. 
c.  This problem relates to one of the big ideas of the course, namely that measurement is an approximation. Also, concepts such as measurement error, precision, and accuracy are evident in this type of problem. 
d.  How do you decide at what point a measurement is inaccurate? In other words, how much error is acceptable? How important is measurement precision in different contexts (i.e., building a bridge or cutting a piece of wrapping paper to wrap a box)? 
e.  Have students measure time and discuss the accuracy of the measurements. Using stopwatches or wristwatches with a stopwatch function, have students try to record a set length of time. Using another watch or clock to track the time, tell the students to "start" their stopwatches. Fifteen seconds later, say "stop" to have the students stop their watches. Students should then write down the time, as precisely as possible, on their watch (e.g., 00:15:09 or 00:15:13 or 00:14:97). Theoretically, all the students should have recorded the same length of time. Their times, however, will likely vary because measurement is an estimate. Discuss why measurements aren't the same, if they are accurate, and what affects precision. 



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