Tuesday, January 19, 2016

How do you cook a Turkey?

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The question below is taken from the New York State Common Core Sample Questions: Regents Examination in Algebra II (Common Core) Fall 2015. The complete file can be found  here.

This question makes reference to Newton's Law of Heating. Unless you are familiar with this law, I suggest you follow this link.

Now my concern: what is this law doing in an Algebra II exam of any kind?

Here we are at exam time, and we throw at our students a concept they are unfamiliar with in such a way that we believe we are only asking them this:
a) Solve for k: \[100 = 325 + \left( {68 - 325} \right){e^{ - 2k}}\]
 b) Use your value for k to solve; \[T = 325 + \left( {68 - 325} \right){e^{ - 7k}}\]

Everything else in this question, other than the use of these two items,  involves the careful reading of a passage in the realm of thermodynamics, interpreting the contents carefully, and properly substituting values into s formulas handed out freely.  All three skills are worthy, but should be tested in a familiar realm. The writer of the question knows that "object" here refers to the turkey, but would that be obvious to the novice, reading such a scenario for the first time?

This question also includes some either dangerous or misleading (or even false) information. 

The most important is that the time needed to bring a refrigerated turkey to room temperature would be far too long, allowing for growth of salmonella among other hazards. The typical cook may wait for the surface of the turkey to feel close to room temperature, but never waits for the whole bird to warm up.

Second, Newton's law of Cooling (the proper name of the law) is based on the object having a uniform temperature. In any other situation the law provides nothing more than an approximation. As noted above, that is not the case when we cook a turkey. (Ever notice that the temperature can read differently when the thermometer is moved to a different location in the turkey?)

Thirdly, take note of this, a typical chart (from Foster Farms)

The turkey in this problem is cooked for 7 hours (who knows, maybe more?). This is either a huge turkey in an industrial oven, or someone who likes their turkey as little on the burnt side.

No matter how I slice it (no pun intended), this problem comes across to me as being totally out of place in an Algebra II exam. It amounts to a "cookbook" problem, (pun unintended) the likes of which have no place even near an end-of-the-year Regents exam in Algebra II.

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