A Year of Nights of Wondering – VII

A student who missed the last class was confronted by this problem on a quiz.

Proportion 1

He had either a vague recollection of a solution method or a strong understanding of the properties of proportions and decided (in my words) to use common numerators.  Thus,

Proportion 2

He noodled around and came up with x = 13 and then clearly checked it.

Proportion 3

Full credit.  Clear understanding of the problem and algebraic correct steps toward the solution.  The written explanation could have been clearer but this was a quiz after all.

I’m not going to start teaching the “least common numerator” method for solving rational expressions (It doesn’t generalize.) and there are easier ways of solving proportions which I am sure this student will “get” quickly.  So a quick compliment and on with the class.

Students’ ways of thinking are so individual and unexpected.  Teachers get the pleasure of such small discoveries everyday.


About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.
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