factoring Seeing Structure in Expressions


john weisenfeld 2

You grade this on Sunday. What do you do on Monday? Go over the procedure that this student almost flawlessly executed?  Again?  What do you emphasize?  Checking your answer?

Thanks to John Weisenfeld for the submission.


4 replies on “Factoring”

I would emphasize that factoring is a process of rewriting an expression as an equivalent expression in a particular way. So, you should be checking that the answer is really equivalent to what you started with. So yeah, checking the answer is definitely a part of the Monday conversation.

This looks like a student who has some idea that there’s something involving common factors to be done, but not with what that means. To them, maybe (4n^3)/(3n^2) and 4n^3 + 3n^2 and 4n^3 * 3n^2 all look pretty similar, and when you tell them in the first two cases that there’s something to be done with the common factor of n^2, it seems arbitrary to them that the thing to be done is different. So maybe it’s time for a whole bunch of “compare and contrast” style exercises on Monday where they tell you about what’s similar and what’s different in each case.

(Also, in response to ccssimath: SIMPLIFY a fraction, please. Again, because I want to emphasize the equivalence.)

Sorry, we never use the hackneyed verb “simplify” in any instruction due to its ambiguity. Which is simpler, 1 1/3 or 4/3? We reduce fractions to lowest terms. It’s mathematically unambiguous.

We suggested going back to the beginning because asking a student to reduce a fraction to lowest terms by factoring reveals if the students knows how to find the GCF. Understanding reducing fractions involves the same skill set and will lead to a better understanding of the rationale underlying factoring algebraic expressions. Otherwise, students proceed by rote, not by understanding.

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