Florida B.E.S.T. MA.912.C.1.3
The Standard
Find limits of rational functions that are undefined at a point.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use substitution to check what happens near the given input. They factor and cancel common factors, then evaluate the simplified expression or compare one-sided behavior.
What Mastery Looks Like
- A student recognizes when direct substitution gives 0/0, factors correctly, and cancels only common factors. The student finds the limit and distinguishes a removable hole from a vertical asymptote.
Common Misconceptions
- Students often treat 0/0 as an answer or assume the limit does not exist. They may cancel terms instead of factors or mistake every zero denominator for a vertical asymptote.
How to Assess It
- Use this exit ticket: Find lim x→3 of (x²−9)/(x−3), then explain why the limit exists even though the original expression is undefined.
Lesson moves
Ways to Teach It
Give pairs a card sort matching rational expressions, simplified forms, graphs, holes, and vertical asymptotes.
Ask students to explain why 0/0 signals more work rather than giving a final answer.
Run a limit relay where teams factor, cancel, evaluate, and classify one rational expression at each station.
Use an average velocity formula that becomes undefined at zero time change, then simplify it to find instantaneous velocity.
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