Florida B.E.S.T. MA.912.C.1.11

MathGrades 9–12Develop an understanding for limits and continuity. Determine limits and continuity.

The Standard

Apply the Intermediate Value Theorem and the Extreme Value Theorem.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students check continuity and interval conditions before making a conclusion. They determine whether a function must reach a value between two outputs or attain absolute maximum and minimum values.
What Mastery Looks Like: Given a graph, formula, and interval, students check whether the needed conditions hold. They state what value or extremum is guaranteed and distinguish existence from exact location.
Common Misconceptions: Students may ignore continuity or forget that absolute extrema require a closed, bounded interval. They may also claim the exact input is known when only the existence of an input is guaranteed.
How to Assess It: Exit ticket: Let f(x)=x³+x−1 on [0,1]. Explain why f(x)=0 has a solution and why f has an absolute maximum and minimum on the interval.

Lesson moves

Pin string between two endpoint values on a coordinate grid, then place horizontal target lines and identify which ones the string must cross.
Show one continuous graph and one graph with a hole, then ask students to write which conclusions are guaranteed and why.
Give pairs theorem cards with condition and conclusion cards, then have teams race to build valid matches and reject invalid ones.
Use hourly temperature data to argue whether a continuous temperature model must reach 70°F and attain a daily high and low.

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