Florida B.E.S.T. MA.912.C.1

MA.912.C.1 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.C.1.1

  Demonstrate understanding of the concept of a limit and estimate limits from graphs and tables of values.

• MA.912.C.1.10

  Given the graph of a function, identify whether a function is continuous at a point. If not, identify the type of discontinuity for the given function.

• MA.912.C.1.11

  Apply the Intermediate Value Theorem and the Extreme Value Theorem.

• MA.912.C.1.2

  Determine the value of a limit if it exists algebraically using limits of sums, differences, products, quotients and compositions of continuous functions.

• MA.912.C.1.3

  Find limits of rational functions that are undefined at a point.

• MA.912.C.1.4

  Find one-sided limits.

• MA.912.C.1.5

  Find limits at infinity.

• MA.912.C.1.6

  Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.

• MA.912.C.1.7

  Find special limits by using the Squeeze Theorem or algebraic manipulation.

• MA.912.C.1.8

  Find limits of indeterminate forms using L'Hôpital's Rule.

• MA.912.C.1.9

  Define continuity in terms of limits.

01

What Students Need to Do

Students estimate and calculate limits from graphs, tables, and formulas, including one-sided limits. They decide whether a function is continuous at a point or across an interval and explain their reasoning.

02

What Mastery Looks Like

A student can determine limits from graphs, tables, and formulas. They compare behavior from both sides and use the function value to justify whether continuity conditions are met.

03

Common Misconceptions

Students often assume the limit must equal the function value. They may say a limit does not exist at a hole, or ignore that the left and right limits differ.

04

How to Assess It

Give students f(x) = (x² − 4)/(x − 2) for x ≠ 2, with f(2) = 5. Ask for the limit at 2 and whether the function is continuous there.

1. 01

   Give pairs a printed graph, two sticky notes, and a ruler; they approach each marked x-value from both sides and record y-values.

2. 02

   Ask, “Can a limit exist when the function value is missing or different?” Students defend an answer with a sketch and two sentences.

3. 03

   Run a card sort matching graphs, tables, formulas, limit values, and continuity claims, then have teams correct one mismatched set.

4. 04

   Model water temperature approaching room temperature with a table, then ask what value it approaches and whether the model changes continuously.

• MA.912.C.4

  Develop an understanding for and determine integrals.

• MA.912.C.2

  Develop an understanding for and determine derivatives.