Florida B.E.S.T. MA.912.AR.5.9
The Standard
Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph logarithmic models and identify domain, range, intercepts, vertical asymptotes, and where the model rises or falls. They solve for unknown inputs or outputs, then explain what answers and restrictions mean in the situation.
What Mastery Looks Like
- A student can choose a useful window, graph the model accurately, and label key features with units. They can solve a related equation and reject values outside the logarithm's domain or the situation's limits.
Common Misconceptions
- Students may allow zero or negative logarithm inputs, or confuse the vertical asymptote with an intercept. They often ignore the log base or treat log(a + b) as log a + log b. They may keep answers that make no sense, such as negative time or impossible measurements.
How to Assess It
- Exit ticket: A population model is t = 3log₂(P/100), where t is hours and P ≥ 100. Find t when P = 800, sketch the graph, and state both domains and the meaning of (100, 0).
Lesson moves
Ways to Teach It
Give equation, graph, and context cards; students match each set, then mark the asymptote, intercepts, and allowed inputs with sticky notes.
Ask, “Why can a logarithmic model have a mathematical domain larger than its realistic domain?” Students answer with one labeled example.
Run a four-corner game using graph cards: domain, asymptote, intercept, or solution; students move to the feature each card tests.
Collect sound levels with a phone app, graph L = 10log₁₀(I/I₀), and explain why large intensity changes produce smaller decibel changes.
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