Maryland Math F.LE.B.6.a

MathGrades 9–12LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

The Standard

F.LE.B.6: Build and interpret logistic functions to model real-world problems.

Sketch and analyze the graphs of logistic functions.

Maryland College and Career Ready Standards for Mathematics (2025) · Interpret expressions for functions in terms of the situation they model.

Teacher's field guide

What Students Need to Do: Students sketch a logistic curve from an equation or table. They show the levels it approaches, find its steepest part, and explain what these features mean in the situation.
What Mastery Looks Like: Students plot key points and draw a smooth S-curve. They place the steepest part near the midpoint between the lower and upper limits and explain why the graph levels off.
Common Misconceptions: Students may draw exponential growth that never slows, or a flat line that touches the upper limit. Some put the fastest change at the highest point instead of near the middle.
How to Assess It: Exit ticket: Sketch y = 100/(1 + 9(1/3)^t) for t ≥ 0, using t = 0, 1, 2, and 3. Mark the upper limit and the point where growth is fastest.

Lesson moves

Give pairs a 100-square grid and graph paper; shade 10, 25, 50, 75, then 90 squares in stages, and plot each total.
Ask: Why does a rumor graph rise fastest near 50 of 100 students, then flatten near 100?
Give groups three graph cards, an S-curve, a straight line, and an exponential curve; have them sort the cards and mark any horizontal limits.
Plot ticket sales of 10, 25, 50, 75, and 90 for a 100-seat theater over five days; estimate when sales slow.

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