Maryland Math F.LE.B.6

F.LE.B.6 is a cluster heading. These are the individual standards under it.

• F.LE.B.6.a

  Sketch and analyze the graphs of logistic functions.

• F.LE.B.6.b

  Compare and contrast the exponential, logarithmic, and logistic models.

• F.LE.B.6.c

  Apply understanding of logarithmic and logistic functions to solve real-world problems.

01

What Students Need to Do

Use a known limit and two data points to write a logistic rule. Use it to predict values and explain why the graph levels off.

02

What Mastery Looks Like

Given a cap and two counts, students write a rule that matches both counts. They identify the starting value and limit, and show where growth is fastest on the graph.

03

Common Misconceptions

Students may mistake slower growth for a falling total. They may use an exponential rule that keeps growing past the limit. Some think the graph reaches its limit on a particular day.

04

How to Assess It

Exit ticket: A club can have 100 members. It has 10 in week 0 and 20 in week 1. Write a logistic rule, predict week 2, and explain what 100 means.

1. 01

   Give pairs five 100-square grids; have them shade 10, 20, 36, 56, and 74 squares to show weekly club membership.

2. 02

   Ask students to write why a curve through (0,10), (1,20), and (2,36) can keep rising while its weekly gains shrink.

3. 03

   Give pairs counts of 10 and 20 in weeks 0 and 1; choose between 100/(1+9(4/9)^t) and 100/(1+4(4/9)^t), then explain.

4. 04

   A workshop has 100 seats and 10 sign-ups in week 0 and 20 in week 1; model when sign-ups might reach 90.

• F.LE.B.5.a

  Interpret the parameters in a logistic function in terms of a context.

• 8.AT.D.10

  Construct and interpret a linear function to model a relationship between two quantities.