NY Next Generation Math AI-F.LE.1.b

MathGrades 9–12Distinguish between situations that can be modeled with linear functions and with exponential functions.

The Standard

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.

New York State Next Generation Mathematics Learning Standards · Construct and compare linear, quadratic, and exponential models and solve problems.

Teacher's field guide

What Students Need to Do: Students recognize Algebra I situations where one quantity changes at a constant rate per unit of another. They represent that relationship with a linear model.
What Mastery Looks Like: The student identifies the two quantities, calculates a constant unit rate, and uses it as the slope. An initial value is included when the context does not begin at zero.
Common Misconceptions: Students may call any steady-looking total linear without checking equal intervals or ignore a starting amount. They may confuse the unit rate with the intercept.
How to Assess It: A taxi charges $4 plus $2.50 per mile. Ask students to explain why the model is linear, write it, and interpret both parameters.

Lesson moves

Build a rate table with equal input intervals and highlight the repeated output change.
Ask students how a starting fee changes a linear model without changing its constant rate.
Play rate detective with contexts that are linear, nonlinear, or missing enough information.
Model hourly pay, constant-speed travel, or per-item cost with a linear equation.

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