NY Next Generation Math AI-F.LE.3
The Standard
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use Algebra I tables and graphs to observe that sustained exponential growth eventually exceeds linear, quadratic, and other polynomial growth. They compare values over a sufficiently long domain rather than judging only early behavior.
What Mastery Looks Like
- The student generates comparable values, identifies where the exponential model overtakes the other model, and explains the long-term pattern. Graph windows or tables extend far enough to support the claim.
Common Misconceptions
- Students may assume exponential values are always larger from the start or choose a window that ends before the crossover. They may generalize from one interval without examining later growth.
How to Assess It
- Compare f(x) equals 2 to the x and g(x) equals x squared using a table from 0 through 10. Ask when exponential growth stays ahead.
Lesson moves
Ways to Teach It
Stack growth cards for linear, quadratic, and exponential sequences across equal input steps.
Ask students why a polynomial can exceed an exponential model early but not indefinitely.
Run a graph-window race to locate crossover points between exponential and polynomial models.
Compare long-term compound growth with fixed yearly additions using a table and graph.
Keep exploring
Related Standards
- AI-F.LE.1.a
Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal facto...
- AI-F.LE.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
- NY-8.F.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a funct...
- AI-F.LE.1.b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
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