NY Next Generation Math AII-F.IF.3

MathGrades 9–12Understand the concept of a function and use function notation.

The Standard

Recognize that a sequence is a function whose domain is a subset of the integers.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students treat an Algebra II sequence as a function whose allowed inputs are selected integers. They connect recursive and explicit sequence notation with function inputs and outputs.
What Mastery Looks Like: The student states an integer domain, maps each index to one term, and evaluates the sequence from either form. Graphs appear as discrete points rather than a connected curve.
Common Misconceptions: Students may connect sequence points continuously, allow noninteger indices, or confuse a term's index with its value. They may omit an initial condition from a recursive definition.
How to Assess It: Give a sub n equals 4 plus 3(n minus 1). Ask for its domain, first four ordered pairs, discrete graph, and a matching recursive rule.

Lesson moves

Place integer input cards and sequence output cards on a discrete function mapping board.
Ask students why a sequence graph should not connect neighboring points even when a formula accepts real inputs.
Play index-value match with recursive rules, explicit rules, ordered pairs, and discrete graphs.
Represent yearly account balances or monthly inventory counts as functions with integer time inputs.

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