Montana Math MT.CORE.ALG.FUN.2

MathGrades 9–12Understand Functions and Expressions

The Standard

Understand the definition of a function and distinguish between functions and relations.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students decide whether each input has exactly one output. They check ordered pairs, tables, arrow diagrams, and graphs.
What Mastery Looks Like: A student can tell whether a relation is a function in each form. They can point to an input with two outputs or show where a vertical line crosses a graph twice.
Common Misconceptions: Some students think two inputs cannot share an output. Others miss that a repeated input paired with different outputs makes a relation fail the function rule.
How to Assess It: Exit ticket: Is {(1, 4), (2, 4), (1, 7)} a function? Name the input that proves your answer.

Lesson moves

Hand out input and output number cards, have pairs build arrow diagrams, then add one arrow that makes a relation fail the function rule.
Sketch (1, 2), (1, 5), and (2, 5); ask students to write which input breaks the function rule and why.
Play function or not with five mini graphs; students raise F or N cards and mark any input with two outputs.
Show a vending machine button chart and ask whether button A3 could lead to both chips and water if the machine follows the function rule.

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