Montana Math MT.CORE.ALG.LIN.1

MathGrades 9–12Linear Functions and Expressions

The Standard

Understand that linear functions have a constant rate of change.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students find how much the output changes as the input changes. They recognize a linear function when the change per unit of input stays the same, even if the output falls.
What Mastery Looks Like: Given a table or graph, students calculate the change in output divided by the change in input between pairs of points. They check that the rate stays the same and use it to predict another value.
Common Misconceptions: Students may compare output values without checking how far the input moves. They may mistake the starting value for the rate or think a falling line cannot be linear.
How to Assess It: Give students x-values 0, 2, 4, 6 and y-values 3, 7, 11, 15. Ask whether the rate is constant and what the output changes by for each one-unit increase in x.

Lesson moves

Build towers of 2, 5, 8, and 11 cubes, then plot height against tower number on graph paper.
Compare y-values (2, 5, 8) and (2, 5, 9) at x = 0, 1, 2; explain which has a fixed rate.
Sort cards labeled x = 0, 1, 2, 3 with y-values (2, 4, 6, 8), (2, 4, 7, 11), and (8, 6, 4, 2) by rate.
Calculate fares for 1, 3, and 5 miles using a $4 starting charge plus $2 per mile; find the cost added per mile.

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