Montana Math MT.CORE.ALG.LIN.2

MathGrades 9–12Linear Functions and Expressions

The Standard

Understand slope as a rate of change and y-intercept as the initial value.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students use a table, graph, or equation to find how much an output changes for each one-unit increase in input. They also find the output when the input is zero.
What Mastery Looks Like: Given a bike rental graph, a student identifies the hourly charge and the cost before riding. They use those amounts to predict the cost for five hours.
Common Misconceptions: Students may call the first point shown on a graph the starting amount, even when its input is not zero. They may use the change in output alone instead of dividing by the change in input.
How to Assess It: Exit ticket: A tank starts with 60 gallons and loses 4 gallons each minute, so G = 60 - 4t. What do 60 and -4 mean, and how much remains after 5 minutes?

Lesson moves

Start with 100 mL in a marked cup, add 50 mL per pour, and have students graph volume against pours.
Show points (2, 11) and (4, 17), and have pairs explain why 11 is not the starting value.
Give pairs prepared graph, equation, and table cards; have them match cards with the same per-step change and value at zero.
Use a bike rental sign showing a $10 base fee and $4 per hour; students calculate costs for 0, 1, and 3 hours.

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