Montana Math MT.CORE.ALG.LIN.3.b
The Standard
- MT.CORE.ALG.LIN.3
- Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Identifying the rate of change and initial value in each representation. Converting between representations, and Writing equations for a line perpendicular or parallel to a given line that passes through a given point.
Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Converting between representations, and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a linear situation into a table, graph, and equation. They also work backward from a graph, table, or equation to describe the situation. They use a graphing tool to check their work.
What Mastery Looks Like
- Given a table of time and distance, a student finds the change per minute, writes an equation, and draws the matching line. They explain what the starting value and rate mean.
Common Misconceptions
- Students may treat the first table entry as the starting value, even when time does not start at zero. They may confuse the total distance with the change per minute or overlook the scale on a graph.
How to Assess It
- Exit ticket: A shuttle starts 12 miles from its stop and travels 3 miles every 5 minutes. Make a table for 0, 5, and 10 minutes, write an equation for miles remaining, and sketch the graph.
Lesson moves
Ways to Teach It
Pairs slide a paper shuttle along a taped number line, moving 3 miles every 5 minutes, then record distance remaining in a table.
Show two graphs with the same slope but different starting values; ask which fits a shuttle starting 12 miles away and why.
Play a four-card matching game with stories, tables, graphs, and equations; students check each set with a graphing app.
Using a publicly posted Arlee Celebration schedule, students choose an event and graph minutes remaining during the hour before its listed start.
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Printable MT.CORE.ALG.LIN.3.b Worksheet
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Related Standards
- MT.PLUS.ALG.POLY.2.b
Converting between factored and standard form symbolically and using representations (e.g., area model), and
- MT.CORE.ALG.QUAD.3.b
Converting between factored, standard, and vertex forms symbolically and using representations,
- MT.CORE.ALG.FUN.3.a
Understanding that different representations highlight different aspects of functions, choosing the representation that is appropriate for the context, and
- MT.CORE.ALG.LIN.3.a
Identifying the rate of change and initial value in each representation.
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