Montana Math MT.CORE.ALG.LIN.3.a
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: Identifying the rate of change and initial value in each representation.
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 situation with a steady rate into a table, graph, and equation. They explain where the starting amount and rate appear in each, and use a graphing tool to check their work.
What Mastery Looks Like
- For a book drive that starts with $40 and earns $5 per book, a student writes y = 5x + 40 and makes a table with 0, 1, and 2 books. Their graph starts at 40 and rises by 5 for each book, and they can explain what both numbers mean.
Common Misconceptions
- Students may swap the starting amount and rate in the equation. They may call the first table value the starting amount when the table begins at x = 1, or draw the graph through (0, 0) when the starting amount is not zero.
How to Assess It
- Exit ticket: A community book sale starts with $25 in donations and earns $7 per book sold. Write an equation, make a table for 0, 1, and 2 books, sketch the graph, and label the starting amount and rate.
Lesson moves
Ways to Teach It
Use play money to model a fictional Blackfeet Community College book drive: $40 to start, $5 per book sold; record a table.
Ask students to write where the $40 and $5 appear on a graph and in an equation, and what each means.
Run a card sort matching tables, graphs, equations, and story cards; students mark each rate and starting value.
Use a spreadsheet to graph the fictional Blackfeet Community College book drive, then explain why doubling books sold does not double the total.
Free download
Printable MT.CORE.ALG.LIN.3.a Worksheet
A ready-to-print activity worksheet aligned to MT.CORE.ALG.LIN.3.a, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- MT.CORE.ALG.LIN.1
Understand that linear functions have a constant rate of change.
- MT.8.F.4
Given linear data relating two quantities, construct a linear function that models the data and interpret the rate of change and initial value of a linear funct...
- MT.CORE.ALG.LIN.4.c
Understanding the relationship between slope-intercept form, the rate of change, and the initial value,
- MT.CORE.ALG.LIN.3.b
Converting between representations, and
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson