Montana Math MT.CORE.ALG.FUN.3.a
The Standard
- MT.CORE.ALG.FUN.3
- Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by: Understanding that different representations highlight different aspects of functions, choosing the representation that is appropriate for the context, and Comparing properties of two functions, including when each is represented in a different way.
Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by: Understanding that different representations highlight different aspects of functions, choosing the representation that is appropriate for the context, and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students show the same relationship with a story, table, graph, and equation. They choose the form that best answers a question and use a graphing tool when it helps.
What Mastery Looks Like
- Given a $4 starting fee plus $2 per mile, a student writes C = 4 + 2m, makes a matching table, and graphs it with sensible scales and labeled axes. They use the equation for an exact fare and the graph to show how the fare grows.
Common Misconceptions
- Students may graph the fare as starting at $0 and leave out the $4 fee. They may use uneven tick marks or think the table values are the only possible fares.
How to Assess It
- Exit ticket: A ride costs $4 plus $2 per mile. Write an equation, make a table for 0, 2, and 4 miles, and sketch a labeled graph; then choose the best form for finding the cost at 13 miles and explain why.
Lesson moves
Ways to Teach It
Give pairs graph paper and a taxi fare card showing $4 to start and $2 per mile; have them fill a table and plot points.
Ask, 'Would you use a graph or an equation to find the taxi fare for 17 miles? Why?'
Hand out taxi stories, fare tables, equations, and graphs, including one graph with the wrong starting fare; teams find the mismatch.
Enter two phone plans, $20 plus $5 per GB and $35 plus $2 per GB, in a spreadsheet; graph costs and compare at 10 GB.
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Related Standards
- MT.CORE.ALG.QUAD.3.a
Choosing the form strategically when writing an expression based on given information and intended use,
- MT.CORE.ALG.FUN.3
Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by: Understa...
- MT.CORE.ALG.FUN.3.b
Comparing properties of two functions, including when each is represented in a different way.
- MT.CORE.ALG.LIN.3.b
Converting between representations, and
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