Montana Math MT.CORE.ALG.FUN.3.b
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: Comparing properties of two functions, including when each is represented in a different way.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students show a function with a story, table, equation, and graph. They label graph axes and choose scales that show the data clearly. They compare two functions even when they are shown in different ways.
What Mastery Looks Like
- Given one plan as a table and another as an equation, a student finds each starting cost and cost per hour. They graph both plans and explain when the costs match and which plan costs less at a given time.
Common Misconceptions
- Students may treat the first table entry as the starting value, even when the input is not zero. They may compare costs at different times or read grid spacing as one unit without checking the scale.
How to Assess It
- Exit ticket: Rental A costs $5 plus $2 per hour; rental B costs $8 at 0 hours, $9 at 1 hour, $10 at 2 hours, and $11 at 3 hours. Graph both on labeled axes, then name which starts cheaper, which rises faster, and when the costs match.
Lesson moves
Ways to Teach It
Give pairs grid paper, a rental cost table, and a cost equation; have them plot both with labeled axes and circle where the lines meet.
Ask students to write why $5 plus $2 per hour costs less than $8 plus $1 per hour at two hours, but not four.
Deal linear cost table, equation, and graph cards; partners compare two unlike cards and justify which plan costs less at four hours.
Print two gym membership price sheets; students graph total cost by month in a spreadsheet, label axes, and compare six-month costs.
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Related Standards
- 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.FUN.3
Represent functions using tables, graphs with appropriate scales and labels, equations, and verbal situations, while using technology strategically by: Understa...
- MT.6.EE.3
Apply the properties of operations including the distributive property, to generate equivalent expressions and determine when two expressions are equivalent.
- MT.8.F.2
Compare properties of two functions using tables, graphs, and equations.
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