Montana Math MT.CORE.ALG.FUN.3

MT.CORE.ALG.FUN.3 is a cluster heading. These are the individual standards under it.

• 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.b

  Comparing properties of two functions, including when each is represented in a different way.

01

What Students Need to Do

Students show a function with a table, graph, equation, and description. They pick the form that helps answer a question and compare two functions shown in different forms.

02

What Mastery Looks Like

A student can compare starting costs and rates when one plan is shown in a table and another in an equation. They label graph axes with units and choose a scale that shows the values they need.

03

Common Misconceptions

Students may treat the first value in a table as the starting value, even when the input is not zero. They may compare points at different inputs or miss how a graph’s scale changes its appearance.

04

How to Assess It

For plans with constant per-GB rates, show Plan A as a table with (0, $8) and (5, $23), and Plan B as C = 5 + 4g. Ask: Which starts cheaper, which costs less at 5 GB, and how could you find where their costs match?

1. 01

   Give pairs a fare story, table, equation, and blank grid; have them plot points and label axes with a sensible scale.

2. 02

   Ask: A table gives exact fares, but a graph shows where costs cross. Which would you use to choose a ticket, and why?

3. 03

   Run a card sort: match each function table to its graph, then circle the larger starting value and steeper rate.

4. 04

   Give students two printed bus fare schedules; use a spreadsheet to graph total cost by rides and choose the cheaper option for 12 rides.

• MT.CORE.ALG.LIN.3

  Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultur...

• MT.8.F.2

  Compare properties of two functions using tables, graphs, and equations.

• MT.7.RP.2

  Recognize and represent proportional relationships between quantities, using tables, graphs, and equations by: Deciding whether a table represents quantities in...