Montana Math MT.8.EE.5
The Standard
Graph proportional relationships, interpret the unit rate as the slope of the graph, and compare two different proportional relationships as tables, graphs, and equations.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use pairs of values to draw a line through (0, 0). They find how much the output changes when the input increases by 1, then use that rate to compare situations shown in different forms.
What Mastery Looks Like
- A student can find the rate from a table, graph, or equation and name its units. They can graph two situations and explain which has the greater rate, even when the given input values differ.
Common Misconceptions
- Students may count grid squares without checking the axis scales, or divide input by output instead of output by input. They may compare output values at different input values rather than finding each rate.
How to Assess It
- Exit ticket: A table shows (hours, dollars) as (0, 0) and (2, 6). Another plan costs y = 4x dollars for x hours. Graph both plans, find each hourly cost, and name the cheaper plan for 3 hours.
Lesson moves
Ways to Teach It
Use grid paper and two colors to plot (0, 0), (1, 3), (2, 6) and (0, 0), (1, 4), (2, 8); draw lines and label rates.
Ask: Two lines pass through the origin, and one is steeper; how can you tell which situation has the higher rate?
Give pairs cards showing y = 2x, y = 3x, y = 4x, plus matching tables and graphs; have them sort by rate.
Use price tags for 12 ounces at $3 and 20 ounces at $4; graph each cost line and compare prices per ounce.
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