Montana Math MT.CORE.ALG.MOD.2
The Standard
Interpret the coefficients in a linear, quadratic, and exponential model in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students explain what the numbers in linear, quadratic, and exponential models mean in a given situation. They identify starting amounts, units, and how each model describes change.
What Mastery Looks Like
- For weekly attendance, a student reads y=40+5t as 40 people to start and 5 more each week. In y=40+5t+2t², they explain that the 2 makes weekly gains grow and that the first week adds 7, not 5. In y=40(1.2)^t, they identify 20% growth per week.
Common Misconceptions
- Students may call every coefficient a starting amount. They may mistake the t coefficient in a quadratic for the first week's increase and ignore the t² term. They may read an exponential factor of 1.2 as 1.2% growth instead of 20%.
How to Assess It
- Exit ticket: Let t be weeks and y be dollars raised at a hypothetical community seedling sale. Explain each number in y=10+2t, y=10+2t+t², and y=10(1.2)^t, then find the quadratic model's increase from week 0 to week 1.
Lesson moves
Ways to Teach It
Give pairs counters and three hypothetical seedling-sale cards: y=10+2t, y=10+2t+t², y=10(2)^t; build dollar totals for weeks 0, 1, and 2.
Read the Salish Kootenai College library webpage, then discuss hypothetical weekly visits y=20(1.1)^t: what do 20 and 1.1 mean?
Play coefficient match with three model cards and cards naming each coefficient's meaning and units; require students to explain each match.
Use a local café's posted drink price to model the cost of t drinks, then explain the coefficient's dollars-per-drink units.
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Printable MT.CORE.ALG.MOD.2 Worksheet
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