Montana Math MT.PLUS.ALG.MOD.2

MathGrades 9–12Modeling

The Standard

Interpret the coefficients in a polynomial, exponential, logarithmic, and trigonometric 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 numbers in an equation mean for the situation it models. They do this for polynomial, exponential, logarithmic, and trigonometric models, using units and local context.

What Mastery Looks Like

A student can explain a polynomial's starting value and changing rate, an exponential growth factor, and the output change caused by multiplying a logarithmic model's input. They can read a sine model's amplitude, midline, and period in context.

Common Misconceptions

Students read a quadratic's squared-term coefficient as a fixed change per unit. They call a 1.04 multiplier 104% growth and treat a log coefficient as change per added unit. They confuse a sine model's amplitude with its full range.

How to Assess It

Exit ticket: Explain -50 in ticket profit P(n)=-0.02n²+8n-50 dollars and 1.04 in savings V(y)=200(1.04)^y dollars, where n is tickets sold and y is years. Then explain 10 in sound level D(r)=10log10(r) decibels, where r is an intensity ratio, and 12 in a sample temperature model near Poplar, T(d)=12sin(2πd/365)+3 °C, where d is days.

Lesson moves

Ways to Teach It

  1. Give pairs a printed sample temperature graph for Poplar; use string and rulers to mark its midline and measure its amplitude in °C.

  2. Ask students: Why does 1.04 in V(t)=200(1.04)^t mean 4% growth, not a $1.04 increase each year?

  3. Run a coefficient relay using P(n)=-0.02n²+8n-50, D(r)=10log10(r), and T(t)=12sin(2πt/365)+3; teams match -50, 10, and 12 to meanings.

  4. Fit NOAA monthly temperatures near Poplar, home to Fort Peck Assiniboine and Sioux communities, to a sine curve and interpret its amplitude.

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