Montana Math MT.CORE.ALG.EXP.1

MathGrades 9–12Exponential Functions and Expressions

The Standard

Understand that exponential functions have a constant common ratio over equal intervals, and identify the common ratio in tables and equations.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students compare outputs when the input changes by the same amount each time. They find the multiplier between outputs in a table and locate the multiplier in an equation.
What Mastery Looks Like: For x-values 0, 1, 2, 3 and outputs 3, 6, 12, 24, a student shows that each output is twice the previous one. In y = 3(2)^x, they identify 2 as the multiplier, not 3.
Common Misconceptions: Students may look for a constant difference instead of dividing consecutive outputs. They may call the starting value in an equation the ratio, or overlook unequal gaps between input values.
How to Assess It: Give students x-values 0, 1, 2, 3 and outputs 80, 40, 20, 10. Ask them to find the multiplier and circle it in y = 80(0.5)^x.

Lesson moves

Fold a sheet of paper four times, record the layers after each fold, and divide each count by the previous count.
Compare 5, 10, 20, 40 with 5, 10, 15, 20; ask which pattern uses the same multiplier each step and why.
Race to match table cards (4, 12, 36; 5, 10, 20) with equation cards (y=4(3)^x; y=5(2)^x), then label each ratio.
Start with $100 in a savings account earning 5% yearly interest; list balances after three years and find the yearly multiplier.

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