Montana Math MT.PLUS.ALG.EXP.1

MathGrades 9–12Exponential and Logarithmic Functions

The Standard

Understand logarithmic functions as the inverse of exponential functions.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students rewrite exponential equations as logarithmic equations and back. They use reversed inputs and outputs to explain how a logarithm finds an exponent.
What Mastery Looks Like: Given 2^3 = 8, students write log_2(8) = 3. On a graph, they match (3, 8) on y = 2^x with (8, 3) on y = log_2(x). They explain why log_2(0) has no real value.
Common Misconceptions: Some students treat log_2(8) as 8 divided by 2. Others think log_2(0) = 0 because 2^0 = 1, or assume a logarithm can take a negative input.
How to Assess It: On an exit ticket, ask: Rewrite 3^4 = 81 as a logarithm, then explain why log_3(0) has no real value.

Lesson moves

Give pairs cards showing (0,1), (1,2), and (3,8) on y = 2^x; have them swap coordinates, plot both sets, and label the inverse.
Ask students to explain in two sentences why log_2(8) = 3 but log_2(0) has no real answer.
Run a matching game with cards labeled 3^4 = 81, log_3(81) = 4, 10^2 = 100, and log_10(100) = 2.
Show a bacteria count that triples each hour from one cell; ask when it reaches 81 cells and have students write the matching logarithm.

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