Montana Math MT.CORE.ALG.EXP.3

MathGrades 9–12Exponential Functions and Expressions

The Standard

Understand the relationship between growth/decay factor and growth/decay rate.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students find a multiplier from a percent change and recover the percent change from a multiplier. They use the multiplier to find a new amount at each time step.
What Mastery Looks Like: Given 500(1.12)^t, a student identifies 12% growth and multiplies by 1.12 to find the next value. Given a 30% decrease each year, they use 0.70 as the multiplier.
Common Misconceptions: Students may call a factor of 0.80 an 80% decrease instead of a 20% decrease. Some use 0.20 as the multiplier for 20% growth. Others subtract the same amount each year instead of taking a percent of the new amount.
How to Assess It: Exit ticket: A $500 bike's value is multiplied by 0.92 each year. What is the yearly percent change, and what is its value after two years?

Lesson moves

Give pairs 150 counters; have them build 100, add 20%, then add 20% of the new pile and record both totals.
Ask students to write why multiplying a balance by 0.85 means it lost 15%, not 85%.
Play a card match with factors 1.06, 0.94, 1.25, and 0.70 and cards naming their matching percent changes.
Show a $200 phone losing 25% of its value each year; students calculate its value after two years using 0.75.

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