Montana Math MT.CORE.NUM.REAL.1

MathGrades 9–12The Real Number System

The Standard

Use reasoning to establish properties of integer exponents, including scientific notation.

2026 Montana Mathematics Content Standards · Numeric Reasoning

Teacher's field guide

What Students Need to Do: Students use multiplication and division to explain why exponent rules work, including zero and negative exponents. They use powers of 10 to write and calculate with numbers in scientific notation.
What Mastery Looks Like: A student can show why (2^3)^2 = 2^6 and 2^-2 = 1/4, rather than just reciting a rule. They can write 0.00062 as 6.2 × 10^-4 and explain the negative exponent.
Common Misconceptions: Students may think 3^-2 means -9 or 3^0 means 0. They may add exponents when raising a power to a power, or move the decimal the wrong way for a negative power of 10.
How to Assess It: Exit ticket: Write 10^3 / 10^5 as a fraction and as a single power, then explain why the results agree. Write 0.0048 in scientific notation.

Lesson moves

Give pairs a 16 cm paper strip to halve repeatedly; have them label the lengths from 2^4 to 2^-2.
Ask students to explain in writing why 5^0 equals 1, using 5^3 / 5^3 as evidence.
Play exponent match: students pair cards showing 2^3 × 2^-5, 2^-2, and 1/4, then explain each match.
Give students virus and cell diameters of 1.2 × 10^-7 m and 1.2 × 10^-5 m; ask which is larger and by how much.

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