Unit Plan 4 (Grade 8 Math): Exponent Essentials—Integer Powers
8th graders master the laws of integer exponents by rewriting and comparing expressions with positive, zero, and negative powers. This weeklong math unit builds structural reasoning, precision in notation, and confidence applying exponent properties to simplify expressions.
Focus: Use properties of integer exponents to rewrite and compare expressions, including negative exponents.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week students develop fluency with integer exponents. They will build and use the laws of exponents (product, quotient, power of a power, power of a product/quotient, zero exponent, negative exponents) to rewrite and compare expressions. Emphasis is on structure (why the rules work), precision with notation, and reasoning about size and order of magnitude.
Essential Questions
- How do exponent properties help me rewrite and simplify expressions efficiently?
- Why does a^0 = 1 and a^-n = 1/(a^n) (for a ≠ 0)?
- How can I compare expressions like 3^5 and 2^7 without a calculator?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Generate equivalent expressions using integer exponent properties (product, quotient, power of a power, power of a product/quotient).
- Interpret and compute with zero and negative exponents, connecting to reciprocals and order of magnitude.
- Compare expressions with exponents and justify which is larger using structural reasoning (common base, common exponent, or bounds).
- Communicate mathematics with clear notation, domain awareness (a ≠ 0 when needed), and step-by-step justification.
Standards Alignment — CCSS Grade 8
- Expressions & Equations 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions (e.g., 3^2 · 3^-5 = 3^-3 = 1/3^3 = 1/27; 2^-3 = 1/2^3 = 1/8; 5^0 = 1).
Success Criteria (student-friendly)
- I can rewrite expressions like 4^3 · 4^-5 and (2^3)^4 using correct laws of exponents.
- I can explain why a^0 = 1 and a^-n = 1/(a^n) using patterns or structure.
- I can compare expressions (for example, 3^5 vs. 2^7) and justify which is larger.
- My work shows clear steps, correct notation, and reasons for each move.