Unit Plan 12 (Grade 6 Math): Exponents & Order of Operations
6th graders master exponents and the order of operations through structured evaluation of numerical and variable expressions. They apply grouping conventions, substitute values accurately, and use estimation and reasoning to ensure precision and clarity in every step.
Focus: Evaluate numerical expressions with whole-number exponents; follow conventions and structure.
Grade Level: 6
Subject Area: Mathematics (Expressions & Equations – Exponents and Evaluation)
Total Unit Duration: 5 sessions (one week), 45-60 minutes per session
I. Introduction
Students develop a solid grasp of whole-number exponents and the order of operations so they can evaluate expressions accurately and efficiently. They connect exponents to repeated multiplication, practice with grouping symbols and nested expressions, and then evaluate variable expressions by substituting values—attending to parentheses and signs. Emphasis: precision, structure, and reasonableness of results.
Essential Questions
- How does an exponent represent repeated multiplication, and how do I read and write it precisely?
- Why do we need a convention (order of operations), and how do grouping symbols affect the result?
- How do I substitute values into an expression and keep track of signs and parentheses?
- How can estimation and structure help me check if an answer is reasonable?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Interpret and compute whole-number exponents as repeated multiplication (for example, 3^4 means 3×3×3×3).
- Evaluate numerical expressions using the order of operations, including exponents and grouping symbols.
- Evaluate algebraic expressions at given values (for example, 3a^2 + 2b when a = -4, b = 5), using parentheses correctly when substituting.
- Explain steps using precise mathematical language, and check reasonableness with estimation or bounds.
- Identify and correct common error patterns (for example, MD/AS must be done left-to-right; negative bases vs a leading negative sign).
Standards Alignment — CCSS Grade 6
- 6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.
- 6.EE.2c: Evaluate expressions at specific values of their variables; include expressions that arise from formulas; perform arithmetic operations (including those with whole-number exponents) in the conventional order when there are no parentheses to specify a particular order. Clarify that multiplication and division are on the same level (left-to-right), and addition and subtraction are on the same level (left-to-right).
Success Criteria — Student Language
- I can read and write exponents and explain them as repeated multiplication.
- I can follow the order of operations with exponents and grouping symbols and show each step.
- I can substitute numbers (including negatives) into an expression using parentheses and compute correctly.
- I can spot and fix errors (for example, -3^2 is not the same as (−3)^2).
- I can explain why my answer is reasonable using estimation or bounds.