Unit Plan 2 (Grade 5 Math): Place Value Patterns & Powers of Ten
5th graders explore digit shifts when multiplying or dividing by powers of ten, using place-value reasoning and exponent notation (10ⁿ). Students model patterns, correct misconceptions like “add a zero,” and explain results with precision across whole and decimal numbers.
Focus: Explore how digits shift by powers of 10 and explain patterns when multiplying/dividing by 10^n using place-value reasoning and exponent notation.
Grade Level: 5
Subject Area: Mathematics (Number & Operations in Base Ten — Place Value & Powers of Ten)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Building on launch-week norms, students deepen place-value understanding by describing and justifying digit shifts when multiplying or dividing by powers of 10. They use exponent notation (10^n) to name powers of ten, connect patterns to place-value charts and models, and explain why “multiply by 10” is a shift, not “add a zero”—especially with decimals.
Essential Questions
- How do digits shift when a number is multiplied or divided by 10^n?
- Why is thinking in terms of place value more reliable than “add/remove zeros,” especially for decimals?
- How does exponent notation (10^n) help us name and predict the size of numbers quickly?
- When is a quick estimate using powers of ten better than exact calculation?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Explain the ten-times/one-tenth relationship among adjacent places and describe digit shifts for 10^n.
- Use exponent notation to represent powers of ten and predict the effect on a number (whole or decimal).
- Multiply and divide numbers (whole and decimal) by 10, 100, 1000, … and explain results using place-value language.
- Diagnose and correct common misconceptions (e.g., “add a zero”) with models and counterexamples.
- Choose when to use a power-of-ten estimate for reasonableness in real contexts.
Standards Alignment — CCSS Grade 5
- 5.NBT.1: In a multi-digit number, a digit in one place represents 10 times what it represents to the right and 1/10 of what it represents to the left.
- 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and in the placement of the decimal point when a decimal is multiplied or divided by a power of 10; use whole-number exponents to denote powers of 10.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify/critique), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can explain why multiplying by 10^n shifts digits left n places and dividing by 10^n shifts them right n places.
- I can write 10^n to name a power of ten and predict what happens to a number (including decimals).
- I can model my reasoning on a place-value chart or with disks/base-ten blocks.
- I can spot and fix the “add a zero” error with a decimal counterexample.
- I can decide when a power-of-ten estimate gives a quick, reasonable check.