Unit Plan 26 (Grade 3 Math): Multiplying by Multiples of 10—Place-Value Patterns
Multiply one-digit numbers by multiples of 10 using place-value models and properties—not “add a zero”—to build patterns, explain tens-based reasoning, and justify efficient strategies.
Focus: Use place-value reasoning to multiply one-digit numbers by multiples of 10 (10–90); analyze patterns and connect to properties of operations (especially the distributive/associative properties).
Grade Level: 3
Subject Area: Mathematics (Number & Operations in Base Ten • Operations & Algebraic Thinking)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build a conceptual model for facts like 6 × 40 using tens as units (e.g., 6 groups of 4 tens = 24 tens = 240). They look for regularity in products (MP.8), record place-value patterns on charts/arrays, and justify strategies with properties of operations rather than “add a zero.”
Essential Questions
- Why does multiplying by a multiple of 10 scale a product by tens?
- How do place-value models and properties (e.g., 6 × (4 × 10) = (6 × 4) × 10) explain shortcuts?
- What patterns do we notice across problems like 3 × 20, 3 × 30, 3 × 40?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Represent one-digit × multiple of 10 using tens rods, arrays, and place-value charts.
- Explain products in terms of tens (e.g., “5 × 30 = 5 groups of 3 tens = 15 tens = 150”).
- Use properties of operations to justify reasoning and efficient computation.
- Generalize patterns in a table (input: factor and multiple-of-10; output: product) and describe the rule.
Standards Alignment — CCSS Grade 3
- 3.NBT.3: Multiply one-digit whole numbers by multiples of 10 (10–90) using strategies based on place value and properties of operations.
- 3.OA.5: Apply properties of operations (associative, distributive, commutative) as strategies to multiply.
- MP.8: Look for and express regularity in repeated reasoning (spot and articulate product patterns).
- (Supporting) MP.6: Attend to precision (units as tens, clear notation).
Success Criteria — Student Language
- I can show one-digit × multiple of 10 with a model and explain my steps.
- I can describe a product in tens (e.g., “24 tens = 240”) using place-value language.
- I can name the property that justifies my shortcut and state the pattern I see.