Unit Plan 7 (Grade 5 Math): Decimal Multiplication—Models to Algorithm
5th graders multiply decimals by whole numbers and other decimals using area models, arrays, and algorithms. Students estimate to predict product size, justify decimal placement with place-value reasoning, and solve real-world problems with precision and clear mathematical communication.
Focus: Multiply decimals by whole numbers and by decimals; build understanding with area models/arrays and connect to place-value algorithms, estimation, and problem solving.
Grade Level: 5
Subject Area: Mathematics (Number & Operations in Base Ten — Decimal Operations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend multiplication to decimal factors. Beginning with models (hundred grids, area rectangles, number-line jumps) and scaling ideas, they transition to a place-value algorithm for decimal × whole and decimal × decimal. Throughout, they use estimation to predict the size of products and justify decimal-point placement.
Essential Questions
- How do area models and partial products show what happens when we multiply with decimals?
- How can estimation help predict the size of a product and check our work?
- Where does the decimal point go in the product—and why?
- How does scaling (grows/shrinks) depend on whether a factor is greater than 1 or less than 1?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Model decimal × whole and decimal × decimal using hundred grids, area rectangles, and number lines.
- Compute products using partial products and a place-value (standard) algorithm, explaining decimal placement using place-value reasoning (not rules-only).
- Use estimation (rounding, compatible numbers, front-end) to predict and verify product size.
- Solve word problems requiring decimal multiplication and units/precision decisions.
- Explain reasoning clearly with labeled models, units, and precise vocabulary.
Standards Alignment — CCSS Grade 5
- 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths using models and strategies based on place value and properties of operations; relate strategies to a written method and explain the reasoning.
- Mathematical Practices emphasized: MP.1 (make sense/persevere), MP.3 (justify/critique), MP.4 (model), MP.6 (precision), MP.7 (structure), MP.8 (regularity).
Success Criteria — Student Language
- I can show decimal multiplication with an area model or number line and connect it to my written method.
- I can place the decimal point in the product and explain why using place value/estimation.
- I can use estimation to predict the product and check reasonableness.
- I can solve word problems and label my units clearly.
- I can critique a solution that uses “just count digits” and give a better place-value explanation.