Unit Plan 7 (Grade 4 Math): Multiplication Strategies—From Arrays to Algorithms
Multiply up to 4-digit by 1-digit and 2-digit by 2-digit using place-value strategies, area models, and partial products, then connect to the standard algorithm with estimation checks for reasonableness.
Focus: Multiply up to 4-digit by 1-digit and 2-digit by 2-digit using place-value strategies, area models, and partial products; transition to the standard algorithm with estimation checks.
Grade Level: 4
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
This week develops conceptual and procedural fluency for multi-digit multiplication. Students decompose numbers by place value, model with arrays/area models, record partial products, and connect these to the standard algorithm. Emphasis: choosing efficient strategies, labeling units, and checking reasonableness with estimation.
Essential Questions
- How does place-value decomposition make multi-digit multiplication easier to see and compute?
- Why do area models and partial products match the standard algorithm?
- How do I know my answer is reasonable (estimation, compatible numbers, magnitude)?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Decompose factors by place value to build area models for 4-digit × 1-digit and 2-digit × 2-digit.
- Compute partial products and combine them accurately, attending to units and place alignment.
- Explain how the distributive property underlies area models and the standard algorithm.
- Use estimation and compatible numbers to predict/verify product size and check reasonableness.
- Solve multi-step word problems requiring multiplication and communicate choices of strategy.
Standards Alignment — CCSS Grade 4 (spiral across the unit)
- 4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations; illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- Mathematical Practices (MP.1–MP.8) threaded throughout.
Success Criteria — Student Language
- I can show my multiplication with an area model and partial products, and explain each step.
- I can use estimation to check if my product is reasonable.
- I can choose the standard algorithm or a model and justify why it’s efficient for this problem.