# Lesson 9

Recording Partial Products: One-digit and Three- or Four-digit Factors

### Lesson Purpose

The purpose of this lesson is for students to multiply a multi-digit number by a one-digit number using an algorithm that uses partial products. Students make connections between this algorithm, rectangular diagrams, and equations.

### Lesson Narrative

In previous lessons, students used diagrams to represent multiplication of a one-digit number and a whole number of up to four digits. They learned to decompose larger factors by place value and used diagrams and corresponding expressions to support them in finding partial products. In this lesson, students learn an algorithm for keeping track of partial products that come from multiplying the digits of the factors. This algorithm that uses partial products lays the foundation for the standard algorithm for multiplication.

Students engage in quantitative and abstract reasoning (MP2) as they relate the partial products in a diagram and in an algorithm. Because this lesson offers an initial exposure to the new notation, students are not required to use an algorithm that uses partial products to multiply. They can rely on other methods they have learned so far.

• Action and Expression
• MLR8

Activity 1: An Algorithm for Noah

### Learning Goals

Teacher Facing

• Multiply multi-digit whole numbers by one-digit numbers using an algorithm that uses partial products.

### Student Facing

• Let’s analyze and try an algorithm that uses partial products.

### Lesson Timeline

 Warm-up 10 min Activity 1 20 min Activity 2 15 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

What part of the lesson went really well today in terms of students learning? What did you do that made that part go well?

### Suggested Centers

• Number Puzzles: Multiplication and Division (4–5), Stage 1: Two-digit Factors (Addressing)
• Compare (1–5), Stage 3: Multiply within 100 (Supporting)

### Print Formatted Materials

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