# Lesson 11

Partial Products and the Standard Algorithm

### Lesson Purpose

The purpose of this lesson is for students to analyze the standard algorithm for multiplication and compare it to an algorithm that uses partial products they saw in earlier lessons.

### Lesson Narrative

In previous lessons, students analyzed and used an algorithm that uses partial products to multiply multi-digit whole numbers. They learned that an algorithm can represent the base-ten diagrams and rectangular diagrams, but it is more efficient for keeping track of and recording partial products.

This lesson extends students’ analysis to include the standard algorithm for multiplication of multi-digit numbers. In grade 4, the standards focus on understanding place value and how it is represented in different methods for finding products. The work here serves to build the groundwork for making sense of the standard algorithm in grade 5, so students are not expected to use the standard algorithm at this time.

• Engagement
• MLR8

### Learning Goals

Teacher Facing

• Identify similarities and differences between algorithms that use partial-products and the standard algorithm for multiplication.
• Make sense of the standard algorithm for multiplication.

### Student Facing

• Let’s compare multiplication algorithms.

### 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

In grade 5, students will use the traditional algorithm. How does the way they analyzed two different algorithms in Activity 2 build toward this work?

### Suggested Centers

• Five in a Row: Multiplication (3–5), Stage 3: Two-digit Factors (Addressing)
• Compare (1–5), Stage 3: Multiply within 100 (Supporting)

### Print Formatted Materials

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