Lesson 3

Partial Products in Algorithms

Lesson Purpose

The purpose of this lesson is for students to multiply multi-digit whole numbers using partial products.

Lesson Narrative

In previous lessons, students multiplied three-digit numbers and two-digit numbers, using strategies based on place value and the properties of operations. Students used diagrams to illustrate and explain their partial products calculations.

In this lesson, students move from diagrams to an algorithm that records partial products which they used in an earlier course when multiplying a two-digit number and a two-digit number. Students relate partial product expressions to diagrams and then analyze a systematic way to record partial products. This work sets students up to learn the standard algorithm in the next lesson.

  • Action and Expression
  • MLR8

Learning Goals

Teacher Facing

  • Multiply a three-digit number and a two-digit number.
  • Represent a partial products algorithm.

Student Facing

  • Let’s find partial products.

Required Materials

Materials to Copy

  • Partial Product Expressions

Required Preparation

Activity 1:

  • Create a set of cards from the blackline master for each group of 2.

CCSS Standards


Building Towards

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 a future lesson, students will learn how to use the standard algorithm for multiplication to multiply multi-digit numbers. How do the diagrams and expressions used in today’s lesson support this work?

Suggested Centers

  • Number Puzzles: Multiplication and Division (4–5), Stage 1: Two-digit Factors (Supporting)

Print Formatted Materials

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Additional Resources

Google Slides

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PowerPoint Slides

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