Lesson 11

Different Partial Quotients

Lesson Purpose

The purpose of this lesson is for students to use the relationship between multiplication and division and place value understanding to divide multi-digit numbers. 

Lesson Narrative

In the previous lesson, students found quotients in a way that makes sense to them. In this lesson, students consider notation to record a partial quotients strategy, which they have used with one-digit divisors in a prior course. Students use the notation to record how dividends can be decomposed in different ways to make different partial quotients. Students consider more efficient ways to make partial quotients based on place value understanding and calculations they are able to do mentally. 
  • Action and Expression

Activity 1: Division Expressions

Learning Goals

Teacher Facing

  • Divide multi-digit whole numbers using place value understanding and the relationship between multiplication and division.

Student Facing

  • Let’s use what we know about multiplication and place value to find quotients.

Required Materials

Materials to Copy

  • Partial Quotient Expressions

Required Preparation

Activity 1:

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

CCSS Standards


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

Reflect on how comfortable your students are asking questions of you and of each other. What can you do to encourage students to ask questions?

Suggested Centers

  • Number Puzzles: Multiplication and Division (4–5), Stage 2: Multi-digit Factors (Addressing)
  • Watch Your Remainder (4–5), Stage 1: One-digit Divisors (Supporting)

Print Formatted Materials

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Student Task Statements pdf docx
Lesson Cover Page pdf docx
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Teacher Guide Log In
Teacher Presentation Materials pdf docx
Blackline Masters zip

Additional Resources

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