Lesson 12

An Algorithm Using Partial Quotients

Lesson Purpose

The purpose of this lesson is for students to learn an algorithm using partial quotients to divide multi-digit numbers by two-digit numbers.

Lesson Narrative

In previous lessons, students used estimation strategies, properties of operations, and the relationship between multiplication and division to divide multi-digit numbers by two-digit divisors. They analyzed different strategies for recording partial quotients.

In this lesson, students move from strategies to algorithms in which the connections to place value, properties of operations, and the relationship between multiplication and division are clear. Students interpret an algorithm using partial quotients with a two-digit divisor for the first time. They used this algorithm with one-digit divisors in grade 4. They practice using this algorithm with less and less scaffolding. Throughout the lesson, the emphasis is on making sense of each step and the different operations used in each step. Students also see that there are many different ways to correctly find a quotient with this algorithm and they are encouraged to find partial quotients that make sense to them. 

  • Representation

Learning Goals

Teacher Facing

  • Make sense of an algorithm using partial quotients.

Student Facing

  • Let's make sense of an algorithm using partial quotients.

Required Preparation

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

Think about a recent time from class when your students were confused. What did you do to support them in reasoning about their confusion together as a community of learners?

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)

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