Lesson 12
An Algorithm Using Partial Quotients
Lesson Purpose
Lesson Narrative
In previous lessons, students used estimation strategies, properties of operations, and the relationship between multiplication and division to divide multidigit numbers by twodigit 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 twodigit divisor for the first time. They used this algorithm with onedigit 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
Addressing
Lesson Timeline
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
Suggested Centers
 Number Puzzles: Multiplication and Division (4–5), Stage 2: Multidigit Factors (Addressing)
 Watch Your Remainder (4–5), Stage 1: Onedigit Divisors (Supporting)
Print Formatted Materials
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