# Lesson 19

Division With and Without Remainders

### Lesson Purpose

The purpose of this lesson is for students to use an algorithm that uses partial quotients to find whole number quotients and remainders with up to four-digit dividends and one-digit divisors. Students also analyze some common errors when using an algorithm that uses partial quotients.

### Lesson Narrative

In this lesson, students deepen and apply what they learned about partial quotients to divide four-digit numbers by single-digit divisors. They also deepen their understanding of an algorithm that uses partial quotients—by noticing how the algorithm shows whether a division would result in a remainder, and by analyzing missteps that are commonly made in an algorithm like it.

• Representation
• MLR2

### Learning Goals

Teacher Facing

• Find whole-number quotients and remainders using an algorithm that uses partial quotients.

### Student Facing

• Let’s find quotients and remainders using an algorithm that uses partial quotients.

### Lesson Timeline

 Warm-up 10 min Activity 1 15 min Activity 2 10 min Activity 3 10 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

Students have encountered many different ways to reason about division in the past few lessons. They might have other unique ways to think about division. Identify one or more ways in which your students’ thinking offered a new insight or a positive surprise today.

### Suggested Centers

• Compare (1–5), Stage 4: Divide within 100 (Supporting)
• Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Supporting)

### Print Formatted Materials

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