Lesson 16
Reason About Quotients
Lesson Purpose
The purpose of this lesson is for students to find quotients involving a whole number and a unit fraction and assess the reasonableness of their answers.
Lesson Narrative
In previous lessons students found the value of quotients of a unit fraction and a whole number. In this lesson they think about comparing the value of these quotients without calculating. For example, students know from earlier work that \(48 \div 4\) is less than \(48 \div 2\) because there are more groups of 2 in 48 than groups of 4. By the same reasoning \(10 \div \frac{1}{3}\) is less than \(10 \div \frac{1}{5}\) because \(\frac{1}{5}\)s are smaller than \(\frac{1}{3}\)s and so it takes more \(\frac{1}{5}\)s to make an amount. This kind of reasoning also shows that \(\frac{1}{4} \div 15\) is less than \(\frac{1}{4} \div 12\) because dividing the same amount into more pieces creates smaller pieces.
 Engagement
Learning Goals
Teacher Facing
 Assess the reasonableness of quotients.
 Divide unit fractions and whole numbers.
Student Facing
 Let’s apply what we know about division to make sure our answers make sense.
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
Reflect on a time your thinking changed about something in class recently. How will you alter your teaching practice to incorporate your new understanding?
Suggested Centers
 Compare (1–5), Stage 8: Divide Fractions and Whole Numbers (Addressing)
 Rolling for Fractions (3–5), Stage 5: Divide Unit Fractions and Whole Numbers (Addressing)
 How Close? (1–5), Stage 6: Multiply to 3,000 (Supporting)
Print Formatted Materials
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