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


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 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)

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