# Lesson 16

### 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.

### 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)

### Print Formatted Materials

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