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
| 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)