Lesson 12

Represent Division of Unit Fractions by Whole Numbers

Lesson Purpose

The purpose of this lesson is for students to use diagrams and equations to represent division of a unit fraction by a whole number.

Lesson Narrative

In the previous lesson, students solved problems about dividing a unit fraction by a whole number in a way that made sense to them. In this lesson, students use tape diagrams to represent division of a unit fraction by a whole number. The tape diagrams used to represent the problems are familiar to students from earlier grades. Here is a tape diagram showing \(\frac{1}{4}\), one out of 4 pieces is shaded:

Diagram

One way to show \(\frac{1}{4} \div 3\) is to divide the \(\frac{1}{4}\) into 3 equal pieces.

Diagram. 4 equal parts. One third of 1 part shaded. Total length, 1.

To see how much is shaded we can divide all of the \(\frac{1}{4}\)s and see that \(\frac{1}{4} \div 3 = \frac{1}{12}\).

Diagram. 12 equal parts. 1 part shaded. Total length, 1.

Students use these diagrams to understand this series of steps representing division of a unit fraction by a whole number throughout the lesson.

  • Engagement

Activity 2: Priya’s Work

Learning Goals

Teacher Facing

  • Make sense of diagrams that represent division of a unit fraction by a whole number.

Student Facing

  • Let’s make sense of diagrams that represent division of a unit fraction by a whole number.

Required Preparation

CCSS Standards

Addressing

Lesson Timeline

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

Teacher Reflection Questions

What did you say, do, or ask during the lesson synthesis that helped students be clear on the learning of the day? How did understanding the cool-down of the lesson before you started teaching today help you synthesize that learning?

Suggested Centers

  • Rolling for Fractions (3–5), Stage 4: Multiply Fractions (Addressing)
  • Compare (1–5), Stage 4: Divide within 100 (Supporting)
  • How Close? (1–5), Stage 7: Multiply Fractions and Whole Numbers to 5 (Supporting)

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