Lesson 2

Represent Unit Fraction Multiplication

Lesson Purpose

The purpose of this lesson is for students to write and evaluate expressions given a diagram that represents the product of two unit fractions.

Lesson Narrative

In the previous lesson, students drew diagrams to represent a unit fraction of another unit fraction in context. The purpose of this lesson is for students to draw diagrams representing products of unit fractions and to examine the relationship between expressions and diagrams in greater depth. Students examine different methods for representing unit fraction products with a diagram and they interpret how a diagram represents a given expression.

This diagram represents both \(\frac {1}{4} \times \frac {1}{3}\) and \(\frac {1}{3} \times \frac {1}{4}\). In future lessons, this diagram will be used to represent multiplication expressions and equations because of its flexibility. 


Student generated diagrams may be different.

In this diagram, we see \(\frac {1}{4} \times \frac {1}{3}\). We would need to adapt the diagram to show \(\frac{1}{3} \times \frac {1}{4}\) more clearly. We could do this by extending the partition lines all the way across.

  • Representation

Learning Goals

Teacher Facing

  • Represent multiplication of unit fractions with diagrams and expressions

Student Facing

  • Let’s write expressions to represent multiplication of unit fractions.

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

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)
  • Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Supporting)
  • Five in a Row: Multiplication (3–5), Stage 4: Three Factors (Supporting)

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