Lesson 7

Fractions as Sums

Lesson Purpose

The purpose of this lesson is for students to decompose a fraction into a sum of fractions with the same denominator in more than one way, and to write an equation for each decomposition.

Lesson Narrative

In previous lessons, students expressed a fraction \(\frac{a}{b}\) as a product of a unit fraction \(\frac{1}{b}\) and a whole number \(a\). In this lesson, students transition to seeing a fraction \(\frac{a}{b}\) as a sum of unit fractions and non-unit fractions with the same denominator. Students see that a fraction with a numerator greater than 1 can be decomposed into sums in different ways. They write equations to record the decomposition (for example, \(\frac{4}{6} = \frac{3}{6} + \frac{1}{6}\)). Later, they write equations to represent addition of fractions with the same denominator.
  • Action and Expression
  • MLR7

Learning Goals

Teacher Facing

  • Recognize that a fraction can be decomposed into a sum of fractions with the same denominator.
  • Write equations to represent fraction decomposition.

Student Facing

  • Let’s write fractions as sums.

Required Materials

Materials to Gather

Required Preparation

Activity 1:

  • Gather \(\frac{1}{4}\)-cup and \(\frac{3}{4}\)-cup measuring cups, if available.

CCSS Standards

Building On


Building Towards

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 the times you observed students listening to one another’s ideas today in class. What norms would help each student better attend to their classmates' ideas in future lessons?

Suggested Centers

  • Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Addressing)
  • Estimate and Measure (1–4), Stage 3: Quarter Inches (Supporting)
  • Target Measurements (2–5), Stage 2: Quarter Inches (Supporting)

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