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
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)