Lesson 7

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.

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.

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

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?