Learn on PengiEureka Math, Grade 4Chapter 28: Exploring a Fraction Pattern

Lesson 1: Find and use a pattern to calculate the sum of all fractional parts between 0 and 1. Share and critique peer strategies.

In this Grade 4 Eureka Math lesson from Chapter 28, students discover and apply a pattern to calculate the sum of all fractional parts between 0 and 1 for both even and odd denominators, such as fourths, sixths, thirds, and fifths. Students use fraction cards to explore how pairing fractions that equal 1 simplifies finding these sums, then compare results across different denominators. The lesson also emphasizes sharing and critiquing peer strategies to deepen understanding of the pattern.

Section 1

Generalize the Sum of a Fractional Series

Property

The sum of the series of fractions $\frac{0}{n} + \frac{1}{n} + \frac{2}{n} + \dots + \frac{n}{n}$ can be found using the general formula:

Sum = \frac{n+1}{2}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Generalize the Sum of a Fractional Series

Property

The sum of the series of fractions $\frac{0}{n} + \frac{1}{n} + \frac{2}{n} + \dots + \frac{n}{n}$ can be found using the general formula:

Sum = \frac{n+1}{2}