In this Grade 4 Eureka Math lesson from Chapter 21, students learn to decompose fractions such as 3/4 and 2/3 into equivalent fractions like 6/8 and 8/12 by partitioning area models into smaller equal units. Students express these equivalences using addition and multiplication sentences with unit fractions, building a concrete understanding of why two fractions with different numerators and denominators can represent the same value. The lesson extends prior work with unit fractions to non-unit fractions across a variety of denominators including fourths, eighths, thirds, and twelfths.
Section 1
Decomposing Fractions Using Area Models
To decompose a fraction, you can partition an area model into smaller, equal-sized pieces. If you partition each of the original pieces into new, smaller pieces, you create an equivalent fraction by multiplying the numerator and denominator by .
Section 2
Writing Addition Sentences for Decomposed Fractions
When a fraction is decomposed, you can write an addition sentence using parentheses to show how each original part is broken down. Each group in parentheses represents one of the original fraction's parts, showing the sum of the new, smaller unit fractions it is now made of.
Expand to review the lesson summary and core properties.
Section 1
Decomposing Fractions Using Area Models
To decompose a fraction, you can partition an area model into smaller, equal-sized pieces. If you partition each of the original pieces into new, smaller pieces, you create an equivalent fraction by multiplying the numerator and denominator by .
Section 2
Writing Addition Sentences for Decomposed Fractions
When a fraction is decomposed, you can write an addition sentence using parentheses to show how each original part is broken down. Each group in parentheses represents one of the original fraction's parts, showing the sum of the new, smaller unit fractions it is now made of.