Representing Fraction Decomposition with Visual Models
This Grade 4 Eureka Math skill teaches students to represent fraction decomposition simultaneously with three connected models: a tape diagram, a number bond, and an addition sentence. All three express the same core idea: a fraction like 4/5 equals 1/5 + 1/5 + 1/5 + 1/5. The tape diagram shades 4 of 5 equal parts, the number bond shows 4/5 branching into four 1/5 unit fractions, and the addition sentence states the sum. This multi-representation approach from Chapter 21 of Eureka Math Grade 4 deepens understanding of fractions as sums of unit fractions.
Key Concepts
The decomposition of a fraction into a sum of unit fractions can be represented by three connected models: a visual tape diagram, a schematic number bond, and a symbolic addition sentence. All three models represent the same core equation: $$\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}} {a \text{ times}}$$.
Common Questions
What three models represent fraction decomposition?
A tape diagram (shaded sections), a number bond (whole broken into parts), and an addition sentence. All three models represent the same fraction as a sum of unit fractions.
How does a tape diagram show the decomposition of 4/5?
Draw a rectangle divided into 5 equal parts and shade 4 of them. Each shaded part represents 1/5.
How does a number bond show the decomposition of 4/5?
Write 4/5 as the whole in a number bond with four branches, each showing 1/5.
What is the addition sentence for the decomposition of 4/5?
4/5 = 1/5 + 1/5 + 1/5 + 1/5. This symbolic form shows all four unit fraction parts adding up to the whole fraction.
Why use multiple representations for fraction decomposition?
Different representations appeal to different learning styles and reinforce the same concept from visual, relational, and symbolic angles simultaneously, building deeper understanding.