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### Overview

To decompose means to break apart. Students already decomposed whole numbers with number bonds, tape diagrams, and place value charts. In fourth grade, they will decompose fractions.

## UP:MA19.4.15

### Vocabulary

• Decomposition
• Unit fraction
• Area model
• Length model
• Equation
• Mixed number
• Visual fraction model
• Whole
• Sum
• Difference
• Recomposition

### Knowledge

Students know:
• Situation contexts for addition and subtraction problems.
• A variety of strategies and models to represent addition and subtraction situations.
• The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
• A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction. Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.

### Skills

Students are able to:
• Decompose fractions as a sum of unit fractions.
• Model decomposition of fractions as a sum of unit fractions.
• Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
• Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.

### Understanding

Students understand that:
• A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
• A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
• The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.

Audio/Video

### Resource Provider

PBS
Accessibility