#### MA19.3.15

Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

### Unpacked Content

## UP:MA19.3.15

### Vocabulary

- Equivalence
- Visual fraction model
- Number line
- Numerator
- Denominator
- Reasoning
- Conclusions
- Comparison
- Point

### Knowledge

- Fractions with different names can be equal.
- Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
- Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
- Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
- Comparing two fractions is only reasonable if they refer to the same whole.
- The meaning of comparison symbols , = .
- Reason about the size of a fraction to help compare fractions.
- Use a variety of area and length models to represent two fractions that are the same size but have different names.
- Use a fraction model to explain how equivalent fractions can be found.
- Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
- Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
- Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts. -Determine when two fractions can not be compared because they do not refer to the same size whole.

### Skills

- Explain equivalence of two fractions using visual models and reasoning about their size.
- Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
- Express whole numbers as fractions.
- Identify fractions equivalent to whole numbers.
- Record comparisons of two fractions using , or = and justify conclusion.
- Explain that the whole must be the same for the comparing of fractions to be valid.

### Understanding

- A fraction is a quantity which can be illustrated with a length model or an area model.
- Two fractions can be the same size but have different fraction names.
- A fraction can be equivalent to a whole number.
- Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
- The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
- The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in a whole.