# 4.2 Fraction Equivalence and Comparison

## Unit Goals

• Students generate and reason about equivalent fractions and compare and order fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.

### Section A Goals

• Make sense of fractions with denominators 2, 3, 4, 5, 6, 8, 10, and 12 through physical representations and diagrams.
• Reason about the location of fractions on the number line.

### Section B Goals

• Generate equivalent fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.
• Use visual representations to reason about fraction equivalence, including using benchmarks such as $\frac{1}{2}$ and 1.

### Section C Goals

• Use visual representations or a numerical process to reason about fraction comparison.

### Glossary Entries

• common denominator
The same denominator in two or more fractions. For instance, $$\frac{1}{4}$$ and $$\frac{5}{4}$$ have a common denominator.

• composite number
A whole number with more than 1 factor pair.

• denominator
The bottom part of a fraction that tells how many equal parts the whole was partitioned into.

• equivalent fractions
Fractions that have the same size and describe the same point on the number line. For example, $$\frac{1}{2}$$ and $$\frac{2}{4}$$ are equivalent fractions.

• factor pair of a whole number
A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.

• multiple of a number
The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.

• numerator

The top part of a fraction that tells how many of the equal parts are being described.

• prime number
A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.