Number and Operations - Fractions (Grade 3)
Grade 3 introduces fractions as numbers. Students build fractions from unit fractions, place them on a number line, recognize simple equivalent fractions, and compare fractions with the same numerator or the same denominator. The NYS test uses partitioned shapes, number lines, and story contexts, and often asks for an explanation of why two fractions are equivalent or which is larger.
Core rules
- A unit fraction 1/b is one equal part of a whole split into b equal parts. A fraction a/b is a copies of 1/b.
- The denominator counts the equal parts in the whole; the numerator counts the parts being described.
- On a number line, partition the interval from 0 to 1 into b equal lengths. The point at the end of the a-th part is a/b.
- Equivalent fractions name the same point: 1/2 = 2/4 = 4/8. Multiply numerator and denominator by the same number to generate them.
- Same denominator: more parts means a larger fraction, so 5/8 is greater than 3/8. Same numerator: a larger denominator means smaller parts, so 1/4 is greater than 1/8.
- Whole numbers can be written as fractions: 4 = 4/1, and 6/3 = 2 because three thirds make one whole.
Worked example
Compare 3/4 and 5/8. Rename 3/4 in eighths: multiply numerator and denominator by 2, giving 6/8. Since 6/8 and 5/8 have the same denominator, compare numerators: 6 is greater than 5, so 3/4 is greater than 5/8.
Traps
Partitioning a shape into unequal parts and still calling them fractions. Counting tick marks on a number line instead of intervals. Thinking 1/8 is greater than 1/4 because 8 is greater than 4. Comparing numerators only when denominators differ. Assuming every fraction is less than 1.