Number and Operations-Fractions
Number and Operations-Fractions introduces fractions as numbers. Grade 3 students build fractions from unit fractions, place them on number lines, recognize simple equivalent fractions, and compare fractions with the same numerator or the same denominator.
Core rules
- A fraction 1/b is the quantity formed by one part when a whole is partitioned into b equal parts (3.NF.A.1).
- A fraction a/b is a copies of 1/b. For example, 3/4 = 1/4 + 1/4 + 1/4 (3.NF.A.2).
- On a number line, divide the interval from 0 to 1 into b equal intervals; the first mark is 1/b.
- Equivalent fractions name the same point: 1/2 = 2/4 = 4/8 (3.NF.A.3).
- Compare fractions with the same denominator by comparing numerators. Compare fractions with the same numerator by reasoning about the size of the parts.
- Whole numbers can be written as fractions: 1 = 4/4 and 3 = 3/1.
Worked example
Compare 3/4 and 3/8. Both have numerator 3, so each is three unit fractions. Fourths are larger than eighths because dividing the same whole into 4 equal parts makes bigger pieces than dividing it into 8. So 3 copies of 1/4 is greater than 3 copies of 1/8: 3/4 > 3/8. A number line confirms it: 3/8 is less than 1/2, while 3/4 is greater than 1/2.
Traps that cost marks
- Thinking 1/8 > 1/4 because 8 > 4. More parts means smaller parts.
- Counting tick marks instead of intervals on a number line, which shifts every fraction by one.
- Partitioning a shape into unequal parts and still calling them fractions of the whole.
- Comparing fractions taken from different-sized wholes.
- Writing 4/4 as 4 instead of 1.