Number and Operations-Fractions
This domain introduces fractions as numbers, not just shaded pieces of a picture. You should name unit fractions, place fractions on a number line, recognize simple equivalent fractions, and compare two fractions with the same numerator or the same denominator.
Core rules
- 1/b is one equal part of a whole split into b parts; 3/b is three of those parts.
- On a number line, the interval from 0 to 1 is split into equal parts, and the end of the third part is 3/b.
- Equivalent fractions name the same amount: 1/2 = 2/4 = 4/8.
- Same denominator: more parts means a larger fraction, so 3/8 > 2/8.
- Same numerator: a larger denominator means smaller parts, so 3/4 > 3/8.
Worked example
Compare 3/4 and 3/8 and explain your answer. Reasoning: both fractions count three parts, but fourths are larger than eighths. On a number line, 3/4 sits closer to 1 than 3/8 does. A model split into 8 equal parts shows that 3/8 is less than half, while 3/4 is more than half. Answer: 3/4 > 3/8.
Traps that cost marks
- Thinking 1/8 > 1/4 because 8 is bigger than 4.
- Comparing numerators when the denominators are different.
- Counting tick marks instead of intervals on a number line.
- Forgetting that 4/4 equals 1 whole, so a fraction can equal or exceed a benchmark.