What is this skill?
Comparing fractions in third grade means deciding which of two fractions is greater when they have the same denominator or the same numerator. With the same denominator, such as 3/8 and 5/8, the pieces are the same size, so the fraction with more pieces is greater: 5/8 > 3/8.
With the same numerator, such as 2/3 and 2/6, there are the same number of pieces, but the pieces are different sizes. Thirds are bigger than sixths, because the whole is cut into fewer parts. So 2/3 > 2/6. Third graders also learn that the comparison only makes sense when both fractions refer to the same size whole: half of a small pizza is not the same amount as half of a large one.
Why it matters
Comparing fractions checks whether a child understands what the numerator and denominator mean. The idea that a bigger denominator means smaller pieces goes against what children know about whole numbers, so working through it builds a much deeper understanding of fractions.
This leads to comparing fractions with different numerators and denominators in fourth grade, to equivalent fractions and to ordering fractions on a number line. It is also useful in everyday life, from recipes to sharing food fairly to understanding that a quarter of an hour is less than a half hour.
Common mistakes
- Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4. Drawing or folding the two fractions shows that eighths are smaller pieces.
- Comparing only the denominators when the numerators are different, or only the numerators when the denominators are different. Ask "Is the bottom number the same, or the top number?" before deciding.
- Reading the comparison symbols backward. Reading the full sentence aloud, like "five-eighths is greater than three-eighths," helps.
- Comparing fractions of different-sized wholes. Use same-sized paper strips or circles for all comparisons.
How to help at home
- Fold same-sized paper strips into halves, thirds, fourths, sixths and eighths, label them, and line them up to compare.
- Ask fair-share questions: "Would you rather have 1/3 of this pizza or 1/6 of it? Why?"
- Use measuring cups when cooking: which holds more, 1/4 cup or 1/2 cup? What about 2/4 cup and 3/4 cup?
- Ask your child to explain each comparison in their own words, using the size or number of pieces.
- Play "closer to one": for pairs like 5/6 and 5/8, ask which one needs a smaller piece added to make a whole. The fraction missing less is the greater one.
Worked examples
These are real questions from the Tutorsaurus comparing fractions practice, with the answers worked out.
Example 1
7/8 ? 3/8
Choices: >, <, =
Answer: >. Same denominator, so compare the tops: 7 vs 3. 7/8 > 3/8.
Example 2
4/5 ? 2/5
Choices: >, <, =
Answer: >. Same denominator, so compare the tops: 4 vs 2. 4/5 > 2/5.
Example 3
3/4 ? 3/5
Choices: >, <, =
Answer: >. Same numerator, so the smaller denominator means bigger pieces. 3/4 > 3/5.