Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Comparing 3/5 and 2/3 is harder than comparing 3/8 and 5/8, because the pieces are different sizes and the numbers alone do not tell the story. Fourth graders learn several ways to decide. They can rename both fractions with a common denominator (3/5 = 9/15 and 2/3 = 10/15, so 2/3 is larger), rename them with a common numerator, or compare each fraction to a benchmark such as 1/2 or 1. For example, 3/8 is less than one half and 4/7 is more than one half, so 3/8 < 4/7 without any calculation.
The standard also insists on a condition that is easy to forget: a comparison only makes sense when both fractions refer to the same whole. Students record their comparisons with >, = or < and justify them, often with a fraction strip or number line drawn to the same length.
Choosing the most efficient strategy for a given pair is itself part of the skill, and strong students explain why a benchmark works faster than common denominators for some pairs.
Students reason that 1/8 is greater than 1/4 because 8 is greater than 4. Folding strips shows that more pieces in the same whole means each piece is smaller.
Some students say 2/3 and 3/4 are equal because each is one piece away from a whole. The missing pieces are different sizes, so the fractions differ.
A student may claim 1/2 of a small pizza is more than 1/2 of a large one is impossible to compare. Stress that symbolic comparisons assume the same whole.
Seeing 3/10 and 2/5, students pick 3/10 because 3 is more than 2. Renaming 2/5 as 4/10 shows that 2/5 is actually larger.
Compare 3/5 and 2/3. Use >, = or <.
Answer: 3/5 < 2/3, because 3/5 = 9/15 and 2/3 = 10/15.
Present pairs that suit different strategies so students learn to choose: same numerator (3/7 vs 3/10), benchmark (5/12 vs 4/6), and genuinely close pairs that need common denominators (5/6 vs 7/8). Discussing which strategy was fastest builds flexibility.
Assessments often present a comparison and ask students to select every true statement or to explain an error. Have students write a one-sentence justification with every comparison so the reasoning becomes automatic.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) <
3/8 is less than one half (4/8), and 4/7 is more than one half (3.5/7). So 3/8 < 4/7.
Answer: A) <
With denominator 24, 5/6 = 20/24 and 7/8 = 21/24. Since 20 < 21, 5/6 < 7/8.
Answer: 4
Multiply top and bottom by 2: 2/5 = 4/10. Since 4/10 > 3/10, 2/5 is larger than 3/10.
Answer: A) Ava is wrong: sixths are smaller pieces than fourths, so 1/6 < 1/4
Cutting the same whole into 6 pieces makes smaller pieces than cutting it into 4. One small piece is less than one bigger piece, so 1/6 < 1/4.
Answer: B) 9/10
Each fraction is missing one or more pieces from a whole: 3/4 misses 1/4, 5/8 misses 3/8, 9/10 misses 1/10 and 2/3 misses 1/3. 1/10 is the smallest gap, so 9/10 is closest to 1.
Answer: =
Divide the numerator and denominator of 4/12 by 4 to get 1/3. They are equal.
A full lesson with slides, activities and an exit ticket on comparing fractions, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 4.NF.A.2 with an answer key, ready in about a minute.
Make a worksheet βTurn comparing fractions into a quiz students answer online that marks itself, with a class summary for you.
Build a test βA familiar fraction such as 1/2 or 1 used as a reference point. If one fraction is less than 1/2 and the other is more, you can compare them without renaming.
A fraction is a part of a specific whole. Half of a large pizza is more food than half of a small one, so fraction comparisons only make sense when the wholes match.