CCSS.Math.Content.3.NF.A.3d
The Standard
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide which fraction is greater when the pair shares a numerator or denominator. They use comparison symbols and explain their choice with equal-sized wholes, drawings, or reasoning.
What Mastery Looks Like
- Students correctly compare fraction pairs and use the right symbol. They justify each answer with equal-sized fraction bars, number lines, or clear reasoning about piece size.
Common Misconceptions
- Students may think a larger denominator means a larger fraction, so they choose 3/8 over 3/5. They may also compare models built from different-sized wholes or reverse the meaning of < and >.
How to Assess It
- Exit ticket: Compare 3/8 and 3/5 using <, >, or =. Draw equal-sized fraction bars and write one sentence explaining your answer.
Lesson moves
Ways to Teach It
Fold equal-sized paper strips into halves, thirds, fourths, and eighths, then place selected fractions side by side to compare them.
Ask, "Which is greater, 2/3 or 2/5, and how do equal numerators help you decide?"
Play Fraction War with cards showing pairs that share a numerator or denominator, and require the winner to explain each comparison.
Compare portions of two same-size pizzas, such as 3/4 and 3/8, and discuss why pizza size must stay equal.
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Printable 3.NF.A.3d Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.3.NF.A.3d, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.3.NF.A.1
Comparing same-numerator or same-denominator fractions depends on knowing a/b as a parts of equal unit fraction size.
- CCSS.Math.Content.1.NBT.B.3
Comparing two-digit numbers supports using greater than, less than, and equal symbols, but fraction size reasoning is a new idea.
- CCSS.Math.Content.3.NF.A.2
Placing fractions on a number line develops fraction size and same-whole reasoning used to compare and justify fractions.
What This Unlocks
Mastery here sets students up for these next.
Keep exploring
Related Standards
- CCSS.Math.Content.3.NF.A.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- CCSS.Math.Content.3.NF.A.3a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- CCSS.Math.Content.4.NF.C.7
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Recor...
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