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
What this standard means
Students need to compare two fractions when the numerators match or the denominators match. They should explain the comparison using the size of the pieces or the number of pieces, not by tricks alone. They also need to remember that both fractions must describe the same-sized whole.
Mastery looks like a student saying, “3/8 is less than 3/6 because sixths are larger pieces than eighths,” then writing 3/8 < 3/6. Common trouble spots are comparing denominators like whole numbers, ignoring the size of the whole, and using symbols backward.
Ways to teach it
- Give pairs fraction strips and ask them to build 2/6 and 2/8, then place the correct comparison symbol between them.
- Ask students to explain in writing: Which is greater, 4/5 or 4/6, and how do you know?
- Show 3/4 and 3/8 on same-sized rectangles, then have students hold up >, <, or = cards.
- Compare slices from two same-sized pizzas, such as 1/2 and 1/4, then discuss why different-sized pizzas would not work.
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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...
- CCSS.Math.Content.4.NF.A.2
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark ...