CCSS.Math.Content.4.NF.B.4b
The standard
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
Common Core State Standards for Mathematics
What this standard means
Students need to see a fraction like 2/5 as two copies of 1/5, then see 3 × 2/5 as three groups of two fifths. They should use drawings, fraction strips, and number lines to show that the total is 6 fifths, or 6/5.
Mastery looks like connecting the picture, repeated addition, and equation without guessing. Students often multiply both the numerator and denominator, or they lose track of what the denominator means. They may also write 6/15 because they treat it like whole-number multiplication only.
Ways to teach it
- Hands-on activity: Give pairs fraction strips and have them build 4 groups of 3/8, then record the total as eighths.
- Discussion prompt: Ask, “Why does 5 × 2/3 have thirds in the answer, not fifteenths?”
- Quick assessment: Students draw a number line model for 3 × 4/6 and write the product as an improper fraction.
- Real-world connection: Use a recipe card where one batch needs 2/5 cup of oil, then find oil needed for 4 batches.
Plan a lesson for CCSS.Math.Content.4.NF.B.4b
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Related standards
- CCSS.Math.Content.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a...
- CCSS.Math.Content.4.NF.B.4a
Understand a fraction a/b as a multiple of 1/b.
- CCSS.Math.Content.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
- CCSS.Math.Content.4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.