CCSS.Math.Content.5.NF.B.4
The standard
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Common Core State Standards for Mathematics · Number and Operations—Fractions
What this standard means
Students need to see fraction multiplication as taking part of a part, not just memorizing steps. They should multiply a fraction by a whole number and a fraction by a fraction, using area models, number lines, and equations. They also need to connect the model to the product.
Mastery looks like a student drawing or reading a model for problems like 2/3 of 3/4, writing the matching equation, and explaining why the answer is smaller or larger. Students often get stuck treating numerator and denominator as separate whole numbers, or expecting multiplication to always make numbers bigger.
Ways to teach it
- Hands-on activity: Have students shade 3/4 of a paper rectangle one way, then shade 2/3 of it the other way and count the overlap.
- Discussion prompt: Ask, "Why is 1/2 × 1/6 smaller than both factors, even though we multiplied?"
- Quick assessment: Give three area models and three equations, then have students match each model to its equation and product.
- Real-world connection: Use a recipe card and ask students to find 2/3 of 3/4 cup of sugar with a drawn model.
Plan a lesson for CCSS.Math.Content.5.NF.B.4
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Related standards
- CCSS.Math.Content.5.NF.B.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
- CCSS.Math.Content.6.NS.A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- 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.5.NF.B
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.