CCSS.Math.Content.5.NF.B.7
The standard
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Common Core State Standards for Mathematics · Number and Operations—Fractions
What this standard means
Students need to model and solve two kinds of division problems: a unit fraction divided by a whole number, and a whole number divided by a unit fraction. They should connect the numbers to a story, a picture, and an equation, not just memorize a rule.
Mastery looks like explaining why 1/3 ÷ 4 is smaller than 1/3, and why 4 ÷ 1/3 is larger than 4. Students often mix up the two problem types, flip the wrong number, or lose the meaning of the answer. Visual models help catch those errors.
Ways to teach it
- Hands-on activity: Give students paper fraction strips and ask them to split 1/2 into 3 equal parts, then write 1/2 ÷ 3.
- Discussion prompt: Ask, “Which is greater, 3 ÷ 1/4 or 1/4 ÷ 3, and how do you know without calculating?”
- Quick assessment: Have students draw and solve 2 ÷ 1/5, then explain what the 10 means in the story.
- Real-world connection: Use a recipe card and ask how many 1/4-cup servings are in 3 cups of flour.
Plan a lesson for CCSS.Math.Content.5.NF.B.7
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Related standards
- CCSS.Math.Content.5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- CCSS.Math.Content.4.NF.B
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
- CCSS.Math.Content.6.NS.A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- CCSS.Math.Content.5.NF.B
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.