Standard: 5.NF.B7a – Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Grade level: Grade 5
Subject: Mathematics
Domain: Numbers & Operations – Fractions
Teacher Overview
This standard focuses on helping students understand how to divide a unit fraction by a non-zero whole number and compute the quotient. It’s crucial because it builds a foundation for more advanced fraction operations and helps students see the relationship between multiplication and division. Students should be comfortable with basic fraction concepts, multiplication, and division of whole numbers. They should understand how to represent fractions visually and be able to use multiplication to verify division results.
After mastering this standard, students will be able to tackle more complex fraction division problems and will be prepared for learning about ratios and proportional relationships.
Common Misconception 1
Some students may believe that dividing by a whole number increases the value of the fraction because they are used to whole number division where the quotient is usually smaller.
Intervention 1
Use visual fraction models to show that dividing a fraction by a whole number results in a smaller fraction. Reinforce this with multiplication to verify the quotient.
Common Misconception 2
Students may confuse the roles of the numerator and the denominator, thinking that the numerator is always divided by the whole number.
Intervention 2
Provide clear examples and visual aids that show the correct process of dividing the entire fraction by the whole number and emphasize the roles of numerator and denominator.
Prerequisite Knowledge
Students should understand basic fraction concepts, including unit fractions and whole numbers. They should be familiar with multiplication and division of whole numbers and the relationship between these operations.
Subsequent Knowledge
Students will develop skills in dividing any fraction by a whole number and will extend their understanding to more complex fraction division problems. This will prepare them for understanding ratios and proportional relationships.
Instructional Activities
- Create story problems that involve dividing a unit fraction by a whole number.
- Use visual fraction models to demonstrate division of fractions.
- Practice problems that require students to verify their answers using multiplication.
