Standard: 5.NF.B7 – Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Grade level: Grade 5
Subject: Mathematics
Domain: Numbers & Operations – Fractions
Teacher Overview
This standard focuses on extending students’ understanding of division to include dividing unit fractions by whole numbers and whole numbers by unit fractions. It is crucial for developing a deeper comprehension of fractions and their operations, which are foundational for higher-level math concepts. Students should have a solid grasp of basic division and multiplication, understand fractions, and know how to represent them. Prior experience with dividing whole numbers is also essential.
After mastering this standard, students will be able to tackle more complex fraction problems, including those with mixed numbers and improper fractions, and apply these skills to solve real-world problems.
Common Misconception 1
A common misconception is that dividing by a fraction is the same as dividing by a whole number. This is incorrect because dividing by a fraction actually involves multiplying by its reciprocal, which can increase the value.
Intervention 1
To remediate this misconception, use visual aids like fraction bars or pie charts to illustrate how dividing by a fraction increases the value. Provide plenty of practice with real-world examples.
Common Misconception 2
Another misconception is that the result of dividing a whole number by a fraction is always smaller. This is incorrect because dividing by a fraction can result in a larger number, depending on the fraction.
Intervention 2
To address this, provide examples and practice problems showing how dividing by a fraction can result in a larger number. Use visual aids and real-world applications to reinforce this concept.
Prerequisite Knowledge
Students should understand basic division and multiplication, be familiar with fractions and how to represent them, and have experience with dividing whole numbers.
Subsequent Knowledge
Students will develop skills in solving more complex fraction problems, including those involving mixed numbers and improper fractions, and will be able to apply these skills to real-world situations.
Instructional Activities
- Using fraction bars to visualize division of fractions
- Cooking activities to practice dividing recipes
- Group work to solve real-world fraction problems
- Interactive online fraction games
- Worksheets with word problems involving fractions
