Standard: 5.NF.B3 – Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Grade level: Grade 5
Subject: Mathematics
Domain: Numbers & Operations – Fractions
Teacher Overview
This standard requires students to understand fractions as a division of the numerator by the denominator. It is crucial as it lays the foundation for more complex operations involving fractions and real-world problem-solving. Students should be comfortable with basic division and have a foundational understanding of fractions, including identifying numerators and denominators.
Once students master this standard, they will be equipped to tackle more complex fraction problems, including operations with fractions and applying fraction concepts to real-world situations.
Common Misconception 1
Some students may think that a fraction like 3/4 means dividing 3 by 4 to get 3. This is incorrect because 3/4 actually means 3 parts out of 4 equal parts.
Intervention 1
Use visual fraction models to demonstrate that 3/4 means dividing something into 4 equal parts and taking 3 of those parts.
Common Misconception 2
Another common misconception is that fractions cannot represent quantities greater than one. This is incorrect because fractions can indeed represent quantities greater than one, such as improper fractions and mixed numbers.
Intervention 2
Provide examples of improper fractions and mixed numbers, and use visual aids to show how these fractions represent quantities greater than one.
Prerequisite Knowledge
Students should have a solid understanding of basic division and multiplication. They should also be familiar with the concept of fractions, including how to identify the numerator and denominator.
Subsequent Knowledge
After mastering this standard, students will be able to solve more complex word problems involving fractions, including addition, subtraction, multiplication, and division of fractions. They will also be able to apply these skills in real-world contexts.
Instructional Activities
- Use fraction circles to visualize division problems.
- Create word problems involving sharing items equally.
- Use fraction strips to compare and contrast different fractions.
- Solve real-world problems involving division and fractions.
- Group activities where students divide objects and represent the division as fractions.
