Standard

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?

Student Language:

• "I can understand that fractions are really the division of a numerator by the denominator."
• "I can solve word problems where I divide whole numbers to create an answer that is a mixed number."

Explanation

About the Math, Learning Targets, and Rigor

This standard calls for students to extend their work of partitioning a number line from third and fourth grade. Students are expected to demonstrate their understanding using concrete materials, drawing models, and explaining their thinking when working with fractions in multiple contexts. They read 5/3 as “five thirds” and after many experiences with sharing problems, learn that 5/3 can also be interpreted as “5 divided by 3.”

Resources

Videos

• Khan Academy
  • Scroll to 5.NF.3, click on skill, find videos on left side of each skill
• Learn Zillion

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 5th grade at bottom, then 5.NF.3
• Common Core Sheets

Released Assessment Questions

PARCC

Common Core State Standards

5.NF.3-1

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

• Tasks do not have a context.

STUDENT SAMPLE RESPONSE

5.NF.3-2

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?

• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.
• Note that one of the italicized examples in standard 5.NF.3 is a two-prompt problem.

STUDENT SAMPLE RESPONSE

Performance Indicators: 5.NF.3-1, 5.NF.3-2

Level 5: Exceeds Expectations

Solves word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Interprets the fraction as division of the numerator by the denominator.

Identifies a simple model representing the situation.

Describes a model to represent the situation.

Level 4: Meets Expectations

Solves word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Interprets the fraction as division of the numerator by the denominator.

Critiquing/Reasoning Standards

5.C.2-3

Base explanations/reasoning on the relationship between multiplication and division.

(Content Scope: Knowledge and skills articulated in 5.NF.3, 5.NF.4a)

Performance Indicators: 5.C.2-3

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student constructs and communicates a well-organized and complete written response based on explanations/reasoning using the:

• properties of operations
• relationship between addition and subtraction
• relationship between multiplication and division

Response may include:

• a logical/defensible approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, reasonings, and approaches, utilizing mathematical connections (when appropriate). Provides a counter-example where applicable.

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student constructs and communicates a well-organized and complete written response based on explanations/reasoning using the:

• properties of operations
• relationship between addition and subtraction
• relationship between multiplication and division

Response may include:

• a logical/defensible approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, reasonings, and approaches, utilizing mathematical connections (when appropriate).