Standard

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Student language:

• "I can label fractions on a number line because I know the space between any two numbers can be thought of as a whole."

Note: Grade 3 expectations are limited to fractions with denominators 2, 3, 4, 6, and 8

Explanation

About the Math, Learning Targets, and Rigor

The number line diagram is the first time students work with a number line for numbers that are between whole numbers (e.g., that 1/2 is between 0 and 1).

3.NF.2a

On a number line from 0 to 1, students partition (divide) it into equal parts and recognize that each segmented part represents the same length.

For example, in the number line diagram below, the space between 0 and 1 is divided (partitioned) into 4 equal regions. The distance from 0 to the first segment is 1 of the 4 segments from 0 to 1 or 1/4.

3.NF.2b

Students label each fractional part based on how far it is from zero to the endpoint.

For example, on the number line below, the distance from 0 to the third segment is 3 segments that are each one-fourth long. Therefore, the distance of 3 segments from 0 is the fraction 3/4.

Resources

Videos

• Instructional Video (12:25 - 13:45)
• Khan Academy
  • scroll to 3.NF.2, click on a skill, watch videos on left side in each skill
• Learn Zillion
  • 3.NF.2a
  • 3.NF.2b

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 3rd grade at bottom, then 3.NF.2
• Common Core Sheets
  • 3.NF.2a
  • 3.NF.2b

Released Assessment Questions

PARCC

3.NF.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

• Fractions may be greater than 1.
• Fractions equivalent to whole numbers are limited to 0 through 5.
• Fractions equal whole numbers in 20% of these tasks.
• Tasks have “thin context”2 or no context.
• Tasks are limited to fractions with denominators 2, 3, 4, 6, and 8.

STUDENT SAMPLE RESPONSE

3.NF.A.Int.1

In a contextual situation involving a whole number and two fractions not equal to a whole number, represent all three numbers on a number line diagram, then choose the fraction closest in value to the whole number.

• Fractions equivalent to whole numbers are limited to 0 through 5.
• Fraction denominators are limited to 2, 3, 4, 6 and 8.

Performance Indicators: 3.NF.2, 3.NF.A.Int.1

Level 5: Exceeds Expectations

• Understands 1/b is equal to one whole that is partitioned into b equal parts – limiting the denominators to 2, 3, 4, 6 and 8.
• Represents 1/b on a number line diagram by partitioning the number line between 0-1 into b equal parts recognizing that b is the total number of parts.
• Demonstrates the understanding of the quantity a/b by marking off a parts of 1/b from 0 on the number line and states that the endpoint locates the number a/b.
• Applies the concepts of 1/b and a/b in real-world situations.
• Describes the number line that best fits the context.

Level 4: Meets Expectations

• Understands 1/b is equal to one whole that is partitioned into b equal parts – limiting the denominators to 2, 4 and 8.
• Represents 1/b on a number line diagram by partitioning the number line between 0-1 into b equal parts recognizing that b is the total number of parts.
• Demonstrates the understanding of the quantity a/b by marking off a parts of 1/b from 0 on the number line.

Critiquing Standards

3.C.6-1

Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response)

(Content scope: Knowledge and skills articulated in 3.NF.2)

• Tasks are limited to fractions with denominators 2, 3, 4, 6, and 8.
• Fractions equivalent to whole numbers are limited to 0 through 5.

Performance Indicators: 3.C.6-1

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on operations using concrete referents such as diagrams- -including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:

• a logical 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
• determination of whether an argument or conclusion is generalizable
• evaluating, interpreting, and critiquing the validity of other’s responses, approaches, and reasoning, and providing a counterexample where applicable

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which may include:

• a logical 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
• evaluating, interpreting, and critiquing the validity of other’s responses, approaches, and reasoning.