3.NF.2
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
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
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
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.