Standard

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Student language:

• "I can show and understand that fractions are equal parts of 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

This standard refers to the sharing of a whole being partitioned or split. Fraction models in third grade include area (parts of a whole) models (circles, rectangles, squares) and number lines.

In 3.NF.1 students should focus on the concept that a fraction is made up (composed) of many pieces of a unit fraction, which has a numerator of 1. For example, the fraction 3/5 is composed of 3 pieces that each have a size of 1/5 .

Vocabulary

• numerator
  • Example: the 5 in 5/6
  • The numerator represents the number of segments that the number is to the right of 0.
  • For the fraction 5/6, if you count 5 segments of 1/6 , you end up at 5/6 .
• denominator
  • Example: the 6 in 5/6
  • The denominator represents the total number of equal parts between 0 and 1.
  • For the fraction 5/6, there are six equal segments between 0 and 1 so each segment is 1/6 .

Some important concepts related to developing understanding of fractions include:

• Understand fractional parts must be equal-sized.
• The number of equal parts tells how many make a whole. (4 equal parts means the whole is broken into fourths and 4/4 equals 1 whole)
• As the number of equal pieces in the whole increases, the size of the fractional pieces decreases. (1/2 is larger than 1/3 because a half of a pizza is larger than a third. The same is true for a third being larger than one fourth of a pizza.) See 3.NF.3.
• The size of the fractional part is relative to the whole.

Resources

Videos

• Instructional Video (11:00 - 12:24)
• Khan Academy
  • scroll to 3.NF.1, 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.1
• Common Core Sheets

Released Assessment Questions

PARCC

3.NF.1

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• Tasks do not involve the number line.
• Fractions equivalent to whole numbers are limited to 0 through 5.
• 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.