3.NF.1

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.

1/2

2/3

3/5

2/4

1/4

Resources

Videos


EngageNY Lessons


Extra Practice


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.