Non-unit Fractions on the Number Line

10 min

Narrative

The purpose of this Choral Count is for students to practice counting by 14\frac{1}{4} and to notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students will locate fractions on the number line, using their knowledge of unit fractions. Save the recorded count to compare to a count in an upcoming lesson.

Launch

  • “Count by 14\frac{1}{4}, starting at 14\frac{1}{4}.”
  • Record as students count. Record 4 fractions in each row, and then start a new row. There will be 4 rows.
  • Stop counting and recording at 164\frac{16}{4}.
Teacher Instructions
  • “What patterns do you see?”
  • 1–2 minutes: quiet think time
  • Record responses.
Solution Steps (4)
  1. 1
    Count by 1/4 starting at 1/4
    →1/4, 2/4, 3/4, 4/4, 5/4, ... up to 16/4
  2. 2
    Notice pattern in numerator
    →Top number (numerator) increases by 1 each count
  3. 3
    Notice pattern in denominator
    →Bottom number (denominator) stays at 4
  4. 4
    Learn vocabulary
    →Denominator = number of equal parts, Numerator = number of parts described

Sample Response

Sample responses:

  • The top part of the fraction goes up by 1.
  • The bottom part of the fraction doesn’t change.
  • The rows end at counts of 4 in the top, like 4, 8, 12, 16.
Activity Synthesis (Teacher Notes)
  • “How is counting by fractions the same as counting by whole numbers? How is it different?” (The top of the fraction is just like counting by whole numbers, going up by 1. The bottom of the fraction is different because it doesn’t change.)
  • Consider asking:
    • “Who can restate the pattern in different words?”
    • “Does anyone want to add an observation on why that pattern is happening here?”
    • “Do you agree or disagree? Why?”
  • “This is a place where it’s helpful to talk about the top part of the fraction and the bottom part of the fraction. We have words for those parts. The bottom part of a fraction is called the denominator. It tells how many equal parts into which the whole is partitioned. The top part of a fraction is called the numerator. It tells how many of the equal parts are being described. Look for places in today's lesson where that terminology might help you explain your reasoning.”
  • Display the terms “denominator” and “numerator” along with their definitions, and keep them displayed throughout the lesson.
Standards
Building Toward
  • 3.NF.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  • 3.NF.A.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.

15 min

10 min

10 min