Equivalent Fractions

10 min

Teacher Prep
Required Preparation
  • Have recording of choral count by one-fourth available, from a previous lesson.

Narrative

The purpose of this Choral Count is to invite students to practice counting by 12\frac{1}{2} and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students recognize and generate equivalent fractions. In the Activity Synthesis, students have the opportunity to notice that both 22\frac{2}{2} and 44\frac{4}{4} are equal to 1 whole.

Launch

  • “Count by 12\frac{1}{2}, starting at 12\frac{1}{2}.”
  • Record as students count. Record 2 fractions in each row, and then start a new row. There will be 4 rows.
  • Stop counting and recording at 82\frac{8}{2}.
Teacher Instructions
  • “What patterns do you see?”
  • 1–2 minutes: quiet think time
  • Record responses.
Solution Steps (5)
  1. 1
    Count by 1/2 starting at 1/2
    →1/2, 2/2, 3/2, 4/2, 5/2, 6/2, 7/2, 8/2
  2. 2
    Notice pattern in numerator
    →Numerator increases by 1 each count
  3. 3
    Notice pattern in denominator
    →Denominator stays at 2
  4. 4
    Identify whole numbers in count
    →2/2=1, 4/2=2, 6/2=3, 8/2=4 (every 2nd fraction is a whole number)
  5. 5
    Compare to counting by 1/4
    →2/2 and 4/4 both equal 1 whole

Sample Response

Sample responses:
  • The denominator of the fraction never changes.
  • The numerator of the fraction is increasing by 1.
  • Each row ends with a number you say when you count by 2.
Activity Synthesis (Teacher Notes)
  • Display the count by 14\frac{1}{4} from a previous lesson. There should be 4 rows and 4 fractions in each row, with the count ending at 164\frac{16}{4}.
  • “How are these two counts the same? How are they different?” (The denominator stays the same in both counts—4 for the last count, and 2 for today’s count. The numerators change in the same way because they both count by 1. They start a new line at 22\frac{2}{2} and 44\frac{4}{4}, which are both whole numbers.)
  • Consider asking:
    • “Who can restate the pattern in different words?”
    • “Does anyone want to add an observation as to why that pattern is happening here?”
    • “Do you agree or disagree? Why?”
Standards
Addressing
  • 3.NF.3.b·Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
  • 3.NF.A.3.b·Recognize and generate simple equivalent fractions, e.g., <span class="math">\(1/2 = 2/4\)</span>, <span class="math">\(4/6 = 2/3\)</span>. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
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

20 min