Equivalent Fractions

10 min

Narrative

The purpose of this Warm-up is to elicit students’ prior understanding of equivalence and strategies for comparing fractions. To determine equivalence, students may rely on familiarity with benchmark fractions, use fraction strips, or think about the relative sizes of the fractional parts. Students may also use their knowledge about fractions with the same numerator or denominator. In any case, students have opportunities to look for and make use of structure (MP7).

This is the first time students experience the True or False? routine in grade 4. Students should be familiar with this routine from a previous IM grade. However, they may benefit from a brief review of the steps involved.

Launch

  • Display one statement.
  • “Give me a signal when you know whether the statement is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategy.
  • Repeat with each statement.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 48=78\frac{4}{8}=\frac{7}{8}
  • 34=68\frac{3}{4}=\frac{6}{8}
  • 26=28\frac{2}{6}=\frac{2}{8}
  • 63=42\frac{6}{3}=\frac{4}{2}

Sample Response

  • False: 4 eighths can’t be the same size as 7 eighths.
  • True: In each 1 fourth there are 2 eighths, so in 3 fourths there are 6 eighths.
  • False: A sixth is greater than an eighth, so 2 sixths is greater than 2 eighths.
  • True: 6 thirds make 2, and 4 halves also make 2.
Activity Synthesis (Teacher Notes)
  • If no students refer to a visual representation (a tape diagram or number line) to explain why 34=68\frac{3}{4}=\frac{6}{8} is true, ask how one of these representations could help with their explanation.
  • “For the pair of fractions that you know are not equal, can you tell which fraction is greater? How?”
Standards
Building Toward
  • 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

20 min

15 min