Use Equivalent Fractions to Compare

10 min

Narrative

The purpose of this Warm-up is to draw students’ attention to inequality statements. It reminds them of the meaning of inequality symbols and how to read the statements, which will be useful when students compare fractions later in the lesson. The Warm-up also elicits observations that an equation or inequality can be true or false. While students may notice and wonder many things, observations about comparison and about the meaning of the symbols and statements are the important discussion points.

Launch

  • Groups of 2
  • Display the four statements.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

5<85 < 8

92>412\frac{9}{2} >4\frac{1}{2}

4 =324  = \frac{3}{2}

13<12\frac{1}{3} <\frac{1}{2}

Sample Response

Students may notice:

  • The statements use <,=,<, =, and >> symbols.
  • There are fractions, whole numbers, and mixed numbers.
  • Some fractions are greater than 1, and some are less than 1.
  • Some statements are true, and some are false.

Students may wonder:

  • What do the << and >> symbols mean?
  • How can I compare 92\frac{9}{2} and 4124\frac{1}{2}?
  • How can we correct statements that are not true?
Activity Synthesis (Teacher Notes)
  • “What does each statement say?”
  • If needed, guide the class to read each statement aloud.
  • “Which of these statements are true? Which ones are not?” (The first and last are true. The second and third are false.)
  • “Why are they false?” (92\frac{9}{2} is equal to, not greater than, 4 wholes and 12\frac{1}{2}. Four is greater than 32\frac{3}{2}.)
Standards
Addressing
  • 4.NF.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols &gt;, =, or &lt;, and justify the conclusions, e.g., by using a visual fraction model.
  • 4.NF.A.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <span class="math">\(&gt;\)</span>, =, or <span class="math">\(&lt;\)</span>, and justify the conclusions, e.g., by using a visual fraction model.

20 min

15 min