Compare Fractions with the Same Denominator

10 min

Narrative

The purpose of this Warm-up is to elicit the idea that the size and the number of unit fractions can help us compare fractions. Students can see that the two diagrams have the same-size parts, but they cannot see how much of one diagram is shaded, prompting them to think about the number of shaded parts. While students may notice and wonder many things about these images, what fractions could be represented by the partially hidden strip is the important discussion point.

Launch

  • Groups of 2
  • Display the image.
  • “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?

Two strips, one partially shaded, the other partially shaded and partially covered.

Sample Response

Students may notice:
  • The parts on the strips are the same size.
  • The bottom strip shows 34\frac{3}{4}.
  • Part of the top strip is covered.
Students may wonder:
  • How many parts are shaded on the top strip?
  • Is the top strip more shaded than the bottom strip?
  • Is the top strip less shaded than the bottom strip?

Synthesis

  • “How many parts could be shaded on the top strip? Could less than 34\frac{3}{4} be shaded? Could more than 34\frac{3}{4} be shaded?” (If 2 parts are shaded, that's 24\frac{2}{4}, which is less than 34\frac{3}{4}. If 3 parts are shaded, that's 34\frac{3}{4}. If the whole strip is shaded, that's 44\frac{4}{4}, which is more than 34\frac{3}{4}.)
Standards
Building Toward
  • 3.NF.3.d·Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • 3.NF.A.3.d·Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the 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