In earlier lessons, students compared two fractions that share the same denominator or the same numerator. In this activity, students use that understanding to compare a large set of fractions that are arranged into rows and columns. The fractions in each row share the same numerator and those in each column share the same denominator. 

• “¿Cómo decidiste cuál fracción era la mayor?” // “How did you decide which fraction was the greatest?”
• Suggest that students compare fractions with the same numerator, but one that is more familiar (such as those in Row 1). “¿Cuál es mayor:  o ? ¿ o ?” // “Which is greater, or ? or ?” Or ask them to compare unit fractions, such as and .

• Invite students to share their responses and reasoning. Highlight responses that clarify that:
  • In each column, the fraction in row 5 is the greatest because it has the greatest numerator of all fractions with the same denominator. (The size of the fractional parts is the same, so the fraction with the most parts is greatest.) 
  • In each row, the fraction in Column A is greatest because it has the smallest denominator of all fractions with the same numerator.  (The number of parts is the same, so the fraction with the largest parts is greatest.)
• “¿Cómo supieron que  es la mayor fracción de toda la tabla?” // “How did you know that is the greatest fraction in the entire table?”
  • It is the greatest fraction in row 5 and in Column A.
  • It is more than 8 wholes. All the other fractions are less than that.)

In this activity, students apply previous reasoning about the size of fractions and their knowledge about fractions that are equivalent to to classify and compare fractions. Along the way, students have opportunities to make new observations about the structure of fractions that are less than , greater than but less than 1, and greater than 1 (MP7).

The activity calls for the use of colors as a way to code fractions in different groups. If colored pencils are not available, students can code the fractions by putting circles, triangles, and squares around the fractions. In either case, a key or legend should be created.

Invite students to share their strategies for comparing fractions in the last question of the this activity. 

“¿Cómo compararon las fracciones en las que ni el numerador ni el denominador eran iguales?” // “How did you compare fractions in which neither the numerator nor the denominator are the same?” (We compared them to or 1.)

“¿Cómo les ayudó el código de colores (o la comparación con  o 1)?” // “How did the color coding (or comparison to or 1) help?” (Knowing whether a fraction is greater or less than 1, or greater or less than , can help us tell which one is greater.  All the fractions circled in yellow (less than ) are less than all the numbers in green (greater than but less than 1). All fractions in green are less than all fractions in purple (greater than 1).