The purpose of this activity is for students to revisit ideas about how to partition shapes into halves, thirds, and fourths. Students sort a set of shapes into categories, based on their shared attributes. Monitor for students who distinguish shapes that have been partitioned into equal-size parts and shapes that have not. This distinction will be used to review what it means for a part of a shape to be a half, a third, or a fourth.

Sorting the shapes gives students an opportunity to identify important common characteristics or structures, in this case the number and the size of the parts (MP7). When students specify that halves, thirds, and fourths of a shape need to be equal in size, they are attending to precision (MP6).

Students will use the cards again during the Lesson Synthesis.

• Invite groups to share their categories and the shapes in the categories.
• Choose as many different types of categories as time allows, but ensure that one set of categories distinguishes between shapes partitioned into equal parts and shapes that are not.
• Attend to the language that students use to describe their categories and shapes, and give students opportunities to describe more precisely how shapes are partitioned.
• Highlight the use of terms, such as “halves,” “thirds,” “fourths,” and “equal-size pieces or parts.”

The purpose of this activity is for students to partition rectangles into thirds, fourths, sixths, and eighths before learning the names “sixth” and “eighth.” Students do so by folding rectangular strips of paper into equal-size parts. While folding, students may notice that thirds can be further partitioned to make sixths and that fourths can be further partitioned to make eighths, which will be explored more in a future lesson. The focus of the Activity Synthesis should be on naming sixths and eighths, as they are new terms for students.

Students will use the partitioned rectangles during the Lesson Synthesis.

• Select previously identified students to share how they folded the rectangles into 6 and 8 equal parts.
• Consider asking:
  • “¿Cómo usaron las particiones en 4 partes iguales para partir en 8 partes iguales?” // “How did you use the partitions of 4 equal parts to partition into 8 equal parts?”
  • “¿Cómo usaron las particiones en 3 partes iguales para partir en 6 partes iguales?” // “How did you use the partitions of 3 equal parts to partition into 6 equal parts?”
  • “¿Alguien quiere compartir otra observación sobre la manera en la que _____ hizo la partición?” // “Does anyone want to add an observation to the way _____ partitioned?”
• Display poster:

  número de partes iguales	nombre de cada parte
  2	medio
  3	tercio
  4	cuarto
  6
  8

  // 

  number of equal parts	name of each part
  2	half
  3	third
  4	fourth
  6
  8

• “Cuando partimos una figura en 6 partes iguales, cada parte se llama un ‘sexto’. Cuando partimos una figura en 8 partes iguales, cada parte se llama un ‘octavo’” // “When we partition a shape into 6 equal parts, each part is called a ‘sixth.’ When we partition a shape into 8 equal parts, each part is called an ‘eighth.’“
• Add “sexto” // “sixth” and “octavo” // “eighth” to the chart, and keep it displayed.