Lesson 1

This warm-up prompts students to compare four shapes that have been partitioned and examine the features of the shapes and the partitions. The observations here prepare students to explore fractions later in the lesson and enable the teacher to hear how students describe the features that they see. During the synthesis, ask students to explain the meaning of any terminology they use, such as partition, whole, parts, pieces, equal, and halves.

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “¿Por qué no podemos decir que D está dividida en medios?” // “Why can’t we say that D is split into halves?” (The pieces or parts aren’t the same size. The pieces have to be equal.)
• “Otra palabra que podemos usar para decir que algo está dividido en pedazos o partes es partición. Hacer una partición significa dividir en partes” // “Another word we can use to say something was split into pieces or parts is partition. Partition means to split into parts.”

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 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.

• Create a set of cards from the blackline master for each group of 2.

• Groups of 2
• Give one set of pre-cut cards to each group of students.
• “Tómense un minuto para examinar las tarjetas. ¿Qué observan? ¿Qué se preguntan?” // “Take a minute to look at the cards. What do you notice? What do you wonder?” (Students may notice: There are different shapes. The shapes are split or partitioned. Students may wonder: Why are they partitioned into different numbers of pieces or parts? Why are some of the pieces or parts equal and some are not?)
• 1 minute: quiet think time
• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Con su pareja, clasifiquen en categorías las figuras de las tarjetas. Prepárense para explicar sus categorías y por qué las figuras de cada categoría van juntas” // “Work with your partner to sort the shapes on the cards into categories. Be prepared to explain your categories and why the shapes in each category belong together.”
• 8 minutes: partner work time
• Monitor for groups that sort shapes based on whether they are partitioned into equal parts.

• Select groups to share their categories and the shapes in the categories.
• Showcase as many different types of categories as time allows, but ensure that one set of categories distinguishes between shapes that were partitioned into equal parts and shapes that were not.
• Attend to the language that students use to describe their categories and shapes, giving them opportunities to describe more precisely how shapes were partitioned.
• Highlight the use of terms such as halves, thirds, fourths, and equal-sized pieces or parts.

The purpose of this activity is for students to partition rectangles into thirds, sixths, fourths, and eighths before learning the name of sixths and eighths. Students do so by folding rectangular strips of paper into equal-sized 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 synthesis should be on naming sixths and eighths, as these are new terms for students.

Students will use the partitioned rectangles during the lesson synthesis.

• Each student needs 4 copies of the rectangle from the blackline master.
• Have extra rectangles available for students who need more than one try to fold the rectangles into equal parts.
• Create poster for synthesis:

• Groups of 2
• “Acabamos de observar algunas figuras que estaban partidas. Ahora ustedes van a partir algunos rectángulos en partes iguales” // “We just looked at some shapes that were partitioned. Now you’re going to partition some rectangles into equal parts.”
• Give each student 4 rectangles.

• “Vamos a hacer dobleces para partir estos rectángulos. Doblen cada rectángulo en 3, 6, 4 u 8 partes iguales. Dibujen rectas en los dobleces que hicieron para partir los rectángulos. Prepárense para compartir cómo doblaron sus rectángulos” // “We are going to fold to partition these rectangles. Fold each rectangle into 3, 6, 4, or 8 equal parts. Draw lines where you folded to partition the rectangles. Be prepared to share how you folded your rectangles.”
• 3–5 minutes: independent work time
• “Ahora compartan con su pareja cómo doblaron sus figuras” // “Now, share how you folded your shapes with your partner.”
• 2–3 minutes: partner discussion
• Monitor for students who used partitioning into 3 or 4 equal parts to partition into 6 or 8 equal parts to highlight during 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 _____ partes iguales para partir en _____ partes iguales?” // “How did you use the partitions of _____ equal parts to partition into _____ 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 displayed.