# Lesson 1

Nombremos las partes

## Warm-up: Cuál es diferente: Figuras con partes (10 minutes)

### Narrative

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.

### Launch

• 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

### Activity

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

### Student Facing

¿Cuál es diferente?

### Activity Synthesis

• “¿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.”

## Activity 1: Clasificación de tarjetas: Particiones (15 minutes)

### Narrative

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.

MLR2 Collect and Display. Collect the language students use while sorting the shapes. Display words and phrases such as: partition, split, parts, equal parts, equal-sized parts, halves, thirds, fourths, whole, and so on. During the synthesis, invite students to suggest ways to update the display: “¿Qué otras palabras o frases deberíamos incluir?” // “What are some other words or phrases we should include?” Invite students to borrow language from the display as needed.

### Required Materials

Materials to Copy

• Card Sort: Partitions

### Required Preparation

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

### Launch

• 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.

### Activity

• “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.

### Student Facing

Tu profesor te dará un grupo de tarjetas que muestran algunas figuras que están partidas.

Clasifica las tarjetas en 2 categorías de tu elección. Prepárate para explicar lo que significan tus categorías.

### Activity Synthesis

• 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.

## Activity 2: Doblemos y nombremos (20 minutes)

### Narrative

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.

Action and Expression: Develop Expression and Communication. Provide access to pre-formatted papers that will be used to fold into rectangles. For example, papers would have dotted lines showing students where to fold for each rectangle.
Supports accessibility for: Social-Emotional Functioning, Visual-Spatial Processing

### Required Materials

Materials to Copy

• Fold and Name

### Required Preparation

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

### Launch

• 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.

### Activity

• “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.

### Student Facing

Dobla cada rectángulo que te dé tu profesor en 3, 6, 4 u 8 partes iguales. Dibuja rectas en los dobleces que hiciste para partir los rectángulos. Prepárate para explicar cómo doblaste tus figuras.

### Activity Synthesis

• Select previously identified students to share how they folded the rectangles into 6 and 8 equal parts.
• “¿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.

## Lesson Synthesis

### Lesson Synthesis

“Antes, habíamos usado el término ‘un medio’ para referirnos a cada parte cuando una figura completa estaba partida en 2 partes iguales. Habíamos dicho ‘un tercio’ cuando había 3 partes iguales y ‘un cuarto’ cuando había 4 partes iguales” // “In the past, we’ve used the term ‘a half’ to refer to each part when one whole shape is partitioned into 2 equal parts. We’ve said ‘a third’ when there are 3 equal parts, and ‘a fourth’ when there are 4 equal parts.”

“Hoy aprendimos a usar ‘un sexto’ para referirnos a cada parte cuando una figura completa está partida en 6 partes iguales y ‘un octavo’ cuando está partida en 8 partes iguales” // “Today, we learned to use ‘a sixth’ to refer to each part when a whole shape is partitioned into 6 equal parts and ‘an eighth’ when it is partitioned into 8 equal parts.”

“Además de usar palabras para describir estas partes iguales, también podemos usar números” // “In addition to using words to describe these equal parts, we can also use numbers.”

Write each fraction as it is named:

“Un medio se puede escribir como el número $$\frac{1}{2}$$” // “One half can be written as the number $$\frac{1}{2}$$.”
“Un tercio se puede escribir como el número $$\frac{1}{3}$$” // “One third can be written as the number $$\frac{1}{3}$$.”
“Un cuarto se puede escribir como el número $$\frac{1}{4}$$” // “One fourth can be written as the number $$\frac{1}{4}$$.”

“¿Cómo escribiríamos un sexto y un octavo como números?” // “How would we write one sixth and one eighth as numbers?” ($$\frac{1}{6}$$ and $$\frac{1}{8}$$)

“Los números que usamos para describir las partes de un todo que está partido en partes iguales se llaman fracciones. Al todo le llamaremos ‘la unidad’. Cada fracción tiene dos partes que están separadas por una barra” // “The numbers we use to describe the parts of a whole that has been partitioned into equal parts are called fractions. Each fraction has two parts separated by a bar.”

“¿Qué creen que representa la parte que está debajo de la barra?” // “What do you think the part below the bar represents?” (the number of equal parts the whole has been partitioned into)

“¿Qué hay del 1 que está encima de la barra?” // “What about the 1 above the bar?” (the one in “one half,” “one third,” and so on)

Display a square partitioned into 2 equal parts with each part labeled with $$\frac{1}{2}$$, such as:

“Podemos marcar las partes iguales de una figura con fracciones. Si este cuadrado es la figura completa o 1, cada parte es un medio o $$\frac{1}{2}$$” // “We can label the equal parts in a shape with fractions. If this square is the whole shape or 1, each part is one half or $$\frac{1}{2}$$.”

“Busquen todas las tarjetas de la primera actividad que muestran una figura partida en 2 partes iguales. Marquemos cada mitad con la fracción $$\frac{1}{2}$$” // “Find all the cards from the first activity that show a shape partitioned into 2 equal parts. Let's label each half with the fraction $$\frac{1}{2}$$.”

“Marquemos las partes de cada uno de sus rectángulos con fracciones” // “Let’s label the parts in each of your rectangles with fractions.”