# Lesson 2

Nombremos partes como fracciones

## Warm-up: Cuál es diferente: Partes sombreadas (10 minutes)

### Narrative

This warm-up prompts students to compare four rectangles that have been partitioned and partially shaded. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about the characteristics of the items and the quantities they represent. During the synthesis, ask students to explain the meaning of any terminology they use, such as partition, equal parts, halves, and thirds.

### Launch

• Groups of 2
• Display the image.
• “Escojan una que sea diferente. Prepárense para explicar 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 cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

### Activity Synthesis

• “¿Podemos marcar las partes con fracciones? ¿Por qué sí o por qué no?” // “Can we label the parts with fractions? Why or why not?” (We can label the parts in A, B, and D with fractions because they are equal in size, but not in C because the parts aren’t the same size.)
• “¿Cómo se llaman las partes de las figuras A, B y D?” // “What do we call the parts in A, B, and D?” (“Halves” in A and D, and “thirds” in B.)
• “¿Qué fracciones usamos para marcar las partes de las figuras A, B y D?” // “What fractions do we use to label the parts in A, B, and D?” ($$\frac{1}{2}$$ in A and D, and $$\frac{1}{3}$$ in B.)
• Consider asking: “Encontremos al menos una razón por la que cada una es diferente” // “Let’s find at least one reason why each one doesn’t belong.”

## Activity 1: Partamos las tiras (15 minutes)

### Narrative

The purpose of this activity is for students to practice partitioning and labeling equal-sized parts with unit fractions. This provides students a physical tool they can use throughout the unit to make sense of fractions.

Have students keep their fractions strips to use in future lessons. Consider having students glue the fraction strips in their workbook.

When students make halves, fourths, and eighths they observe regularity in repeated reasoning as each piece is subdivided into 2 equal pieces. They observe the same relationship between thirds and sixths (MP8).

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. Check in after students fold and label each fraction strip.
Supports accessibility for: Organization, Attention

### Required Materials

Materials to Copy

• Partition the Strips, Spanish

### Required Preparation

• Use the blackline master to create one set of 6 equal-sized strips for each student.

### Launch

• Groups of 2
• Give each student one set of 6 equal-sized strips.
• “Hoy vamos a hacer tiras de fracciones” // “Today we are going to make fraction strips.”
• Demonstrate how to fold a strip into two halves. Emphasize that all the strips should be folded to make vertical partitions as shown in student responses.

### Activity

• “Tómense unos minutos para doblar cada tira de forma que las partes representen medios, tercios, cuartos, sextos u octavos. Usen una tira para cada fracción” // “Take a few minutes to fold each strip so that the parts represent halves, thirds, fourths, sixths, or eighths. Use one strip for each fraction.”
• “Tracen rectas sobre los dobleces con un lápiz y después marquen cada parte con la fracción que le corresponde” // “Mark your folding lines with a pencil, and then label each part with the correct fraction.”
• 5–7 minutes: independent work time
• Monitor for students who fold their strips into fourths, sixths, and eighths by folding halves, thirds, and fourths, respectively, in half.
• “Compartan con su compañero cómo partieron sus tiras y cómo marcaron las partes” // “Share how you partitioned your strips and how you labeled the parts with your partner.”
• 2–3 minutes: partner discussion

### Student Facing

Tu profesor te va a dar algunas tiras de papel. Cada tira representa 1.

Dobla cada tira de forma que las partes representen una de las siguientes fracciones. Usa una tira para cada fracción.

• medios
• cuartos
• octavos
• tercios
• sextos

Cuando termines de doblar las tiras, traza rectas sobre los dobleces con un lápiz y luego marca cada parte con la fracción que le corresponde.

### Activity Synthesis

• Invite students to display their partitioned strips. Keep a full set of fraction strips displayed.
• Ask previously identified students to share how they fold their strips to get 4, 6, and 8 equal parts.
• If not apparent from students' explanations, highlight that fourths, sixths, and eighths can be found by partitioning each half, third, and fourth, respectively, into two equal parts.

## Activity 2: Partamos, coloreemos e intercambiemos (20 minutes)

### Narrative

Previously, students partitioned rectangular pieces of paper into 2, 3, 4, 6, and 8 equal parts by folding. The purpose of this activity is for students to partition rectangles by drawing and continue to practice naming the parts with the unit fractions $$\frac{1}{2}$$, $$\frac{1}{3}$$, $$\frac{1}{4}$$, $$\frac{1}{6}$$, and $$\frac{1}{8}$$. It’s important that students try to make the parts as close to equal-sized as they can, but student drawings do not need to be exact. After they practice partitioning, students partition and shade, but don’t label, a fraction on a rectangle, then trade with a partner to determine the fraction their partner has shaded. The synthesis focuses on how to name a single equal part, such as one sixth, rather than talking about all the equal parts in a shape, such as sixths. This will be helpful as students use non-unit fractions to name multiple equal parts in the next lesson.

MLR8 Discussion Supports. At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain their process for partitioning their rectangles and determining how to label each part. Invite groups to rehearse what they will say when they share with the whole class.

• Groups of 2

### Activity

• “Trabajen en el primer problema con su compañero. Partan cada rectángulo y marquen cada parte” // “Work with your partner to complete the first problem. Partition each rectangle and label each part.”
• 5–7 minutes: partner work time
• For each rectangle, have a group share how they partitioned the rectangle into equal-sized parts and what fraction they used to label each part.
• “Completen la parte a del siguiente problema individualmente. Partan el rectángulo y coloreen una parte para mostrar una fracción, pero no la marquen. No le digan a su compañero cómo partieron ni qué número están mostrando” // “Complete part a of the next problem on your own. Partition the rectangle and shade to show a fraction, but don’t label it. Don’t tell your partner how you are partitioning or what number you are showing.”
• 2 minutes: independent work time
• “Ahora, intercambien los rectángulos con su compañero y respondan la siguiente parte del problema usando el rectángulo de su compañero. Cuando ambos terminen, compartan cómo razonaron” // “Now, trade rectangles with your partner and answer the next part of the problem using their rectangle. When you are both finished, share your reasoning.”
• 1–2 minutes: independent work time
• 1–2 minutes: partner work time

### Student Facing

1. Parte cada rectángulo en medios, tercios, cuartos, sextos y octavos. Después, marca cada parte con la fracción que le corresponde.

medios

tercios

cuartos

sextos

octavos

1. Haz una partición del rectángulo en partes de igual tamaño. Colorea una de esas partes.

2. Intercambia el rectángulo con un compañero. Si el rectángulo completo es 1, ¿qué número representa la parte coloreada? Explica tu razonamiento.

### Activity Synthesis

• Have 2–3 students display their shaded rectangles.
• For each rectangle, ask, “¿Cómo supieron qué fracción del rectángulo coloreó su compañero?” // “How did you know what fraction of the rectangle your partner shaded?” (I counted the equal parts in the rectangle. There were four equal parts, so I knew my partner shaded a fourth.)

## Lesson Synthesis

### Lesson Synthesis

Display a rectangle with each part labeled with the unit fraction and a rectangle shaded to show the unit fraction, such as:

sextos

un sexto o $$\frac{1}{6}$$

“¿Cómo saben que el primer diagrama muestra sextos?” // “How do you know the first diagram shows sixths?” (It has six equal parts.)

“¿Por qué creen que el segundo diagrama está marcado con un sexto?” // “Why do you think the second diagram is labeled one sixth?” (Only 1 of the six parts is shaded, so it’s just one of the sixths. We are focusing on one of the sixths.)

“El primer diagrama muestra sextos porque el rectángulo está partido en seis partes iguales. Cada parte es un sexto. El segundo diagrama muestra un sexto porque hay seis partes iguales y describimos cuántas partes están sombreadas. En este caso, una de las partes está sombreada” // “The first diagram shows sixths because the rectangle is partitioned into six equal parts. Each part is one sixth. The second diagram shows one sixth because there are six equal parts and we are describing how many parts are shaded. In this case, one of the parts is shaded.”