# Lesson 1

Representaciones de fracciones (parte 1)

## Warm-up: ¿Qué sabes sobre $\frac{1}{2}$? (10 minutes)

### Narrative

The purpose of this warm-up is to invite students to share what they know about the number $$\frac{1}{2}$$ and elicit ways in which it can be represented. It gives the teacher the opportunity to hear students’ understandings about and experiences with fractions, $$\frac{1}{2}$$ in particular. The fraction $$\frac{1}{2}$$ is familiar to students and will be central in the first activity.

### Launch

• Groups of 2
• Display the number $$\frac{1}{2}$$.
• 1 minute: quiet think time

### Activity

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

### Student Facing

¿Qué sabes sobre $$\frac{1}{2}$$?

### Activity Synthesis

• “¿De qué maneras diferentes podemos representar $$\frac{1}{2}$$?” // “What different ways can we represent $$\frac{1}{2}$$?” (Cut an object, a rectangle, or another shape into two equal parts, mark the middle point between 0 and 1 on a number line.)

## Activity 1: Tiras de fracciones (20 minutes)

### Narrative

The purpose of this activity is for students to use fraction strips to represent halves, fourths, and eighths. The denominators in this activity are familiar from grade 3. The goal is to remind students of the relationships between fractional parts in which one denominator is a multiple of another. Students should notice that each time the unit fractions on a strip are folded in half, there are twice as many equal-size parts on the strip and that each part is half as large.

In the discussion, use the phrases “número de partes” // “number of parts” and “tamaño de las partes” // “size of the parts” to reinforce the meaning of a fraction.

Engagement: Provide Access by Recruiting Interest. Provide choice and autonomy. Provide access to different colored strips of paper students can use to differentiate each fraction.
Supports accessibility for: Organization, Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• Fraction Strips

### Required Preparation

• Each group of 2 needs 4 strips of equal-size paper (cut lengthwise from letter-size or larger paper or use the provided blackline master).

### Launch

• Groups of 2
• Give each group 4 paper strips and a straightedge.
• Hold up one strip for all to see.
• “Cada tira representa 1” // “Each strip represents 1.”
• Label that strip with “1” and tell students to do the same on one of their strips.
• “Tomen una nueva tira. ¿Cómo la pueden doblar para que muestre medios?” // “Take a new strip. How would you fold it to show halves?”
• 30 seconds: partner think time
• “Piensen en cómo mostrar cuartos en la próxima tira y octavos en la última tira” // “Think about how to show fourths on the next strip and eighths on the last strip.”

### Activity

• 10 minutes: partner work time
• Monitor for students who notice that each denominator is twice the next smaller denominator.

### Student Facing

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

1. Usa las tiras para representar medios, cuartos y octavos.

Usa una tira para cada fracción y marca las partes.

2. ¿Qué observas sobre el número de partes o el tamaño de las partes? Haz al menos dos observaciones.

### Student Response

Students may not see the relationships between fractional parts as a result of imprecise folds on fraction strips. Consider asking: “¿Cómo podemos asegurarnos de que todas las partes de una tira sean iguales?” // “How could we make sure that each part on a strip is equal?” and “¿Qué herramientas podemos usar para hacer pliegues más precisos?” // “What tools might we use to help make precise folds?”

### Activity Synthesis

• Select a group to share their paper strips and how they found the fractional parts. Ask if others also found them the same way.
• Display one set of completed strips.
• Invite students to share what they noticed about the number and size of the parts on the strips. Highlight the ideas noted in student responses.
• If no students mentions the relationships between the fractions on different strips, encourage them to work with a partner to look for some.
• Remind students that the denominator, the number at the bottom of a fraction, tells us the number of equal-size parts in 1 whole, and the numerator, the number at the top of a fraction, refers to how many of those parts are being described. Consider displaying these terms and their meanings for students to reference.
• Ask students to save the fraction strips for a future lesson.

## Activity 2: Fracciones, representadas (15 minutes)

### Narrative

The purpose of this activity is for students to revisit the meaning of unit fractions with familiar and unfamiliar denominators (3, 5, 6, 10, and 12) and recall how to name and represent them.

As they draw tape diagrams to represent these fractions, students have opportunities to look for structure and make use of the relationships between the denominators of the fractions (MP7). For example, to make a diagram with twelfths they can cut each of 6 sixths in half.

To support students in drawing straight lines on the tape diagrams, provide access to a straightedge or ruler. Students should not, however, use rulers to measure the location of a fraction on any diagram.

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give each student a straightedge.
• “Examinemos otras fracciones y dibujemos diagramas para representarlas. Consideren usar una regla cuando dibujen” // “Let’s look at some other fractions and draw diagrams to represent them. Consider using a straightedge when you draw.”

### Activity

• 7–8 minutes: independent work time
• “Discutan sus respuestas con su pareja. Asegúrense de comentar cómo hicieron los diagramas para $$\frac{1}{6}$$$$\frac{1}{10}$$ y $$\frac{1}{12}$$” // “Discuss your responses with your partner. Be sure to talk about how you created diagrams for $$\frac{1}{6}$$, $$\frac{1}{10}$$, and $$\frac{1}{12}$$.”
• 2–3 minutes: partner discussion
• Monitor for students who:
• notice the relationship of thirds, sixths, and twelfths, and of fifths and tenths
• use the given diagrams to help partition the other diagrams

### Student Facing

2. Estos son cuatro diagramas en blanco. Cada diagrama representa 1. Divide cada diagrama y sombrea una parte para que esa parte represente la fracción dada.

1. $$\frac{1}{6}$$

2. $$\frac{1}{8}$$

3. $$\frac{1}{10}$$

4. $$\frac{1}{12}$$

3. Supongamos que vas a representar $$\frac{1}{20}$$ usando el mismo diagrama en blanco. ¿La parte sombreada va a ser más grande o más pequeña que la parte sombreada del diagrama de $$\frac{1}{10}$$? Explica cómo lo sabes.

### Activity Synthesis

• “¿Cómo supieron cómo partir los diagramas de la segunda pregunta?” // “How did you know how to partition the diagrams in the second question?”
• Select students who use the given diagrams or the relationships between denominators to display their diagrams and share their reasoning.
• “¿Qué relaciones ven entre las fracciones de esta actividad?” // “What relationships do you see between the fractions in this activity?” (Sample responses:
• As the denominator gets larger, each fractional part gets smaller.
• A fifth is twice the size of a tenth, or a tenth is half as big as a fifth.
• Thirds, sixths, and twelfths are related in that a third is 2 sixths and a sixth is 2 twelfths. Fifths and tenths are related in the same way.)

MLR1 Stronger and Clearer Each Time

• “Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan su respuesta. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response to the last question with your partner. Take turns being the speaker and the listener. If you are the speaker, share your response. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 3–5 minutes: structured partner discussion.
• Repeat with 2–3 different partners.
• “Ajusten su respuesta inicial teniendo en cuenta los comentarios de sus compañeros” // “Revise your initial response based on the feedback from your partners.”
• 2–3 minutes: independent work time

## Lesson Synthesis

### Lesson Synthesis

“Hoy recordamos cosas acerca de fracciones. Usamos tiras de fracciones y diagramas para representar fracciones conocidas y algunas fracciones nuevas” // “Today we refreshed our memory about fractions. We used fraction strips and diagrams to represent some familiar and some new fractions.”

Based on students’ work during the lesson, choose the questions that need more discussion:

• “En general, ¿qué representa el denominador de una fracción?” // “In general, what does the denominator in a fraction represent?” (The number of equal parts in 1 whole.)
• “¿Qué nos dice la fracción $$\frac{1}{5}$$?” // “What does the fraction $$\frac{1}{5}$$ tell us?” (The size of one part if 1 whole is split into 5 equal parts.)
• “¿Qué observaron sobre el tamaño de una fracción cuando el denominador se hace más grande?” // “What did you notice about the size of a fraction as the denominator gets larger?” (The size of the fraction gets smaller.) “¿Por qué ocurre esto?” // “Why might that be?” (There are more equal parts in 1 whole, so each part gets smaller.)
• “¿Qué relaciones observamos entre las fracciones que estudiamos hoy?” // “What relationships did we see between the fractions that we studied today?” (The denominators of some fractions are multiples of other fractions. A representation of one fraction can be split into two or three parts to represent another fraction.)