# Lesson 6

Escojamos una escala

## Warm-up: Observa y pregúntate: Escalas de gráficas de barras (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that adjusting the scale changes the size of the bars in a bar graph and can make it easier or more difficult to interpret. While students may notice and wonder many things about these graphs, the different scales in the bar graphs are the most important discussion points.

### Launch

• Groups of 2
• Display the graphs.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• “¿En qué son diferentes las tres gráficas?” // “How are the three graphs different?” (They show the same data, but the bars are different heights. They have different scales.)

## Activity 1: Representemos fichas geométricas (20 minutes)

### Narrative

The purpose of this activity is for students to analyze a scale and create a scaled bar graph. Students consider a large collection of pattern blocks and decide which scale will work best to represent the categorical data. They consider three students’ ideas, choose a scale of 2, 5, or 10, and create a scaled bar graph to represent the categorical data. Students must justify why they agree that a particular scale would be best. During the activity and whole-class discussion, students share their thinking and have opportunities to listen to and critique the reasoning of their peers (MP3). Providing a variety of scales for students to choose from allows for discussion about the benefits of using larger scales for larger groups of objects and the effect of a scale on how easy it may be to read and interpret data in a graph.

Representation: Access for Perception. Provide access to pattern blocks to model the collection of pattern blocks in the student-facing task statement.
Supports accessibility for: Organization, Visual-Spatial Processing

### Launch

• Groups of 2
• Display the image.
• “Observen estas fichas geométricas un momento y piensen en cómo las representarían en una gráfica de barras con escala” // “Take a minute to consider these pattern blocks and think about how you could represent them in a scaled bar graph.”
• 30 seconds: quiet think time

### Activity

• “Ahora, en parejas, respondan las preguntas sobre organizar y representar las fichas geométricas en una gráfica de barras. Prepárense para justificar su elección de la escala” // “Now answer the questions about organizing and representing the pattern blocks in a bar graph with your partner. Be prepared to justify your choice of scale.”
• 12 minutes: partner work
• Monitor for students who used each of the scales to create their bar graph.

### Student Facing

Esta es una colección de fichas geométricas.

Mai, Noah y Priya quieren hacer una gráfica de barras para representar el número de triángulos, cuadrados, trapecios y hexágonos de la colección.

• Mai dice que la escala de la gráfica de barras debería ser 2.
• Noah dice que la escala de la gráfica de barras debería ser 5.
• Priya dice que la escala de la gráfica de barras debería ser 10.

1. ¿Con quién estás de acuerdo? Explica lo que pensaste.
2. Usa la escala que escogiste para hacer una gráfica de barras con escala que represente la colección de fichas geométricas.

### Advancing Student Thinking

If students use a scale of 2, consider asking:

• “¿Cómo decidiste qué escala usar en tu gráfica?” // “How did you decide on the scale to use in your graph?”
• “¿Cómo cambiaría la gráfica si usaras una escala de 5 o de 10?” // “How would using a scale of 5 or 10 affect your graph?”

### Activity Synthesis

• Display selected student work showing each of the scales.
• “¿Qué escala usaron en su gráfica de barras? ¿Por qué escogieron esa escala?” // “What scale did you use for your bar graph? Why did you choose that scale?” (I used a scale of 5 because each amount can be counted by 5. I used a scale of 10 so I don’t have to make as many marks on the scale.)

## Activity 2: Representemos más datos en una gráfica de barras con escala (15 minutes)

### Narrative

The purpose of this activity is for students to represent data in a scaled bar graph. In this activity, the categorical data is presented in a table. Students choose a scale and make a scaled bar graph of the categorical data. Students have prior experience with scales of 2, 5, and 10, and are not directed to a specific scale in this activity. However, due to the larger numbers, it is likely that students choose a scale of 5 or 10. If students struggle to get started, you could suggest a scale of 5 or 10. In the whole-class discussion, students share how their choice of scale affected their graph.

Students will use their scaled bar graphs again in the next lesson.

MLR8 Discussion Supports. During small-group discussion, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “Te escuché decir . . .” // “I heard you say . . . .” Original speakers can agree or clarify for their partner.

### Launch

• Groups of 4
• “¿Cuál es su momento favorito del año?” // “What is your favorite time of the year?”
• 30 seconds: quiet think time
• Share responses.
• “Vamos a hacer una gráfica de barras con escala para representar los momentos favoritos del año de algunos estudiantes de 3er grado” // “We are going to make a scaled bar graph to represent some 3rd grade students’ favorite times of the year.”

### Activity

• “Representen en una gráfica de barras con escala los datos que se muestran en la tabla. Piensen en una escala que tenga sentido para el número de estudiantes” // “Represent the data shown in the table in a scaled bar graph. Think about a scale that makes sense with the number of students.”
• 5–7 minutes: independent work time
• “Compartan sus gráficas con su grupo. Discutan por qué eligieron esas escalas” // “Share your graphs with your small-group. Discuss the scales you chose to use.”
• 2–3 minutes: small-group discussion

### Student Facing

A todos los estudiantes de tercer grado de la escuela les preguntaron: “¿Cuál es tu momento favorito del año?”. Sus respuestas se muestran en esta tabla:

momento favorito del año número de estudiantes
invierno 24
primavera 13
verano 40
otoño 22

Usa los datos de esta tabla para hacer una gráfica de barras con escala.

### Activity Synthesis

• “¿Cómo inflluyó la escala que escogieron en la forma como quedó su gráfica al final?” // “How did the scale you chose for your graph affect how your graph looked in the end?” (Certain scales make it easier or more difficult to read the data. For example, with a scale of 10, it might be more difficult to read the exact values from the graph.)

## Lesson Synthesis

### Lesson Synthesis

Display the bar graphs from today’s lesson.

“De lo que aprendieron hoy, ¿qué les va a ayudar a tomar decisiones sobre cómo hacer gráficas con escala en el futuro?” // “What did you learn today that will help you make decisions about how to create scaled graphs in the future?” (You can pick scales that match the data. If there's mostly larger numbers, you might pick a scale like 5 or 10. The scale can help make the graph easier to read.)

Math Community

After the cool-down, ask students to individually reflect on the following question: “¿Cuál de las normas creen que fue la más importante en su trabajo de hoy y por qué?” // “Which one of the norms did you feel was most important in your work today, and why?” Students can write their responses on the bottom of their cool-down paper, on a separate sheet of paper, or in a math journal.

Tell students that as their math community works together over the course of the year, the group will continually add to and revise its “Doing Math” and “Norms” actions and expectations.