# Lesson 2

Representemos datos y resolvamos problemas

## Warm-up: Cuántos ves: Puntos en grupos (10 minutes)

### Narrative

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the number of dots they see. They also make connections between the images to determine the number of dots. Grouping strategies and skip-counting by 2, 5, and 10 offer a review of grade 2 work and build toward multiplication in future lessons. In the synthesis, students revisit the language of “how many more” to prepare them to use data from a bar graph to solve “how many more” problems throughout this lesson.

### Launch

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Flash the image.
• 30 seconds: quiet think time

### Activity

• Display the image.
• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

### Student Facing

¿Cuántos ves? ¿Cómo lo sabes?, ¿qué ves?

### Student Response

Teachers with a valid work email address can click here to register or sign in for free access to Student Response.

### Activity Synthesis

• “¿Cuántos puntos más había en la tercera imagen que en la segunda imagen? ¿Qué ecuación corresponde a lo que pensaron?” // “How many more dots were in the third image than in the second image? What equation matches your thinking?” (There were 2 more dots in the image. $$8 + 2 = 10$$.)

## Activity 1: Cómo vamos a casa (15 minutes)

### Narrative

The purpose of this activity is for students to create a bar graph that includes features that help communicate the data clearly. A class picture graph is created, and students make a bar graph using that data. During the synthesis, focus attention on similarities and differences between picture and bar graphs. When you create the blank “ways to get home” picture graph for the launch, feel free to adjust the categories based on how your students get home from school. When students label their graphs, including a title, a key, and numbers if they make a bar graph, they are communicating clearly and precisely (MP6).

MLR8 Discussion Supports. Synthesis: Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking

### Required Materials

Materials to Gather

### Required Preparation

• Create a visual display with a blank bar graph that will be large enough to fit a column of sticky notes in each category.

### Launch

• Groups of 2
• Display an empty picture graph with labels along the bottom axis for bike, walk, van, bus, car, and train.
• Give each student a small sticky note.
• Have each student draw a smiley face on their sticky note.
• “Pongan su carita feliz en la gráfica dependiendo de cómo van a casa desde la escuela” // “Put your smiley face on the graph based on how you get home from school.”
• “¿Qué debemos agregar a la gráfica de dibujos de la clase para comunicar los datos claramente?” // “What needs to be added to the class picture graph to communicate the data clearly?” (A title. A key so we know what each smiley face represents.)
• Facilitate addition of title and key to class picture graph.

### Activity

• “Observen los datos que se muestran en la gráfica de dibujos de la clase. En parejas, representen esos datos en una gráfica de barras. Asegúrense de incluir las partes de la gráfica que ayuden a que los demás la entiendan” // “Represent the data shown in the class picture graph on a bar graph with your partner. Make sure to include the parts of the graph that will help someone else read it.”
• 5–7 minutes: partner work time

### Student Facing

1. Sigue las instrucciones de tu profesor para organizar y representar los datos de la clase con una gráfica de dibujos.
2. Haz una gráfica de barras que represente los mismos datos de cómo van a casa los estudiantes de la clase.

### Student Response

Teachers with a valid work email address can click here to register or sign in for free access to Student Response.

### Advancing Student Thinking

If students create bar graphs that do not match the data in the class picture graph, consider asking:

• “Cuéntame cómo hiciste tu gráfica de barras” // “Tell me about how you made your bar graph.”
• “¿Cómo nos ayudan los datos de la gráfica de dibujos de la clase a hacer la gráfica de barras?” // “How could we use the data in the class picture graph to help make the bar graph?”

### Activity Synthesis

• “¿En qué se parecen nuestra gráfica de dibujos y nuestra gráfica de barras?” // “How are our picture graph and bar graph alike?” (They both show the same data. They have the same categories.)
• “¿En qué son diferentes nuestra gráfica de dibujos y nuestra gráfica de barras?” // “How are our picture graph and bar graph different?” (The picture graph has a key, but the bar graph has a scale. For the picture graph, you have to count each picture but in the bar graph, you can use the numbers on the side to tell how many.)

## Activity 2: Preguntas sobre una gráfica de barras (20 minutes)

### Narrative

The purpose of this activity is for students to answer one- and two-step “how many more” questions using data represented in a bar graph. Students decide if statements about the data in the bar graph from the previous activity are true or false and then answer questions about the data. When students use expression, equations, or describe adding or subtracting to find how many more or less, they show they can decontextualize and recontextualize the data to make sense of and solve the problems (MP2). You will generate the questions students answer in this task from the class graph.

Representation: Access for Perception. Read the directions and statements aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language

• Groups of 2

### Activity

• “Ahora van a usar su gráfica de barras para decidir si cada afirmación es verdadera o falsa” // “Now you’re going to use your bar graph to decide if statements are true or false.”
• 1–2 minutes: independent work time
• 3–5 minutes: partner discussion
• As students work, decide which categories will go in the question stems for the next problem.
• Consider providing these sentence stems if students need support explaining their reasoning:
• “Yo supe que la afirmación era falsa porque . . .” // “I knew the statement was false because . . .”
• “Yo supe que la afirmación era verdadera porque . . .” // “I knew the statement was true because . . .”
• “¿Cómo supieron si cada afirmación era verdadera o falsa?” // “How did you know if each statement was true or false?”
• Share responses.
• Guide the whole class to fill in blanks in question stems using the previously identified categories.
• “Usen los datos de su gráfica de barras para responder las preguntas” // “Use the data in your bar graph to answer the questions.”
• 3–5 minutes: partner work time

### Student Facing

1. Estas son afirmaciones sobre cómo van a casa los estudiantes de nuestra clase. Decide si cada afirmación es verdadera o falsa. Explícale a tu pareja cómo pensaste.

1. Más estudiantes van a casa a pie que de cualquier otra forma.
2. Más estudiantes van a casa en bus que en automóvil.
3. Menos estudiantes van a casa a pie que en bicicleta.
4. Más estudiantes van a casa a pie o en bicicleta que en camioneta.
2. Llena los espacios siguiendo las instrucciones de tu profesor. Después, contesta cada pregunta.
1. “¿Cuántos estudiantes más van a casa $$\underline{ \phantom{{\Huge{0000000000}}}}$$ que $$\underline{ \phantom{{\Huge{0000000000}}}}$$?”
2. “¿Cuántos estudiantes más van a casa $$\underline{ \phantom{{\Huge{0000000000}}}}$$ o
$$\underline{ \phantom{{\Huge{0000000000}}}}$$ que $$\underline{ \phantom{{\Huge{0000000000}}}}$$?”

### Student Response

Teachers with a valid work email address can click here to register or sign in for free access to Student Response.

### Advancing Student Thinking

If students find differences that do not match the data in the graph, consider asking:

• “¿Cómo respondiste las preguntas?” // “How did you answer the questions?”
• “¿Cómo podrías usar las gráficas para responder las preguntas?” // “How could you use the graphs to answer the questions?”

### Activity Synthesis

• Ask students to share their responses to each compare problem.
• “¿Hay alguna duda que tengan todavía sobre cómo responder estas preguntas a partir de la gráfica de barras?” // “Do you have any lingering questions about how to answer these questions from the bar graph?”
• Consider asking: “¿Qué ecuación corresponde a lo que pensaron?” // “What equation matches your thinking?”

## Lesson Synthesis

### Lesson Synthesis

Display a student-created bar graph.

Generate a few questions for students to answer about how they get home using the bar graph. For example, you might ask:

• “¿Cuántos estudiantes más _______________ que _______________?” // “How many more students _______________ than _______________?”
• “¿Cuántos estudiantes menos _______________ que _______________?” // “How many fewer students _______________ than_______________?”
• “¿Cuántos estudiantes más _______________ o _______________ que _______________?” // “How many more students _______________ or _______________ than _______________?”

Have students answer the questions and share their reasoning.

Math Community

After the Cool-down, give students 2–3 minutes to discuss any revisions to the “Doing Math” actions in small groups. Share ideas as a whole group and record any revisions.

## Cool-down: Preguntas sobre una gráfica de barras (5 minutes)

### Cool-Down

Teachers with a valid work email address can click here to register or sign in for free access to Cool-Downs.