# Lesson 8

Más preguntas sobre gráficas de barras con escala

## Warm-up: Conversación numérica: Sumas repetidas (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding groups of 2 and groups of 5. These understandings help students develop fluency and will be helpful later in this lesson when students need to be able to use data in scaled bar graphs to solve one- and two-step “how many more” and “how many fewer” problems. Students use the structure of the expressions and repeated reasoning when they use methods based on skip-counting by 2 or 5 or counting on 2 or 5 from a previous known value (MP7, MP8).

### Launch

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$2 + 2 + 2 + 2 + 2$$
• $$2 + 2 + 2 + 2 + 2 + 2$$
• $$5 + 5 + 5 + 5 + 5 + 5$$
• $$5 + 5 + 5 + 5 + 5 + 5 + 5$$

### Activity Synthesis

• “¿Qué estrategia que no hubieran usado antes podrían usar en el futuro?” // “What is a strategy that you hadn’t used before that you might use in the future?” (Thinking about one more group if I already know part of the problem. Skip-counting.)
• “¿Alguien puede expresar el razonamiento de _____ de otra forma?” //“Who can restate _____’s reasoning in a different way?”
• “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
• “¿Alguien resolvió el problema de otra forma?” // “Did anyone solve the problem in a different way?”
• “¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”

## Activity 1: Nuevo año escolar (20 minutes)

### Narrative

The purpose of this activity is to introduce MLR6, Three Reads, and solve a two-step “how many fewer” problem using data presented in a scaled bar graph. The routine prompts students to read a problem three times for different purposes to support them in making sense of the problem (MP1).

### Launch

• Groups of 2

• “Dejen sus libros de trabajo cerrados” // “Keep your books closed.”
• Display only the graph, without revealing the question.
• “Vamos a leer esta gráfica 3 veces” // “We are going to read this graph 3 times.”
• 1st read: “Durante un momento, lean los datos que se muestran en esta gráfica” // “Take a moment to read the data displayed by this graph”
• “¿De qué trata esta gráfica?” // “What is this graph about?” (It’s about how students are feeling about the new year.)
• 1 minute: partner discussion
• Listen for and clarify any questions about the context.
• 2nd read: “Lean e interpreten la gráfica por segunda vez. ¿Qué cantidades están representadas? ¿Qué se puede contar o medir en esta situación?” // “Read and interpret the graph a second time. What quantities are represented? What can be counted or measured in this situation?” (We can count the number of students in each category.)
• 30 seconds: quiet think time
• 2 minutes: partner discussion
• Record quantities on a display for all to see.
• Reveal the question.
• “¿Qué estrategias podemos usar para resolver este problema?” // “What are some strategies we can use to solve this problem?” (We could add the 24 plus 25 to see how many students are nervous or curious. We could subtract how many students are nervous or curious from the number of students that are excited.)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

### Activity

• 5-7 minutes: partner work time
• Monitor for students who:
• add 25+23 and then subtract 55-48
• subtract 55-23 and then subtract 32-25
• subtract 55-25 and then subtract 30-23

### Student Facing

A un grupo de estudiantes le preguntaron: “¿Cómo te sientes con el nuevo año escolar?”. Sus respuestas se muestran en esta gráfica de barras:

¿Cuántos estudiantes más están emocionados que nerviosos o curiosos por el nuevo año escolar?

### Activity Synthesis

• Have 1-2 selected students share their solution and strategy.
• Display the steps of Three Reads routine and keep displayed for the next activity.
• “¿Cómo les ayudó leer tres veces el problema a darle sentido?” // “How did reading the problem three times help you make sense of the problem?” (I was more comfortable with the problem each time I read it. It made more sense every time I read the problem. I noticed different details each time I read it.)

## Activity 2: Usemos gráficas de barras para resolver problemas (15 minutes)

### Narrative

The purpose of this activity is for students to practice the Three Reads math language routine on their own and use data presented in a scaled bar graph to solve a two-step “how many more” situation. The Three Reads routine has students read a problem three times for different purposes to support them to make sense of the problem and persevere in solving it (MP1).

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.
Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which problem to start with or decide the order to complete the task.
Supports accessibility for: Social-Emotional Functioning

### Launch

• Groups of 2
• “¿Qué tipos de plantas ven cuando caminan a casa desde la escuela?” // “What types of plants do you see on your way home from school?” (Trees. Bushes. Flowers. Vines.)
• Share responses.

### Activity

• Display the graph.
• “Trabajen individualmente para resolver los problemas usando la gráfica. Si les ayuda, pueden usar la rutina ‘Tres lecturas’” // “Work independently to use the graph to solve the problems. You can use the Three Reads routine if it’s helpful to you."
• 7–10 minutes: independent work time
• Monitor for students who solve the one-step problems by:
• using the bars on the graph to count up to or back from one number to another.
• using equations to show adding or subtracting by place.
• Monitor for students who solve two-step problems by:
• adding two numbers then subtracting the sum from another number.
• subtracting a number, then subtracting again from the difference.

### Student Facing

La gráfica de barras muestra cuántos árboles de cada tipo vio Clare camino a casa. Usa la gráfica para responder las preguntas. Muestra cómo pensaste. Usa expresiones o ecuaciones.

1. ¿Cuántos pinos más que abetos vio Clare?
2. ¿Cuántos pinos más que robles o arces vio Clare?
3. ¿Cuántos robles menos que pinos vio Clare?
4. ¿Cuántos arces o robles menos que abetos vio Clare?

### Student Response

If students find the sum of all categories or don't find a solution to the problems, consider asking:

• “Dime cómo comenzaste a resolver este problema” // “Tell me about how you started this problem?”
• “¿Cómo podrías usar la información de la gráfica para resolver el problema?” // “How could you use the information from the graph to solve the problem?”

### Activity Synthesis

• Have 1-2 students share the method, including any expressions or equations they used to solve the first problem.
• Have 2-3 students share the expressions or equations they used to solve the last problem.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (Some people added the maple and oak trees together and then subtracted it from the number of fir trees. Some people subtracted the number of maple trees from fir trees and then subtracted the number of oak trees. Each way found the same number of trees.)

## Lesson Synthesis

### Lesson Synthesis

Display equations from the first problem in the last activity.

“¿Como usaron lo que saben sobre decenas y unidades para resolver los problemas?” // “How did you use what you know about tens and ones to solve the problems?” (Some questions I saw I could just count by 10 on the graph because the scale was 10. We didn’t subtract all at once. We subtracted the tens, then the ones. We were thinking about how to get to the next ten to make adding the tens easier.)

“En el futuro, ¿cómo podrían usar la estrategia ‘Tres lecturas’ solos, sin ayuda de un compañero?” // “In the future, how could you use the Three Reads strategy on your own, without a partner?” (We could use it any time by thinking what the problem is about. We can read the problem to look for what can be measured or counted in the problem. We can read it to think about strategies we could use to solve the problem.)