# Lesson 1

Números enteros en la recta numérica

## Warm-up: Observa y pregúntate: Reglas y rectas numéricas (10 minutes)

### Narrative

The purpose of this warm-up is for students to make sense of a new representation and how it is similar to and different from a ruler. If possible, display an actual ruler next to the number line. This will be useful when students create their own number lines in a later activity. While students may notice and wonder many things about these images, the connections between the features of a number line and a ruler are the important discussion points.

### Launch

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

### Activity

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

### Student Facing

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• “Hoy vamos a pensar en cómo nos podría ayudar el primer diagrama cuando pensamos en números” // “Today, we are going to think about how the first diagram might be helpful when thinking about numbers.”

## Activity 1: ¿Qué es una recta numérica? (15 minutes)

### Narrative

The purpose of this activity is for students to learn the features of a number line. Students make sense of and use the features of number lines, such as the sequence of numbers moving from left to right and equal spacing between tick marks to locate and represent whole numbers. In the synthesis, students describe how they filled in the missing numbers on a number line and how they located and represented a specific number.

Representation: Internalize Comprehension. Begin by asking, “¿Esta recta numérica le recuerda a alguien algo que hayamos visto antes? ¿A qué aspectos de la regla / las herramientas de medición teníamos que prestarles especial atención? ¿Piensan que será parecido o diferente para una recta numérica?” // “Does this number line remind anyone of something we have seen before? What were some important aspects of the ruler/measuring tools that we had to pay close attention to? Do you think they will be similar or different for a number line?”
Supports accessibility for: Memory, Conceptual Processing, Organization

### Launch

• Groups of 2
• Display the number line image from the warm up.
• “Este diagrama se llama una recta numérica. ¿Qué observan acerca de esta recta numérica?” //  “This diagram is called a number line. What do you notice about this number line?” (It has tick marks like a ruler. The numbers go in order. There is a point at 4. The numbers are equally spaced.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• “Observamos algunas cosas importantes acerca de las rectas numéricas” // “We noticed some important things about number lines.”
• Summarize the points recorded.
• If it did not come up, make sure the list includes:
• There is the same amount of space between each tick mark on the number line like a ruler.
• The numbers on the number line are listed in order from left to right like on a ruler. Each number represents a length from 0.
• A dot, called a point, on the number line represents a specific number.
• “¿Este punto qué número representa? Expliquen” // “What number does this point represent? Explain.” (4, because the point is right above the 4. It is 4 length units from 0.)
• 30 seconds: quiet think time
• 30 seconds: partner discussion
• Share responses.

### Activity

• “Ahora van a trabajar con la recta numérica. Tienen una recta numérica a la que le faltan números en las marcas. Escriban debajo de cada marca el número que ella representa. Ubiquen diferentes puntos en la recta numérica y márquenlos con un punto” // “Now you are going to do some work with the number line. You have a number line that is missing labels on the tick marks. Label each tick mark with the number it represents. Locate different points on the number line and mark them with a point.”
• 5 minutes: independent work time
• If students finish early, ask them to extend the number line and label different points.

### Student Facing

1. Escribe debajo de cada marca el número que representa.

2. Ubica el 6 en la recta numérica. Márcalo con un punto.

3. Ubica en la recta numérica un número que sea mayor que 6. Márcalo con un punto.

4. Escribe debajo de cada marca el número que representa.

5. Ubica el 9 en la recta numérica. Márcalo con un punto.

6. Ubica en la recta numérica un número que sea menor que 9. Márcalo con un punto.

### Student Response

If students draw a point in a location other than a number greater than 6 or less than 9, give students a ruler. Consider asking:

• “Al mirar esta regla, ¿qué medida es más larga que 6 cm?” // “Looking at this ruler, what is a measurement that is longer than 6 cm?”
• “¿Cómo puedes mostrar ese número en la recta numérica?” // “How could you show that number on the number line?”

### Activity Synthesis

• Display the number line with only 0, 5, and 10 labeled.
• “¿Cómo supieron qué números debían escribir debajo de las marcas?” // “How did you know which numbers to use to label the tick marks?” (It’s like a ruler, I figured out how many length units each tick mark was from 0. I just counted because I know the numbers need to go in order from left to right.)

## Activity 2: Haz tu propia recta numérica (20 minutes)

### Narrative

The purpose of this activity is for students to learn that numbers are represented on a number line as lengths from 0. Students choose their own length unit to make equally spaced tick marks and label them 0–20. In the synthesis, students compare their number lines and notice that on a given number line the length between successive numbers should be the same. This length represents 1 length unit (the unit interval). Students also notice that, unlike tools that are used to measure standard length units, number lines can use any size of length unit to represent a set of numbers, as long as it's the same between consecutive numbers.

In order to make an accurate number line, students will need to make strategic use of materials in order to measure the units on their number line. This could be a paper clip or a staple or the equally spaced lines on a lined sheet of paper (MP5).

Students will use the number line they create in an upcoming lesson.

MLR8 Discussion Supports. Synthesis. Display sentence frames to support small-group discussion: “Las rectas numéricas son parecidas porque . . .” // “The number lines are the same because . . . .” and “Las rectas numéricas son diferentes porque . . .” // “The number lines are different because . . . .”

### Required Materials

Materials to Gather

### Required Preparation

• Each student needs a sentence strip or a 2430 inch rectangular strip of paper.
• Each group of 2 students needs access to assorted objects that can be used as a length unit to construct number lines (base-ten blocks, inch tiles, paper clips, large erasers, small sticky notes).

### Launch

• Groups of 2
• Give students a long rectangular strip of paper, like a sentence strip, and access to different objects to create a number line.

### Activity

• “Ahora van a crear su propia recta numérica. Pueden usar cualquiera de las herramientas que tienen para crear una recta numérica que represente los números del 0 al 20” // “Now you’re going to create your own number line. You can use any of the tools provided to create a number line that represents the numbers from 0 to 20.”
• 10 minutes: independent work time
• Monitor for students who choose different objects as their length unit and create accurate number lines.
• 2 minutes: partner discussion

### Student Facing

1. Haz una recta numérica que vaya de 0 a 20.

2. Ubica el 13 en tu recta numérica. Márcalo con un punto.

3. Ubica el 3 en tu recta numérica. Márcalo con un punto.

4. Compara tu recta numérica con la de tu compañero.

### Student Response

If students create a number line with tick marks spaced different lengths apart, consider asking:

• “¿Qué objeto usaste para hacer tu recta numérica? ¿Puedes mostrarme cómo lo usaste?” // “What object did you use to make your number line? Can you show me how you used it?”
• “¿Cómo puedes usar tu objeto para comprobar que tus marcas estén igualmente espaciadas?” // “How can you use your object to check to see that your tick marks are equally spaced?”

### Activity Synthesis

• Display 3 student number lines that have different sized unit intervals.
• “¿En qué se parecen y en qué son diferentes estas representaciones?” // “What is the same and what is different about these representations?” (They all have equally spaced tick marks. They all show 0 to 20 in order. They all show a point on 3 and 13. The length of the space they used between tick marks is different. They used different objects to create their number lines.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos sobre la recta numérica, que es una representación visual de los números. Aprendimos que, al igual que con las reglas y los diagramas de puntos, los números pueden ser representados por marcas para mostrar su longitud medida desde 0 en la recta numérica. También aprendimos que podemos mostrar números específicos en una recta numérica marcándolos con un punto” // “Today we learned about the number line, which is a visual representation of numbers. We learned that, just like with rulers and line plots, numbers can be represented by tick marks to show their length from 0 on the number line. We also learned that you can show specific numbers on a number line by marking them with a point.”

Display the 3 student number lines from the last activity.

“¿Cómo pueden los puntos en distintas rectas numéricas representar el mismo número?” // “How can the points on each number line represent the same number?“ (They used different units, but they all show that 3 is 3 length units from 0 and 13 is 13 length units from 0.)