# Lesson 2

Características de una recta numérica

## Warm-up: Conteo grupal: Contemos de 5 en 5 (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting by 5 and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson and future lessons when students show their thinking on the number line. When students notice patterns and explain why they think they occur based on their understanding of operations and the structure of ten, they look for and express regularity in repeated reasoning (MP7, MP8).

### Launch

• “Cuenten de 5 en 5, empezando en 0” // “Count by 5, starting at 0.”
• Record as students count.
• Stop counting and recording at 100.

### Activity

• “¿Qué patrones ven?” // “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Activity Synthesis

• “¿Alguien puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
• “¿Alguien quiere compartir otra observación sobre por qué ocurre ese patrón aquí?” // “Does anyone want to add an observation about why that pattern is happening here?” ($$5 + 5 = 10$$, so when you count by 5 two times you make a new ten.)

## Activity 1: La recta numérica de la clase (20 minutes)

### Narrative

The purpose of this activity is for students to reason together about the relative position of numbers on the number line. Students place number cards on the number line, which is represented by yarn strung across the classroom. Students reason about where their number should be placed based on their understanding of the count sequence and by reasoning about the relative distance of numbers from 0 and each other. As more numbers are called, students revise their number locations to be more precise (MP6, MP7). Throughout the activity, encourage students to reflect on the length between numbers and whether it is an accurate representation of the number relationships.

It is recommended that students are called in a random order. This will provide students opportunities to revise their thinking about the position of their number when more information is added to the number line representation.

Action and Expression: Develop Expression and Communication. Some students may benefit from access to a blank number line with equally spaced tick marks on it. Students can then label the tick marks as the numbers are put on the number line to see the appropriate spacing and where the missing numbers lie.
Supports accessibility for: Organization, Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• Class Number Line Cards (0–30)

### Required Preparation

• Hang yarn across the classroom (yarn should be hung taut to resemble a line) for students to hang their number cards on.
• Create a set of number cards from the blackline master.
• Fold the number cards so they can be hung on the line.

### Launch

• Give each student a number card.
• It is not necessary to hand out all of the cards.

### Activity

• “Hoy van a crear una recta numérica de la clase para representar los números del 0 al 30” // “Today, you are going to create a class number line to represent the numbers from 0 to 30.”
• “Cuando los llame, ubiquen su tarjeta de números en la recta numérica” // “When I call you, place your number card on the number line.”
• Place the 0 card to demonstrate how to place a number on the string and to show where the number line begins.
• Invite students to hang their cards in a random order.
• When students place their numbers, ask:
• “¿Cómo decidieron dónde ubicar su número en la recta numérica?” // “How did you decide where to place your number on the number line?”
• “¿Qué ajustes debemos hacerle a la recta numérica? ¿Por qué?” // “What revisions do we need to make to the number line? Why?”
• Pause to check in and revise thinking as needed. If students need prompting for justifying their reasoning for number placement based on length, consider asking:
• “¿Qué tan cerca de ___ debe estar tu número?” //  “How close should your number be to ___?”
• “¿Tu número debe estar más cerca de ___ que de ___?” // “Should your number be closer to ___ than ___?”

### Activity Synthesis

• “Las rectas numéricas representan la longitud de los números desde 0 y nos ayudan a ver qué tan cerca están los números entre sí” //  “Number lines represent the length of numbers from 0 and help us see how close numbers are to each other.”
• “¿Cómo ajustaron la ubicación de su número a medida que se agregaban más números?” // “How did you adjust the location of your number as more numbers were added?” (Sometimes we had to make more room or move cards because the new number needed to fit in between numbers. The more numbers that were already on the number line, the easier it was to be precise.)
• “Al examinar nuestra recta numérica, ¿qué ajustes finales se pueden hacer para que nuestra recta numérica sea más precisa?” // “Looking at our number line, what final revisions could be made to make our number line more precise?”

## Activity 2: Analicemos rectas numéricas (15 minutes)

### Narrative

The purpose of this activity is for students to analyze number lines to determine whether they represent numbers within 10 as lengths from 0. Students analyze number line diagrams that do not have equal unit intervals or have tick marks that are not properly labeled. Students discuss what needs to be added or changed in order to make these number line diagrams accurate (MP3, MP6).

This activity uses MLR8 Discussion Supports. Advances: speaking, conversing

• Groups of 3

### Activity

• “A Jada, Andre y Elena les pidieron que crearan un diagrama de recta numérica para representar los números del 0 al 10” // “Jada, Andre, and Elena were asked to create a number line diagram to represent the numbers from 0 to 10.”
• “Individualmente, examinen la recta numérica de cada estudiante. Piensen en 1 cosa que consideren que el estudiante hizo bien cuando representó los números del 0 al 10 y en 1 cosa que consideren que debe ajustar. Prepárense para compartir con su grupo” // “Look at each student’s number line on your own. Think of 1 thing you think the student did well when they represented 0–10 and 1 thing you think they should revise. Be prepared to share with your group.”
• 90 seconds: independent work time
• “Analicen cada recta numérica con su grupo” // “Discuss each number line with your group.”
MLR8 Discussion Supports
• Display sentence frames to support small-group discussion:
• “Una cosa que _____ hizo bien fue . . .” // “One thing _____ did well was . . .”
• “Una cosa que _____ debe ajustar es . . .” // “One thing _____ should revise is . . .”
• 5 minutes: small-group discussion
• “Todos los estudiantes deben ajustar sus rectas numéricas. Para cada recta numérica, escriban qué deben hacer para arreglarla” // “All of the students need to revise their number lines. For each number line, write what they should do to fix it.”
• 5 minutes: independent work time
• Monitor for students who explain why each diagram needs revising by describing the labels and the space between each number.

### Student Facing

Recta numérica de Andre

Recta numérica de Elena

1. ¿Cómo debe ajustar Jada su recta numérica?
2. ¿Cómo debe ajustar Andre su recta numérica?
3. Recta numérica de Elena

¿Cómo debe ajustar Elena su recta numérica?

4. Completa los números para crear tu propia recta numérica.

### Student Response

If students say that a number line does not need revisions, provide students with a ruler. Consider asking:

• “¿En qué se parecen y en qué se diferencian la recta numérica de _____ y la regla?” // “What is the same and what is different between ____’s number line and the ruler?”
• “¿Cómo puedes usar la forma en que están espaciadas y numeradas las marcas de un regla para describir cómo puede  _____ ajustar su recta numérica?” // “How could you use the way the tick marks are spaced and labeled on a ruler to describe how ____ could revise their number line?”

### Activity Synthesis

• Display Jada’s number line diagram.
• Select previously identified students to share how Jada should revise her number line.
MLR8 Discussion Supports
• Support student use of “length” to describe revisions. For example, revoice the student statement “the numbers are wrong” as “the numbers do not show the correct lengths from 0.”
• “¿Qué cosas hizo bien Jada cuando representó los números del 0 al 10 en una recta numérica?” // “What are some things Jada did well when representing the numbers 0–10 on a number line?” (All of the numbers were listed and are in order. She started with 0 and used tick marks. The tick marks are equally spaced.)
• If time permits, repeat for each diagram.

## Lesson Synthesis

### Lesson Synthesis

“Hoy creamos nuestra propia recta numérica de la clase y analizamos rectas numéricas. ¿En qué debemos pensar cuando creamos una recta numérica para representar números?” // “Today we created our own class number line and analyzed number lines. What do we need to think about when creating a number line to represent numbers?” (We should use the same amount of space between each tick mark. We should make sure labels on tick marks show the right length from 0 and are the right length from each other. We can think about a ruler to check if the number line makes sense.)