# Lesson 8

Números de tres dígitos en la recta numérica

## Warm-up: Conteo grupal: Contemos de 10 en 10 y de 100 en 100 (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting by 10 and 100 and notice patterns in the count. This is the first time students are introduced to the number 1,000. Although students in grade 2 do not need to understand the unit of a thousand, students will work with 1,000 on a number line in this lesson to deepen their understanding of the structure of the base-ten system.

### Launch

• “Cuenten de 10 en 10, empezando en 0” //“Count by 10, starting at 0.”
• Record in a column as students count.
• Stop counting and recording at 100.
• “Cuenten de 100 en 100, empezando en 0” //“Count by 100, starting at 0.”
• Record the count in a new column next to the first.
• Stop counting and recording at 1,000.

### Activity

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

### Activity Synthesis

• Draw three number lines that show counting by 1, 10, and 100, such as:
• “¿Qué patrones ven?” // “What patterns do you see?” (All 3 number lines show 10 jumps. They all start at zero, but end with different numbers.)

## Activity 1: Marquemos números de tres dígitos (20 minutes)

### Narrative

The purpose of this activity is for students to connect their understanding of the counting sequence within 1,000 and their understanding of place value to the structure of the number line. In the launch, students make sense of 3 number lines that have different unit intervals. They may reason about the numbers each tick mark represents by counting by 1, 10, or 100. Other students may notice that there are 10 lengths (unit intervals) and relate this to decomposing a ten or hundred to describe the numbers represented by each tick mark. Throughout the activity, encourage students to make connections between the reasoning they use based on counting and their understanding of place value as they write three-digit numbers and make sense of the structure of the number line (MP7).

MLR8 Discussion Supports. Invite students to begin partner interactions by repeating the questions “¿Cómo van a contar?” // “How will you count?” and “¿Cómo lo saben?” // “How do you know?” This gives both students an opportunity to produce language.

### Launch

• Groups of 2
• Display the images of the 3 number lines.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 30 seconds: quiet think time
• Share and record responses.
• “¿En qué se parecen o en qué son diferentes estas rectas numéricas?” // “What is the same or different about these number lines?” (They all have 10 sections between the start and end marks. They are the same length, but the tick marks represent different numbers. They all start with zero.)
• 30 seconds: quiet think time
• Share responses.
• “Tómense unos minutos para ubicar y marcar 30, 300 y 3 en la recta numérica” // “Take a few minutes to locate and label 30, 300, and 3 on a number line.”
• 3 minutes: independent work time

### Activity

• “Ahora van a mirar algunas rectas numéricas con un compañero y a identificar los números representados por los puntos” // “Now you are going to look at some more number lines with a partner and identify the numbers represented by the points.”
• “Discutan con su pareja y decidan si pueden contar las marcas de 1 en 1, de 10 en 10 o de 100 en 100 en cada recta numérica. Después, marquen cada punto con el número que representa” // “For each number line, discuss with your partner and decide if you can count the tick marks by 1, 10, or 100. Then label each point with a number it represents.”
• 8 minutes: partner work time
• Monitor for students who recognized they needed to count by 1 for the number line showing 620–630.

### Student Facing

¿Qué observas? ¿Qué te preguntas?

Ubica y marca 30, 300 y 3 en una recta numérica.

Marca cada punto con el número que el punto representa.

### Student Response

If students label number lines with numbers that do not correspond to the count pattern, consider asking:

• “¿Cómo decidiste de qué forma marcar el punto?” // “How did you decide how to label the point?”
• “¿Qué números están representados por las marcas en esta recta numérica?” // “What numbers do the tick marks on this number line represent?”
• “Mirando el número del principio y el del final, ¿qué patrón para contar a saltos puedes usar para contar las marcas?” // “Looking at the starting and ending numbers, what skip-counting pattern could you use to count the tick marks?”

### Activity Synthesis

• Display the image for the number line showing 620–630.
• Invite previously identified students to share how they identified 629.
• “¿Cómo pueden demostrar que el punto representa 629?” // “How can you prove that the point represents 629?”
• “¿Qué números están representados por las marcas en esta recta numérica? ¿Cómo contaron las marcas?” // “What numbers do the tick marks represent on this number line? How did you count the tick marks?”
• As time permits, invite students to share how they identified other points.

## Activity 2: Representemos números de tres dígitos en una recta numérica (15 minutes)

### Narrative

The purpose of this activity is for students to use their place value understanding to locate numbers on a number line. Number lines are given with a starting number, 10 length units marked with tick marks, and an ending number. None of the tick marks are labeled. Students determine the size of the units based on the range of the number line. For example, if the starting and ending numbers are 0 and 100, they may reason that the unit represented by the tick marks is ten because there are 10 tens in a hundred. Once students have determined the unit marked on the number line, they are able to count to find the location of each number. Students may begin to notice that when the two ticks at the right and left of the number line are 100 apart, the individual tick marks go up by 10 and when the two tick marks at the right and left of the number line are 10 apart, the individual tick marks go up by 1 (MP8).

Representation: Internalize Comprehension. Invite students to label tick marks on the number line, or identify the value of the middle tick mark for a frame of reference to solve the problem. Discuss how identifying and labeling other parts of the number line help you get closer and closer to the point you are trying to find.
Supports accessibility for: Organization, Memory, Attention

• Groups of 2

### Activity

• “Ahora van a ubicar y a marcar números de tres dígitos en la recta numérica” // “Now you are going to locate and label three-digit numbers on the number line.”
• “Tómense unos minutos para hacerlo solos y prepárense para explicárselo a sus parejas” // “Take a few minutes to try them on your own and be ready to explain to your partner.”
• 5 minutes: independent work time
• “Ahora, comparen con su pareja y compartan cómo pensaron” // “Now compare with a partner and share your thinking.”
• If students are not finished, they can work together.
• 5 minutes: partner discussion
• Monitor for different ways students determine the unit represented on the number line for representing 940 such as:
• counting by ones, tens, and hundreds to see which one gets them to the ending number
• using the starting and ending numbers to determine what the unit must be

### Student Facing

Ubica y marca cada número en la recta numérica. Si te ayuda, escribe el número que corresponde a cada marca.

1. 700

2. 472

3. 940

4. 356

5. 590

### Activity Synthesis

• Display the number line showing 900–1,000.
• Invite a student to demonstrate their strategy of trial and error to determine how to label the tick marks.
• Invite another student to demonstrate their strategy of reasoning about the starting and ending numbers. (I know the difference between 900 and 1,000 is 100 and there are 10 length units. Each one must be 10 because there are 10 tens in a hundred.)
• “¿En qué se parecen y en qué son diferentes las formas en las que ellos decidieron cuál era la unidad en esta recta numérica?” // “What is the same and different about how they decided the unit on this number line?” (They both counted to see how many tick marks were there. _____ tried counting by 1 and then 10, but _____ counted by 10 right away.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy representaron números de tres dígitos en rectas numéricas” // “Today you represented three-digit numbers on number lines.”

Display the images of the number lines from the launch.

“Si yo quisiera ubicar y representar 80 en una recta numérica, ¿cuál debería escoger? Expliquen” // “If I wanted to locate and represent 80 on a number line, which one should I choose? Explain.” (You should choose the one that shows 0–100 because if you count by 10 you will find 80. It won’t be on the 0–10 one and it would be hard to find on the 1,000 one even though it could go in between 0 and the first mark.)