# Lesson 4

Comparemos números en una recta numérica

## Warm-up: Conversación numérica: Restemos cincos (10 minutes)

### Narrative

The purpose of this Number Talk is for students to subtract with multiples of 5. As students share strategies based on place value or related to adding on or subtracting multiples of 5, record their thinking using a number line diagram. Students connect their mental strategies to the representation of moving a length of 5, 10, or 20 from one number to another on the number line. The understandings elicited here will be helpful in later lessons when students represent sums and differences on number lines.

### 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

• Record answers and strategy. Use a number line diagram when possible.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$35 - 5$$

• $$35 - 10$$

• $$35 - 15$$

• $$35 - 25$$

### Activity Synthesis

• “¿Cómo les ayudaron las primeras 2 expresiones a pensar en las últimas 2?” // “How did the first 2 expressions help you think about the last 2?” (I know that $$5 - 5 =0$$ because all of the ones are being taken away. Then I just take the tens from the tens.)

## Activity 1: Comparemos los números (20 minutes)

### Narrative

The purpose of this activity is for students to compare two numbers and justify their comparison based on the location of each number on the number line. Using the number lines students created in a previous lesson, students represent numbers by placing counters as points on the number line. Students recognize that given any two numbers, the number farther to the right represents a greater value than the number to the left (MP7).

Engagement: Provide Access by Recruiting Interest. Give students a context to relate the number line to. For example, a frog jumping on lily pads, or a rabbit hopping. The counters can represent the animal hopping along the number line.
Supports accessibility for: Conceptual Processing, Attention

### Required Materials

Materials to Gather

### Required Preparation

• Each student will need their number line they made in Lesson 1.
• Each group of 2 needs 3 number cubes and 2 counters.

### Launch

• Groups of 2
• Give each group 3 number cubes and 2 counters.
• Assign Partner A and B.

### Activity

• “Van a usar la recta numérica que hicieron y a trabajar con un compañero. Decidan con su compañero cuál de las dos rectas numéricas van a usar” //  “You will use the number line you created and work with a partner. Decide with your partner whose number line you will use.”
• As needed, demonstrate the task with a student.
• “Soy el compañero A. Voy a lanzar los 3 dados numéricos y a encontrar la suma” // “I am Partner A. I am going to roll the 3 number cubes and find the sum.”
• “Después, tomo una ficha y la ubico en la recta numérica para representar la suma” // “Then, I take a counter and place it on the number line to represent the sum.”
• “Ahora es el turno de mi compañero. Hace lo mismo y ubica su ficha en la misma recta numérica para representar la suma de sus números” // “Now it’s my partner's turn. They do the same thing and put their counter on the same number line to represent the sum of their numbers.”
• “Después, decidimos cuál número es mayor y explicamos cómo lo sabemos” // “Then, we decide which number is greater and explain how we know.”
• “Por último, usamos los símbolos $$<$$, $$>$$ o $$=$$ para escribir nuestra comparación” // “Last, we use the $$<$$ , $$>$$, or $$=$$ symbols to record our comparison.”
MLR8 Discussion Supports
• If needed, remind students to use comparison vocabulary (less than, greater than, equal to) to read the symbols and their comparisons.
• If needed, invite students to chorally repeat the phrases that each symbol represents.
• 10 minutes: partner work time
• Monitor for students who explain comparisons:
• based on lengths from 0
• using the language “to the left” and “to the right”

### Student Facing

• Compañero A:
• Lanza 3 dados numéricos y encuentra la suma.
• Ubica una ficha en el lugar de la suma en la recta numérica.
• Compañero B:
• Lanza 3 dados numéricos y encuentra la suma.
• Ubica una ficha en el lugar de la suma en la recta numérica.
• Decidan cuál número es mayor y expliquen.
• Usen  $$<$$, $$>$$ o $$=$$ para comparar los 2 números representados en su recta numérica.
Compañero A $$<$$, $$>$$ o $$=$$ Compañero B

### Student Response

If students write comparison statements that are not true, consider asking:

• “¿Cómo puedes usar la recta numérica para mostrar que ___ es mayor que o menor que ___?” // “How can you use the number line to show that ___ is greater than or less than ___?”

### Activity Synthesis

• Invite 2–3 previously identified groups to share comparisons and their explanations.
• “¿Qué observan acerca de los números que están más a la derecha?” // “What do you notice about the numbers that are farther to the right?” (They were greater. They represent a greater length from zero.)

## Activity 2: Comparemos números más grandes (15 minutes)

### Narrative

The purpose of this activity is for students to use a number line to compare larger numbers. In the first activity, students compared numbers on a number line with all of the tick marks labeled. In this activity, only the multiples of 5 are labeled. Students locate and label numbers on the number line and compare them. Listen for the language students use to explain how they know a number is greater than or less than another number, including those based on the lengths the numbers represent from 0 (MP6).

### Required Materials

Materials to Gather

Materials to Copy

• Number Line to 100

### Required Preparation

• Each group of 2 needs 2 number cubes and a dry erase marker.
• Put number line recording sheets into sheet protectors. The recording sheets will be used in upcoming lessons.

### Launch

• Groups of 2
• Give each group a number line, 2 number cubes, and a dry erase marker.

### Activity

• “Van a trabajar un poco más en comparar números en una recta numérica. Lo van a hacer con otro compañero” // “You are going to do some more work comparing numbers on a number line with a new partner.”
• “Esta vez van a usar una recta numérica que va del 0 al 100” // “This time you will use a number line that goes from 0100.”
• “Cada uno va a lanzar 2 dados numéricos y va a formar un número de dos dígitos” // “Each of you will roll 2 number cubes and create a two-digit number.”
• “Ubiquen y marquen ambos números en la recta numérica” // “Locate and label both numbers on the number line.”
• “Después, usen $$<$$$$>$$$$=$$ para comparar los números. Expliquen cómo saben que su comparación es verdadera” // “Then compare the numbers using $$<$$, $$>$$, or $$=$$. Explain how you know your comparison is true.”
• 10 minutes: partner work time
• Monitor for student comparisons where both numbers are close on the number line (within 10) and where numbers are farther apart (greater than 30).

### Student Facing

• Cada compañero lanza 2 dados numéricos y forma un número de dos dígitos.
• Cada uno ubica y marca su número en la recta numérica.
• Usa >, < o = para comparar los números.
• Explica por qué tu comparación es verdadera.
Compañero A $$<, > \text{o} =$$ Compañero B

### Activity Synthesis

• Invite a previously identified group to share a comparison where the numbers are close.
• Display the number line from the activity to record student comparison or have students display their work so all students can see.
• “¿La comparación de _____ es verdadera? Expliquen” // “Is _____’s comparison true? Explain.” (Yes, it is true because _____ [larger number] is farther to right. It represents a longer length from 0 than the smaller number.)
• Repeat with a previously identified group with a comparison where numbers are farther apart.
• “¿Cuál comparación tiene una diferencia más grande entre los dos números? Expliquen” // “Which comparison has a bigger difference between the two numbers? Explain.” (_____ has a bigger difference. You can tell because the length between them is much larger than the length between the other two numbers.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy usamos rectas numéricas para comparar números, y pensamos qué tan cerca o qué tan lejos están del cero y entre sí. Usamos lo que sabemos sobre comparar longitudes para comparar los números. También usamos palabras que indican posición, como 'a la derecha' o 'a la izquierda', para hablar de cuál número era menor o era mayor” // “Today, we used number lines to compare numbers and thought about how close or far away they are from zero and each other. We used what we know about comparing lengths to compare the numbers. We also used position words like to the left or right to talk about which number was less or more.”

Display or draw:

“Si A y B son puntos que representan números en esta recta numérica, ¿cuál número es menos? ¿Cómo lo saben?” // “If A and B are points that represent numbers on this number line, which number is less? How do you know?” (A, because it is farther to the left than B. A, because it is closer to zero. A, because B represents a longer length from 0.)