# Lesson 5

Comparemos números decimales

## Warm-up: Verdadero o falso: Números decimales (10 minutes)

### Narrative

The purpose of this warm-up is for students to compare different ways of representing a decimal number. It will be important in this and future lessons to write a given decimal in a different form. For example, it is convenient to write 7.3 as 7.300 in order to compare it to 7.299.

### Launch

• Display one statement.
•  “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

En cada caso, decide si la afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.

• $$7.06 = 7.006$$
• $$7.06 = 7.060$$
• $$7.06 = 7.600$$

### Activity Synthesis

• “¿Cómo decidieron si la segunda ecuación es verdadera?” // “How did you decide if the second equation is true?” (I looked at the value of the digits in each place. They are all the same except for an extra 0. But 0 thousandths does not change the value of the number.)

## Activity 1: Más lejos y más rápido (10 minutes)

### Narrative

The purpose of this activity is for students to compare decimals using the context of distance. Students should have access to hundredths grids, if they choose to use them. Monitor for students who compare the decimals using

• place value reasoning to compare the 1 tenth for Diego's throw with the 1 hundredth for Jada's throw
• hundredths grids for the decimal part of the throws
• number lines, recalling work from a previous course

When students decide to compare the decimals using number lines or hundredths grids, they are using appropriate tools strategically (MP5).

MLR8 Discussion Supports. Encourage students to begin partner discussions by reading their written responses aloud. If time allows, invite students to revise or add to their responses based on the conversation that follows.

### Required Materials

Materials to Copy

• Small Grids

### Launch

• Groups of 2
• Display the image in student workbook.
• “¿Alguna vez han lanzado un frisbee?” // “Have you ever thrown a frisbee?”
• Poll the class.
• “Un frisbee es un disco. En los Juegos Olímpicos hay una prueba llamada ‘lanzamiento de disco’. Los competidores lanzan un disco metálico lo más lejos que puedan” // “A frisbee is a disc. In the Olympics, there is an event called the discus throw. Participants try to throw a metal disc as far as they can.”

### Activity

• 2 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who use reasoning named in the activity narrative.

### Student Facing

1. Diego y Jada estaban compitiendo para ver quién podía lanzar el frisbee más lejos. Diego lanzó el frisbee a 5.10 metros. Jada lanzó el frisbee a 5.01 metros.

¿Quién lanzó el frisbee más lejos?
Prepárate para explicar cómo pensaste.

2. Tyler y Han estaban compitiendo para ver quién podía nadar más rápido de un lado al otro de la piscina. Tyler atravesó la piscina en 35.15 segundos. Han atravesó la piscina en 35.30 segundos. ¿Quién atravesó la piscina más rápido? Prepárate para explicar cómo pensaste.

### Activity Synthesis

• Ask previously selected students to share their solutions.
• “En ambos problemas comparamos números decimales. ¿En qué son diferentes los problemas?” // “Both problems are about comparing decimals. How are the problems different?” (The units are different in the two problems. One is meters and the other is seconds. In one problem, the winner has the greater number and in the other problem, the winner has the lesser number.)

## Activity 2: Lo más lejos que vuela un frisbee (20 minutes)

### Narrative

The purpose of this activity is for students to use place value understanding to find decimals that are greater than or less than given numbers. Students work with the frisbee context from the previous activity. They choose decimals for possible distances which are in between the given distances of frisbee throws. Then they list several possible distances in increasing order. Students may use many strategies which all rely on place value:

• using hundredths grids or other diagrams
• using expanded form and comparing the value in each place

Make hundredths grids available for students.

When students use strategies that are based on place value they are looking for and making use of place value structure (MP7).

Representation: Internalize Comprehension. Activate or supply background knowledge. Provide a blank place value chart for students to use as a reference.
Supports accessibility for: Memory, Conceptual Processing

### Required Materials

Materials to Copy

• Small Grids

### Launch

• Groups of 2
• Display: 0.01, 0.001
• “¿Cuál es mayor? ¿Cómo lo saben?” // “Which is greater? How do you know?” (0.01 because it’s a hundredth and that’s more than a thousandth or 0.001.)

### Activity

• 6–8 minutes: partner work time
• “Reúnanse con otra pareja. Entre todos, hagan una lista en orden creciente de todas las distancias que escribieron para los lanzamientos de Tyler y de Priya” // “Get together with a different pair of students and list all of your distances for Tyler and for Priya in increasing order.” (Answers vary.)
• 4–5 minutes: group work time

### Student Facing

Recuerda que Diego lanzó el frisbee a 5.1 metros y Jada a 5.01 metros. Encuentra 2 respuestas posibles para cada pregunta.

1. Han lanzó el frisbee más lejos que Diego. ¿Qué tan lejos puede haber lanzado el frisbee Han?
2. Tyler lanzó el frisbee más lejos que Diego, pero a menos de 6 metros. ¿Qué tan lejos puede haber lanzado el frisbee Tyler?
3. Mai lanzó el frisbee a una distancia menor que la de Jada. ¿A qué distancia puede haber lanzado el frisbee Mai?
4. Priya lanzó el frisbee a una distancia menor que la de Jada, pero a más de 5 metros. ¿A qué distancia puede haber lanzado el frisbee Priya?

### Activity Synthesis

• Invite students to share their distances for Mai and Priya.
• “¿Cómo encontraron algunas distancias posibles para los lanzamientos de Mai?” // “How did you find some possible distances for Mai?” (I could pick any number that was 5 or less so there were lots of choices, 5, 4, 4.7, 4.8)
• “¿En qué fue diferente encontrar una distancia para un lanzamiento de Priya a encontrar una distancia para un lanzamiento de Mai?” // “How was finding a distance for Priya different than finding a distance for Mai?” (I had to pick a number that was bigger than 5 but Priya had just 1 hundredth. I could not find a number using just hundredths. I had to use thousandths because they’re smaller than hundredths.)
• “¿Qué estrategias usaron para ordenar los números de su grupo?” // “What strategies did you use to put the numbers in your group in order?” (We had some duplicate numbers so we needed to find those. We looked at the whole number and then the tenths, hundredths, and thousandths to find which number was the greatest.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy usamos nuestra comprensión del valor posicional para comparar números decimales” // “Today we used place value understanding to compare decimals.”

Display:

$$0.51 = 0.510$$

$$0.52 = 0.520$$

“¿Cómo les puede ayudar esto a encontrar números que están entre estos dos números?” // “How is this helpful for determining numbers that come between these two numbers?” (We can name all the thousandths. There aren’t any hundredths between 0.51 and 0.52.)

“Digan un número que esté entre 0.51 y 0.52. ¿Cómo lo saben?” // “What is a number that is between 0.51 and 0.52? How do you know?” (0.513 because it has 3 more thousandths than 0.51 but it is still smaller than 0.52 which has an extra hundredth.)