# Lesson 11

Comparaciones usando valores posicionales (parte 2)

## Warm-up: Verdadero o falso: Mayor que o menor que (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for working with the value of the digits in a three-digit number. These understandings help students consider place value when comparing three-digit numbers. This will be helpful later when students compare three-digit numbers without visual representations.

### 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

Decide si cada afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.

• $$86 > 80 + 4$$
• $$400 + 40 + 6 < 846$$
• $$330 < 300 + 3$$
• $$500 + 50 > 505$$

### Student Response

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### Activity Synthesis

• “¿Cómo les podría ayudar la forma desarrollada a decidir si la expresión $$330 < 300 + 3$$ es verdadera o falsa?” // “How could expanded form help you decide whether the expression $$330 < 300 + 3$$ is true or false?” (I knew that 30 is 3 tens and 3 is only 3 ones, so 330 is greater than 303.)

## Activity 1: Comparemos y expliquemos (15 minutes)

### Narrative

The purpose of this activity is for students to compare three-digit numbers based on their understanding of place value. They are invited to explain or show their thinking in any way that makes sense to them. A number line is provided. Students may revise their thinking after locating the numbers on the number line, or may choose to draw diagrams to represent their thinking. During the activity synthesis, methods based on comparing the value of digits by place are highlighted.

For the last problem, students persevere in problem solving as there are many ways to make most of inequalities true but students will need to think strategically in order to fill out all of them. In particular, 810 can be used in the first, second, or fourth inequality but it needs to be used in the fourth because it is the only number on the list that is larger than 793.

Representation: Develop Language and Symbols. Represent the problem in multiple ways to support understanding of the situation. For example, have one group member place the numbers on a number line to verify which number is greater. Another option is to have one group member make the numbers using base-ten blocks to prove which is greater.
Supports accessibility for: Conceptual Processing, Organization

### Launch

• Groups of 2
• “En el calentamiento vieron que las diferentes formas de escribir un número pueden ayudarlos a pensar sobre el valor de cada dígito” // “In the warm-up, you saw that different forms of writing a number can help you think about the value of each digit.”
• Write $$564\phantom{3} \boxed{\phantom{33}}\phantom{3}504$$ on the board.
• “¿Qué símbolo haría que esta expresión sea verdadera? Expliquen” // “What symbol would make this expression true? Explain.” (>, because they both have 500, but the first number has 6 tens or 60 and the second number has 0 tens.)

### Activity

• “Hoy van a comparar números de tres dígitos examinando el valor posicional” // “Today you will be comparing three-digit numbers by looking at place value.”
• “Si les ayuda, pueden usar diagramas en base diez o la forma desarrollada para pensar sobre el valor posicional” // “If it helps, you can use base-ten diagrams or expanded form to help you think about place value.”
• “Inténtenlo solos y después comparen con su pareja” // “Try it on your own and then compare with your partner.”
• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who compare the numbers without drawing base-ten diagrams or using a number line.

### Student Facing

Compara los números.

1. $$>$$, $$=$$, o $$<$$

521

$$\boxed{\phantom{33}}$$

523

Explica o muestra cómo pensaste. Si te ayuda, usa un diagrama o una recta numérica.

2. $$>$$, $$=$$, o $$<$$

889

$$\boxed{\phantom{33}}$$

878

Explica o muestra cómo pensaste. Si te ayuda, usa un diagrama o una recta numérica.

3. Ubica los números en los espacios en blanco para hacer que cada ecuación sea verdadera. Usa cada número solo una vez. Si te ayuda, usa diagramas en base diez o la recta numérica.

810

529

752

495

1. $$\underline{\hspace{1 cm}} > 519$$
2. $$687 < \underline{\hspace{1 cm}}$$
3. $$\underline{\hspace{1 cm}} < 501$$
4. $$\underline{\hspace{1 cm}} > 793$$

### Student Response

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### Advancing Student Thinking

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

• “¿Puedes leer cada afirmación en voz alta?” // “Could you read each statement aloud?”
• “¿Cómo supiste que tu afirmación es verdadera?” // “How did you know your statement is true?”
• “¿Cómo puedes usar el diagrama en base diez o la recta numérica para mostrar si tu afirmación es verdadera o falsa?” // “How could you use the base-ten diagram or number line to help you show whether your statement is true or false?”

### Activity Synthesis

• Display $$564 > 504$$ .
• Display $$500 + 60 + 4 > 500 + 4$$.
• “Decidimos que esta afirmación era verdadera. ¿Cómo podemos usar la forma desarrollada de estos números para justificar lo que pensamos?” // “We decided that this was a true statement. How does the expanded form of these numbers help justify our thinking?” (We can see the value of each place, so we can compare each digit.)
• Invite previously selected students to share how they compared numbers without drawing diagrams or using the number line.

## Activity 2: Juguemos “El más grande de todos“ (20 minutes)

### Narrative

The purpose of this activity is for students to learn stage 2 of the Greatest of Them All center. Students use digit cards to create the greatest possible number. As each student draws a card, they choose where to write it on the recording sheet. Once a digit is placed, it can’t be moved. Students compare their numbers using $$<$$, $$>$$, or $$=$$. The player with the greater number in each round gets a point.

Students should remove cards that show 10 from their deck.

MLR2 Collect and Display. Synthesis: Direct attention to the words collected and displayed on the anchor chart from the previous lessons. Invite students to borrow place value language from the display as needed.
Advances: Conversing, Reading

### Required Materials

Materials to Gather

Materials to Copy

• Greatest of Them All Stage 2 Recording Sheet, Spanish

### Launch

• Groups of 2
• Give each group a set of number cards and each student a recording sheet.
• “Ahora van a jugar con su pareja ‘El más grande de todos’” // “Now you will be playing the Greatest of Them All center with your partner.”
• “Van a tratar de formar el número de tres dígitos más grande que puedan” // “You will try to make the greatest three-digit number you can.”
• Display number cards and recording sheet.
• Demonstrate picking a card.
• “Si saco un (2), tengo que decidir si lo quiero poner en la posición de las centenas, las decenas o las unidades para formar el número de tres dígitos más grande” // “If I pick a (2), I need to decide whether I want to put it in the hundreds, tens, or ones place to make the largest three-digit number.”
• “¿En dónde piensan que lo debo poner?” // “Where do you think I should put it?” (I think it should go in the ones place because it is a low number. In the hundreds place, it would only be 200.)
• 30 seconds: quiet think time
• Share responses.
• “Al mismo tiempo, mi pareja también toma tarjetas y construye un número” // “At the same time, my partner is picking cards and building a number, too.”
• “Por turnos, tomen tarjetas y escriban cada dígito en un espacio” // “Take turns picking a card and writing each digit in a space.”
• “Léanle a su pareja sus comparaciones en voz alta” // “Read your comparison aloud to your partner.”

### Activity

• “Ahora jueguen unas cuantas rondas con su pareja” // “Now play a few rounds with your partner.”
• 15 minutes: partner work time

### Activity Synthesis

• Select a group to share a comparison statement. For example: $$654 > 349$$ and $$349 < 654$$.
• “Observé que los compañeros tenían afirmaciones de comparación distintas para los mismos números. ¿Cómo pueden ser ambas verdaderas?” // “I noticed that partners had different comparison statements for the same numbers. How can they both be true?”
• “Si tomo un 8, ¿en dónde lo debo ubicar y por qué?” // “If I draw an 8, where should I choose to place it and why?” (I would put it in the hundreds place since it’s almost the highest number I could draw. I might not get 9. With 800, I have a good chance for my number to be larger than my partner’s.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy comparamos números examinando los dígitos y pensamos en cómo usar los dígitos para formar el número más grande posible” // “Today we compared numbers by looking at the digits and thought about how to use digits to make the greatest number possible.”

Display digits 2, 0, and 9 (in a vertical list).

“¿Cuál es el número más grande que pueden formar con estos dígitos?” // “Using these digits, what is the greatest number you can make?” (920)

“Usando estos dígitos, ¿cuál es el número de tres dígitos más pequeño que pueden formar?” // “Using these digits, what is the smallest three-digit number you can make?” (209, because a three-digit number cannot start with zero.)

## Cool-down: Comparaciones de valor posicional (5 minutes)

### Cool-Down

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