# Lesson 10

Comparaciones usando valores posicionales (parte 1)

## Warm-up: Conversación numérica: Sumemos decenas (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for mentally adding a multiple of 10 to a number. Building on their understanding of place value, students add tens to tens. When students notice that only the digit in the tens place is changing and make connections between the tens in each expression, they look for and make use of structure and express regularity in repeated reasoning (MP7, MP8). These understandings help students develop fluency and will be helpful in later lessons when students will add using strategies based on place value.

### 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

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$36 + 40$$
• $$46 + 30$$
• $$59 + 40$$
• $$69 + 30$$

### Activity Synthesis

• “¿Cómo puede ayudarles la primera expresión a encontrar el valor de la segunda?” // “How could the first expression help you find the value of the second one?” (46 is 10 more than 36, and 30 is 10 less than 40, so the answer is the same. They have the same number of tens.)

## Activity 1: Comparemos por posición (15 minutes)

### Narrative

The purpose of this activity is for students to learn that when comparing three-digit numbers, it is helpful to start by comparing the value of the hundreds. In this activity, the base-ten diagrams are not organized by place and do not mirror the structure of a three-digit number. Students learn that when comparing numbers in which one number has more hundreds than the other, it is not necessary to consider the tens and ones.

Engagement: Provide Access by Recruiting Interest. Invite students to share situations and examples of comparing numbers in their real lives. For example, cars in a parking lot, students in a grade level, and so on, to bring a context to the work in the lesson.
Supports accessibility for: Memory, Conceptual Processing

### Launch

• Groups of 2
• Display the image.
• “¿Quién tiene más? ¿Cómo lo saben?” // “Who has more? How do you know?” (Tyler has 2 hundreds, but Mai only has 1. He has more.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.

### Activity

• “Hoy van a comparar cantidades representadas por diagramas en base diez” // “Today you will compare quantities represented by base-ten diagrams.”
• “Comparen los diagramas. Escriban el valor de cada cantidad como un número de tres dígitos y usen los símbolos de mayor que, menor que o igual para comparar los números” // “Compare the diagrams. Write the value of each quantity as a three-digit number and use the greater than, less than, or equal to symbols to compare the numbers.”
• 8 minutes: independent work time
• “Comparen con un compañero” // “Compare with a partner.”
• 2 minutes: partner discussion

### Student Facing

¿Quién tiene más? ¿Cómo lo sabes?

Compara los diagramas en base diez.

Escribe cada valor como un número de tres dígitos. Usa los símbolos $$<$$, $$>$$ o $$=$$ para comparar los números.

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

### Student Response

If students write something other than $$224 = 224$$ for the last problem, consider asking:

• “¿Cómo decidiste de qué forma escribir cada valor como un número de tres dígitos? ¿Cómo comparaste los números?” // “How did you decide how to write each value as a three-digit number? How did you compare the numbers?”
• “¿Hay unidades en base diez de las que haya 10 o más?” // “Are there any units that have 10 or more?”
• “¿Cómo cambió tu respuesta al componer una nueva unidad en base diez?” // “How did composing a new unit change your answer?”

### Activity Synthesis

• Share responses for the first two comparisons.
• “¿Cómo saben que su afirmación es verdadera?” // “How did you know your statement is true?”
• “¿Qué unidad en base diez fue más importante para decidir cuál cantidad era mayor?” // “What unit was most important in deciding which quantity was greater?”
• Display the images for $$224 = 224$$.
• “¿Cuál valor es mayor? ¿Cómo lo saben?” // “Which value is greater? How do you know?” (The two quantities are equal. Both diagrams represent 224. One had 2 hundreds, but the other had 1 hundred and 12 tens.)
• Record $$224 = 224$$.
• “Cuando comparan números basándose en diagramas en base diez, ¿en qué piensan para decidir cuál cantidad es mayor? Expliquen” // “When comparing numbers based on base-ten diagrams, what do you think about to help you decide which quantity is greater? Explain.” (First we need to find out how many hundreds each number has, but sometimes that means we have to count the tens to see if there are enough to make another hundred. If a number has more hundreds, we know that number is greater.)

## Activity 2: Comparemos centenas, decenas y unidades (20 minutes)

### Narrative

The purpose of this activity is for students to extend their understanding of comparing three-digit numbers to include amounts in which the values in the hundreds place and tens place are the same in both numbers. In the last activity, students learned that by comparing the hundreds you can determine the greater value without considering the tens and ones. In this activity, they recognize the need to compare hundreds to hundreds, tens to tens, and ones to ones when the digits are the same in the numbers being compared.

MLR8 Discussion Supports. If necessary, invite students to repeat their reasoning using mathematical language: “¿Pueden decir eso otra vez, usando el lenguaje de valor posicional?” // “Can you say that again, using place value language?”

• Groups of 2

### Activity

• “En la actividad anterior vimos que si un número tiene más centenas que otro número, tiene mayor valor” // “In the last activity we saw that if one number has more hundreds than another number it has the greater value.”
• “Van a comparar más cantidades representadas por diagramas en base diez” // “You will compare more quantities represented by base-ten diagrams.”
• “Comparen los diagramas. Escriban el valor de cada cantidad como un número de tres dígitos y usen los símbolos de mayor que, menor que o igual para comparar los números” // “Compare the diagrams. Write the value of each quantity as a three-digit number and use the greater than, less than, or equal to symbols to compare the numbers.”
• “Con su pareja, comparen números y discutan cómo pensaron en cada problema” // “Work with your partner to compare numbers and discuss your thinking for each problem.”
• 15 minutes: partner work time
• Monitor for students who use precise language to explain how they knew that $$338 > 336$$ based on comparing the value of each digit.

### Student Facing

Compara los diagramas en base diez. Escribe cada valor como un número de tres dígitos. Usa los símbolos $$>$$, $$<$$ o $$=$$ para comparar los números.

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

$$\underline{\hspace{1.5cm}}\phantom{3}\boxed{\phantom{33}}\phantom{3}\underline{\hspace{1.5cm}}$$

5. En el último problema, ¿cómo supiste cuál valor era mayor?

### Activity Synthesis

• Invite previously selected students to share how they compared 338 and 336.
• Display 445 _____ 447.
• “Según lo que aprendieron, ¿cómo pueden saber cuál número es mayor sin usar los bloques?” // “Based on what you learned, how can you tell which number is larger without using the blocks?” (I can look at a number and see how many hundreds, tens, and ones there are without the diagrams.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy comparamos números de tres dígitos con la ayuda de diagramas en base diez” // “Today, we compared three-digit numbers with the help of base-ten diagrams.”

Display the image from the launch of the first activity.