# Lesson 16

Resolvamos todo tipo de problemas de comparación

## Warm-up: Verdadero o falso: Múltiplos de 10 (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for composing a ten when adding within 100. This will be helpful in the lesson as students add within 100 to find unknown values in Compare problems. It also helps students develop fluency with addition within 100 and deepens their understanding of the properties of operations and structure of whole numbers (MP7).

### 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 cómo pensaste.

• $$18 + 5 = 18 + 2 + 3$$
• $$28 + 5 = 30 + 3$$
• $$38 + 4 = 40 + 3$$

### Activity Synthesis

• “¿Cómo podrían cambiar 28 + 5 para que sea 30 + 3?” // "How could you change 28 + 5 to be 30 + 3?" (I could take 2 from 30 and add it to 3.)

## Activity 1: Un paseo a la biblioteca (20 minutes)

### Narrative

The purpose of this activity is for students to represent and solve Compare story problems. Students label a tape diagram based on the given information and represent the unknown with a question mark. When students connect the story problem and the diagram, they look for and make sense of the structure of the problem (MP2).

In the launch of the activity, it may be helpful to ask students to share what they know or have questions about in regards to a library to ensure each student has access into the context and understands books are checked out and returned.

MLR8 Discussion Supports. Synthesis: Give students 2–3 minutes to plan what they will say and practice with a partner before they present to the class. Encourage them to ask each other questions by using sentence frames such as, “¿Puedes decir algo más sobre . . . ?” // “Can you say more about . . .?” and, “¿Por qué decidiste . . . ?” // “Why did you . . . ?”
Advances: Speaking, Conversing, Representing
Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide in which order to complete the problems. Allow the students to choose where to start.
Supports accessibility for: Attention, Social-Emotional Functioning

### Launch

• Groups of 2
• Read the first part of the task statement.
• “¿Quién devolvió más libros?” // “Who returned more books?”
• 1 minute: quiet think time
• Share responses.
• “¿Cómo lo saben?” // “How do you know?”

### Activity

• “Van a seguir trabajando en este problema y a resolver otro parecido. Hay un diagrama que van a usar para representar cada problema. Pueden marcar el diagrama primero o contestar las preguntas primero y después marcar el diagrama” // “You’re going to keep working on this problem and solve another one like it. There is a diagram to use to represent each problem. You can choose to label the diagram first or answer the questions and then complete the diagram.”
• 10 minutes: independent work time
• Monitor for students who started with the tape diagram on each problem to share during the synthesis.
• If students finish early, ask them if they can write their own problem that can be represented by a diagram.

### Student Facing

1. Priya y Andre devolvieron libros a la biblioteca. Priya devolvió 29 libros. Andre devolvió 8 libros más que Priya.

1. ¿Quién devolvió más libros?
2. Usa el problema-historia para completar el diagrama.
3. ¿Cuántos libros devolvió Andre?
2. Anoche, Andre leyó 45 páginas de su libro. Priya leyó 20 páginas menos que Andre.

1. ¿Quién leyó más páginas?
2. Usa el problema-historia para completar el diagrama.
3. ¿Cuántas páginas leyó Priya?

### Advancing Student Thinking

If students identify which student has more, but the labels do not reflect this, consider asking, “¿Puedes explicar cómo decidiste dónde poner cada palabra?” // "Can you explain how you decided where each label should go?" “¿Cómo sabes cuál cantidad es más grande o más pequeña?” // "How do you know which quantity is bigger or smaller?" “¿Cómo se conecta esto con la historia?” // "How does this connect to the story?"

### Activity Synthesis

• Display student work for the first problem.
• Students explain their work, describing how they used the tape diagram.
• “¿Alguien tiene alguna pregunta para _____ sobre su razonamiento o su trabajo?” // “Does anyone have a question for _____ about their thinking or work?”
• “¿Cómo supieron dónde poner los números y el signo de interrogación en este problema?” // “How did you know where to put the numbers and the question mark in this problem?”
• Repeat for second problem.

## Activity 2: Resolvamos problemas de comparación (20 minutes)

### Narrative

This activity begins with the use of the Three Reads Math Language Routine. This routine helps students practice a way to make sense of a problem and persevere in solving it (MP1). The purpose of this activity is for students to analyze and solve a variety of Compare problems. Students may use tape diagrams or any other method that makes sense to them to solve each story problem. Monitor for the different methods students use, including drawings other than tape diagrams and the use of equations. Also, monitor for how students compute and describe their computations when finding the unknown values. Listen for methods based on place value and making a ten.

Students begin the activity by looking at the first story problem displayed, rather than in their books.  At the end of the launch, students open their books and work on the story problems. If students do not show their reasoning using a tape diagram and their equation does not match the story problem, ask them to describe the mathematics of the story problem by explaining what each quantity represents in the context of the story. As needed, draw an unlabeled tape diagram to support student thinking.

This activity uses MLR6 Three Reads. Advances: reading, listening, representing.

### Launch

• Groups of 2

• Display only the story problem stem for question 1, without revealing the question.
• “Vamos a leer este problema-historia 3 veces” // “We are going to read this story problem 3 times.”
• 1st read: “Jada leyó 10 páginas menos que Noah. Noah leyó 27 páginas” // "Jada read 10 fewer pages than Noah. Noah read 27 pages."
• “¿De qué se trata esta historia?” // “What is this story about?”
• 1 minute: partner discussion.
•  Listen for and clarify any questions about the context.
• 2nd read: “Jada leyó 10 páginas menos que Noah. Noah leyó 27 páginas” // “Jada read 10 fewer pages than Noah. Noah read 27 pages.”
• “De todas las cosas que hay en esta historia, ¿cuáles podemos contar?” // “What are all the things we can count in
this story?” (We could count the pages Jada read, the books, the pages they read together.)
• 30 seconds: quiet think time
• 2 minutes: partner discussion
• Share and record all quantities.
• Reveal the question(s)
• 3rd read: Read the entire problem, including the question, aloud.
• “¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?” (We could make a tape diagram. We could write equations.)
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion

### Activity

• “Hoy van a resolver problemas con su pareja. Muestren cómo pensaron. Usen dibujos, números, palabras o una ecuación” // “Today, you’re going to solve problems with your partner. Show your thinking using drawings, numbers, words, or an equation.”
• “Recuerden hacerse preguntas mientras le dan sentido al problema y hacen representaciones” // “Remember to ask yourselves questions as you make sense of the problem and create representations.”
• 12 minutes: partner work time
• As students work, monitor for different representations to share during the synthesis:
• tape diagrams
• equations
• other labeled drawings or diagrams.

### Student Facing

1. Jada leyó 10 páginas menos que Noah. Noah leyó 27 páginas. ¿Cuántas páginas leyó Jada?
2. Noah duró 25 minutos leyendo. Jada duró 30 minutos más que Noah leyendo. ¿Cuántos minutos duró Jada leyendo?
3. Jada leyó 47 páginas del libro. Noah leyó 20 páginas del libro. ¿Cuántas páginas menos leyó Noah?
4. Noah apiló 14 libros más que Jada. Jada apiló 28 libros. ¿Cuántos libros apiló Noah?

### Activity Synthesis

• Display student work that shows different ways to represent how many more minutes Jada spent reading.
• “¿En qué se parecen estas representaciones? ¿En qué son diferentes?” // “What’s the same about their representations? What’s different?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• “¿Cómo les ayudó su representación a decidir si sumar o restar?” // “How did your representation help you decide whether to add or subtract?”
• If time, discuss computation strategies:
• adding and subtracting tens with tens (problems 2 and 3)
• decompose to make a ten (problem 4)

## Lesson Synthesis

### Lesson Synthesis

“Hoy le dimos sentido a muchos problemas de comparación y los resolvimos. ¿Qué hicieron para saber cómo resolver estos problemas?” // “Today we made sense of and solved many Compare problems. What did you do to figure out how to solve these problems?” (Read the problem carefully and several times to figure out who did more, who did less, and the difference. Made a diagram to show all of the information.)

Share and record strategies for all to see.

## Student Section Summary

### Student Facing

En esta sección de la unidad 1, aprendimos a representar y a resolver problemas de comparación. Primero usamos gráficas de barras para encontrar la diferencia entre dos categorías.

¿Cuántos estudiantes más tienen gatos que conejos? Muestra dos formas de encontrar la diferencia.

Aprendimos una nueva representación llamada “diagrama“. Esta nos ayuda a dar sentido a los problemas-historia. Podemos usar diagramas para mostrar qué parte de una comparación debemos encontrar.

Jada leyó 47 páginas del libro. Noah leyó 20 páginas del libro. ¿Cuántas páginas menos leyó Noah?

En este problema vamos a encontrar la diferencia. Sabemos cuántas páginas leyeron Noah y Jada, así que el ? representa la diferencia.