# Lesson 7

Restemos dos dígitos

## Warm-up: Cuántos ves: Componer una decena (10 minutes)

### Narrative

The purpose of this How Many Do You See is to build on what students know about place value to make sense of visual representations of two-digit numbers. When students describe how many they see by grouping tens with tens and ones with ones or composing a ten, they show how they look for and make use of base-ten structure (MP7). This will be helpful when students use base-ten representations to compose and decompose a ten during the lesson.

### Launch

• Groups of 2
• “¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “How many do you see? How do you see them?”
• Display the image.
• 30 seconds: quiet think time

### Activity

• Display the image.
• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

### Student Facing

¿Cuántos ves? ¿Cómo lo sabes?, ¿qué ves?

### Activity Synthesis

• “¿Cuáles dos imágenes tienen el mismo valor? ¿Cómo lo saben?” // “Which two images have the same value? How do you know?”(The first image and the second image both have the same amount. The first one shows 5 tens and 5 ones. I know Image 2 is the same because I know 2 groups of 5 is the same as 1 ten. So it's the same as 5 tens and 5 ones.)

## Activity 1: ¿Cuál es la diferencia? (15 minutes)

### Narrative

The purpose of this activity is for students to subtract a two-digit number from a two-digit number in a way that makes sense to them. Students build on their understanding of decomposing a ten when subtracting a one-digit number from a two-digit number to subtract two-digit numbers. The synthesis is devoted to presenting and comparing techniques students use to find the difference, including diagrams and equations (MP3).

This activity uses MLR8 Discussion Supports. Advances: listening, speaking, conversing

Representation: Develop Language and Symbols. Synthesis: Make connections between representations visible. Ask students to verbalize the connection between the expression and the blocks.
Supports accessibility for: Visual-Spatial Processing, Language, Memory

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Encuentren el valor de cada diferencia y compartan con su pareja su método y su solución” // “Find the value of each difference and share your method and solution with your partner.”
• 7 minutes: independent work time

MLR8 Discussion Supports

• “Después de que su pareja comparta su método, repítanle lo que les dijo” // “After your partner shares their method, repeat back what they told you.”
• Display the sentence frames:
• “Te escuché decir . . .” // “I heard you say . . . .”
• “Nuestros métodos se parecen porque . . .” // “Our methods are alike because . . . .”
• “Nuestros métodos son diferentes porque . . .” // “Our methods are different because . . .”
• 5 minutes: partner discussion
• Monitor for students who use base-ten blocks to show decomposing a ten.

### Student Facing

Encuentra el valor de cada diferencia. Muestra cómo pensaste. Si te ayuda, usa bloques.

1. $$46 - 28 =\underline{\phantom{\hspace{1.05cm}}}$$
2. $$93 - 54 =\underline{\phantom{\hspace{1.05cm}}}$$

### Student Response

Some students may not use base-ten blocks to find the difference. Prompt them to show their thinking in a way that could help others understand. Ask them to write expressions to show the steps they took when appropriate. Consider asking:

• “¿Cómo encontraste el valor de la diferencia?” // “How did you find the value of the difference?”
• “¿Qué podrías agregar a tu diagrama para ayudarle a tu pareja a entender lo que hiciste?” // “What could you add to your diagram to help your partner understand what you did?”
• “¿Cómo podrías usar ecuaciones para mostrar los pasos que seguiste?” // “How could you use equations to show the steps you used?”

### Activity Synthesis

• Invite previously identified students to share.
• “¿Qué hizo _____ para resolver el problema? ¿Cómo podemos anotar eso?” // “What did _____ do to solve the problem? How can we record it?”
• 30 seconds: quiet think time
• Share responses.
• Show how to represent solving with base-ten blocks with drawings and equations.
• “¿En qué se parecen estas representaciones a la forma como _____ usó bloques en base diez para encontrar el valor de la diferencia? ¿En qué son diferentes?” // “How are these representations like the way _____ used base-ten blocks to find the value of the difference? How are they different?”

## Activity 2: Usemos bloques para quitar (20 minutes)

### Narrative

The purpose of this activity is for students to subtract a two-digit number from a two-digit number. In the first activity, students used any method that made sense to them to find the difference. In this activity, they use base-ten blocks to represent the starting number and subtract amounts that require a ten to be decomposed.

### Required Materials

Materials to Gather

Materials to Copy

• Using Blocks to Take Away, Spanish

### Required Preparation

• Create a set of cards from the blackline master for each group of 4.

### Launch

• Groups of 4
• Give each group a set of cards and access to base-ten blocks.

### Activity

• “Ahora van a jugar un juego de tarjetas usando bloques en base diez” // “Now you are going to play a card game using base-ten blocks.”
• “Primero, cada miembro de su grupo va a escoger una tarjeta diferente de jugador: Diego, Lin, Jada o Han” // “First, each member of your group will choose a different player card, Diego, Lin, Jada, or Han.”
• “Escriban el nombre que escogieron. Revuelvan las otras tarjetas y pónganlas boca abajo” // “Write down the name you picked. Mix up the other cards and put them face down.”
• “Ahora cada uno tiene un jugador y un número inicial” // “Now you each have a player and your starting number.”
• “Usen los bloques para representar sus números iniciales” // “Use the blocks to represent your starting numbers.”
• 2 minutes: group work
• Guide students through the rest of the steps:
• “Por turnos, tomen una tarjeta y lean la tarjeta al grupo” //“Take turns picking a card and read the card to the group.”
• “Van a escuchar el nombre de su jugador. Cuando lo escuchen, sigan las instrucciones de la tarjeta” // “Listen for your player’s name and follow the directions on the card.”
• “Compartan lo que pensaron mientras los miembros de su grupo escuchan. Escriban una ecuación para mostrar el nuevo número” // “Share your thinking while your group members listen. Write an equation to show the new number.”
• “Antes de tomar una nueva tarjeta, asegúrense de trabajar en grupo y estar de acuerdo en el nuevo número” // “Before picking a new card, make sure your group works together to agree on the new number.”
• “Van a jugar hasta que hayan leído todas las tarjetas. El número de su jugador debe cambiar dos veces” // “You will keep playing until all of the cards have been read. Your player‘s number should change two times.”
• 15 minutes: group work time
• Monitor for students who:
• discuss decomposing a ten using precise language
• work together to give feedback and resolve any disagreements
• compose tens when adding the ending numbers

### Student Facing

1. Escoge una tarjeta de jugador. Revuelve las otras tarjetas y ponlas boca abajo.

2. Representa tu número inicial con bloques en base diez.

Número inicial: ____________________________

3. Juega por turnos para tomar una tarjeta. Lee la tarjeta al grupo.
4. Vas a escuchar el nombre de tu jugador. Cuando lo escuches, usa los bloques para mostrar el cambio.
5. Explícale a tu grupo lo que pensaste.
6. Escribe una ecuación para mostrar el nuevo número.

Ecuación 1: ________________________________

Ecuación 2: ________________________________

Número final: _____________________________

Comparte este número con tu grupo.

7. Escribe una ecuación para mostrar la suma de los números finales de tu grupo.

### Activity Synthesis

• Invite 12 previously identified students to share with their group.
• “¿Qué preguntas le quieren hacer a __ sobre el método que usó?” // "What questions do you have for __ about their method?"
• “¿En qué se parece este método a la forma como ustedes encontraron los nuevos números de su jugador? ¿En qué es diferente?” // "How was their method the same as how you found your player's new numbers? How was it different?"

## Lesson Synthesis

### Lesson Synthesis

“Hoy usaron varios métodos para restar 2 números de dos dígitos” // “Today you used different methods to subtract 2 two-digit numbers.”

“Resolvieron restas de formas que tienen sentido para ustedes y usaron bloques en base diez para quitar distintas cantidades” // “You solved in ways that make sense to you and you used base-ten blocks to take away different amounts.”

“¿En qué se parecieron restarle un número de dos dígitos a un número de dos dígitos y restarle un número de un dígito a un número de dos dígitos?” // “How was subtracting a two-digit number from a two-digit number the same as subtracting a one-digit number from a two-digit number?" (It was the same because we still had to think about subtracting ones. Sometimes you have to decompose a ten if you need more ones.)

“¿En qué fueron diferentes?” // "How was it different?" (When you subtract a two-digit number, you have to think about subtracting tens too. The number you are subtracting is bigger because it's a two-digit number.)

“¿Cómo les ayudó trabajar con un compañero o un grupo a entender distintas maneras de restar números de dos dígitos?” // "How did working together with a partner or a group help you understand different ways to subtract two-digit numbers?"

Math Community

“En el juego de tarjetas tuvieron que trabajar juntos. ¿De qué formas trabajaron juntos en su grupo?” // “The card game required you all to work together. What are some ways your group worked together?” (We helped each other with keeping track of the blocks. We talked about our thinking. We helped each other if someone was stuck or confused.)