# Lesson 1

¿Cómo componemos una centena?

## Warm-up: Conteo grupal: Contemos más allá de 100 (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting from 90 to 120 by 1 and notice patterns in the count. In this unit, students learn to identify the value of digits, as they write three-digit numbers through 999. In grade 1, students counted beyond 100, but did not consider a hundred as a unit and did not explore the value of each digit by place through the hundreds. Students notice and describe the repeating patterns within the base-ten system (MP7, MP8).

### Launch

• “Contemos de 1 en 1, empezando en 90” // “Count by 1, starting at 90.”
• Record as students count. Record 10 numbers in each row. Then start a new row directly below.
• Stop counting and recording at 120.

### Activity

• “¿Qué patrones ven?” // “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Activity Synthesis

• “¿Cuál número podríamos poner en la cuarta fila?” // “What is a number we could place in the fourth row? Use a pattern we discussed to explain how you know your number would belong.” (You could put 122 in the group with 92, 102, and 112. The ones place has a 2, it is getting bigger by 10, and I think the 1 should stay the same like in 102 and 112.)

## Activity 1: ¿Cómo formamos una centena? (20 minutes)

### Narrative

The purpose of this activity is to introduce students to a new unit, the hundred. Students used connecting cubes to make tens in grade 1 and used tens and ones to count to and represent numbers within 120.

In an earlier unit, students were introduced to base-ten blocks and used base-ten diagrams to represent sums and differences within 100. Students build on this understanding as they use blocks to represent a starting number (96) and add ones until they reach a total value of 100. As students discover they have 10 tens, monitor for language they use to describe the total value of the blocks and the connections they make to their previous work with ones, tens, and three-digit numbers (MP7).

Engagement: Provide Access by Recruiting Interest. Give the students a context to connect to their own lives. Tell the students that the base-ten blocks represent gum. The ones are single sticks of gum and the tens are packs of gum.
Supports accessibility for: Conceptual Processing, Attention

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Display photo of 8 tens and 16 ones.
• “Andre estaba usando bloques en base diez para representar números. ¿Cuántos ven? ¿Cómo lo saben?, ¿qué ven?” // “Andre was using base-ten blocks to represent numbers. How many do you see? How do you see them?” (96. I see 8 tens and 16 ones. I see it as 9 tens and 6 ones.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “Con un compañero, hagan lo que Andre hizo y vean lo que él descubrió a medida que agregaba más bloques” // “Work with a partner to follow along and see what Andre discovered as he adds more blocks.”
• 10 minutes: partner work time
• Monitor for students who explain that the value is 100 by:
• counting by 1 from 80 or by 1 from 96
• counting by 10

### Student Facing

1. ¿Cuántos ves? ¿Cómo lo sabes?, ¿qué ves?
2. Andre agregó más bloques.
1. ¿Cuál es el valor de los bloques de Andre ahora?
2. ¿Cuántas decenas y unidades hay en este número?
3. Andre hizo el mismo número, pero usó el menor número posible de bloques. Dibuja un diagrama en base diez para mostrar cómo se ve el número de Andre ahora. Usa tus bloques en base diez como ayuda.

### Student Response

If students represent 100 with a diagram that includes tens and ones, consider asking:

• “En el diagrama en el que representas el valor total de Andre, ¿puedes explicar de qué manera se usa el menor número posible de bloques?” // “Can you explain how your diagram represents Andre’s total value using the fewest number of blocks possible?”
• “¿Hay alguna manera de representar la misma cantidad sin usar unidades?” // “Is there a way to represent the same amount without any ones?”

### Activity Synthesis

• Invite previously identified students to share how they know the value of Andre’s blocks is 100.
• “Si Andre usó el menor número posible de bloques, ¿cuántas decenas usó?” // “If Andre used the fewest number of blocks, how many tens did he use?” (He had 10 tens.)
• “Si Andre quisiera usar la mayor cantidad posible de bloques para mostrar este número, ¿qué haría?” // “What if Andre wanted to use the greatest amount of blocks to show this number? What would he do?” (He’d decompose all the tens to use only ones. He’d use 100 ones.)
• “En esta actividad, ustedes mostraron que saben que 10 unidades es lo mismo que 1 decena. De la misma manera que 10 unidades es lo mismo que 1 decena, 10 decenas es lo mismo que 1 centena” // “In this activity, you showed you know that 10 ones is the same as 1 ten. Just like 10 ones is the same as 1 ten, 10 tens is the same as 1 hundred.”
• “Una centena es una unidad en base diez que está formada por 10 decenas” // “A hundred is a unit that is made up of 10 tens.”

## Activity 2: Distintas formas de ver el 100 (15 minutes)

### Narrative

The purpose of this activity is for students to make sense of 100 when represented as 100 ones, 10 tens, or 1 unit of a hundred with base-ten blocks or base-ten diagrams. Students compare different ways to describe 100 and connect the descriptions to base-ten diagrams (MP7). Students understand that a hundred is made up of 10 tens and can also be thought of as a unit of 100 ones.

MLR8 Discussion Supports. As students explain their reasoning for each match to their partner, display the following sentence frames for all to see: “Observé _____, entonces emparejé . . .” // “I noticed _____, so I matched . . . .” Encourage students to challenge each other when they disagree.

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 students needs access to at least 1 hundred block.

### Launch

• Groups of 2
• Gives students access to base-ten blocks including at least 1 block that represents 100.
• “En la actividad anterior, vimos que podemos usar 10 decenas para representar 100” // “In the last activity, we saw that we can use 10 tens to represent 100.”
• “Hay un bloque en base diez que representa la unidad de cien. La unidad de cien también la llamamos centena” // “There is a base-ten block that represents the unit of a hundred.”
• Display a tens block.
• “Usamos este bloque para representar una decena” // “We use this block to represent a ten.”
• Display a hundred block.
• “Podemos usar este bloque para representar una centena” // “We can use this block to represent a hundred.”

### Activity

• “En esta actividad, piensen en las diferentes formas de describir 100 y emparejen a los estudiantes con sus diagramas” // “In this activity, think about the different ways to describe 100 and match the students to their diagrams.”
• 5 minutes: independent work time
• “Compartan sus parejas con su compañero y expliquen cómo supieron que las parejas correspondían” // “Share your matches with your partner and explain how you knew.”
• 3 minutes: partner discussion
• “Ahora usen sus bloques para mostrar $$100 + 11$$” // “Now use your blocks to show $$100 + 11$$.”
• 2 minutes: partner work time
• Monitor for students who represent 100 with 1 hundred block and students who represent 100 with tens.

### Student Facing

1. Empareja los diagramas con las afirmaciones. Marca cada diagrama con las letras A, B o C. Prepárate para explicar las parejas que formaste.

1. Priya dijo: “Veo 100 unidades”.
2. Kiran dijo: “Veo 10 decenas”.
3. Lin dijo: “Veo 1 centena”.

____________

____________

____________

2. Representa $$100 + 11$$ usando bloques o un diagrama.

### Student Response

If students match the diagrams to statements that are not the best match, consider asking:

• “¿Cómo decidiste cuál afirmación correspondía a cada diagrama?” // “How did you decide which statement matched each diagram?”
• “¿En qué se parecen o en qué son diferentes estos diagramas?” // “What is the same or different about these diagrams?”

### Activity Synthesis

• “¿Cómo supieron cuál diagrama mostraba la manera en que Lin vio los bloques?” // “How did you know which diagram showed the way Lin saw the blocks?” (Lin said she saw 1 hundred, so she was thinking about the whole thing as a unit.)
• Invite previously identified students to share how they represented $$100 + 11$$.
• “¿De qué manera pueden representar el 100 de la expresión con el menor número posible de bloques?” // “How could you represent the 100 in the expression with the fewest blocks?” (I could use 1 hundred block.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos sobre una unidad en base diez llamada ‘centena’. Kiran, Lin y Priya describieron 100 de distintas formas” // “Today we learned about a unit called a hundred. Kiran, Lin, and Priya described 100 in different ways.”

Display the base-ten diagrams from the previous activity as students share to reinforce the description.

“Completen las siguientes afirmaciones con su compañero” // “Complete the following statements with your partner.”

Display:

“_____ unidades es lo mismo que una centena” // “_____ ones is the same as one hundred.”

“_____ decenas es lo mismo que una centena” // “_____ tens is the same as one hundred.”

Share and record responses.