# Lesson 17

Sumemos 0 y 1

## Warm-up: Observa y pregúntate: Sumar 1 más (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that adding 1 results in the next number in the count sequence, which will be useful when students find the value of expressions with $$+ 1$$ in a later activity. While students may notice and wonder many things about these towers, 1 more being added to each tower and how that affects the total number of cubes are the important discussion points.

### Launch

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas?
¿Qué te preguntas?

### Activity Synthesis

• Point to the tower with 2 cubes and then to the tower with 3 cubes while saying “¿Qué cambió de esta torre a esta otra torre?” // “What changed from this tower to this tower?” (There are still 2 blue cubes, but 1 more yellow cube was put on top.)
• Point to the tower with 2 cubes and then to the tower with 3 cubes while saying “¿Qué expresión podemos escribir para mostrar lo que cambió de esta torre a esta otra torre?” // “What expression can we write to show what changed from this tower to this tower?” ($$2 + 1$$)
• “¿Cuántos cubos piensan que hay en la última torre? ¿Cómo lo saben?” // “How many cubes do you think are in the last tower? How do you know?” (5. I counted them. I know that there is 1 more than the last tower, and 5 is one more than 4.)

## Activity 1: Sumemos 0 y 1 (10 minutes)

### Narrative

The purpose of this activity is to find the value of addition expressions with $$+ 0$$ and $$+ 1$$. Students may connect adding 1 to getting the next number in the counting sequence and will likely observe that adding 0 does not change the number (MP7). These connections will be highlighted in the next activity.

### Required Materials

Materials to Gather

Materials to Copy

• Add 0 and 1 Mat

### Required Preparation

• Each group of 2 needs 1 connecting cube.

### Launch

• Groups of 2
• Display a tower of 3 connecting cubes:
• “Mai tiene una torre de 3 cubos. Mai quiere agregarle 0 cubos a la torre. ¿Qué debe hacer Mai?” // “Mai has a tower with 3 cubes. Mai wants to add 0 cubes to the tower. What should Mai do?” (Nothing. When you add 0, you don’t add anything.)
• 30 seconds: quiet think time
• Share responses.
• Give each group of students a copy of the blackline master and a connecting cube. Give students access to connecting cubes and two-color counters.
• “Tomen turnos con su compañero. Lancen el cubo para descubrir si necesitan sumar 0 o 1. Completen la expresión” // “Take turns with your partner. Roll the cube to figure out if you need to add 0 or 1. Fill in the expression.”
• “Encuentren el valor de la expresión y escriban el número sobre la línea. Si les ayuda, usen objetos o dibujos” // “Find the value of the expression and write the number on the line. You can use objects or drawings if they are helpful.”

### Activity

• 5 minutes: partner work time

### Student Facing

$$4 + \underline{\hspace{1 cm}}$$

$$2 + \underline{\hspace{1 cm}}$$

$$8 + \underline{\hspace{1 cm}}$$

$$3 + \underline{\hspace{1 cm}}$$

$$9 + \underline{\hspace{1 cm}}$$

$$1 + \underline{\hspace{1 cm}}$$

### Activity Synthesis

• “En la siguiente actividad, vamos a examinar las expresiones que escribió un grupo para ver si podemos reconocer algunos patrones” // “In the next activity we will look at the expressions that one group wrote to see if we can notice any patterns.”

## Activity 2: Observemos patrones con + 0 y + 1 (10 minutes)

### Narrative

The purpose of this activity is to notice the pattern that when 0 is added to a number, the number stays the same and the pattern that when 1 is added to a number, the total is the next number in the count sequence, or 1 more (MP7).

MLR2 Collect and Display. Collect the language students use to describe what they notice about the value of the expressions when 0 and 1 are added. Display phrases such as: “Cuando sumamos 0, el total es el mismo número con el que empezamos porque nada se agregó” // “When we add 0, the total is the same number that we started with, because nothing was added.” During the synthesis, invite students to borrow language from the display as needed.
Representation: Internalize Comprehension. Synthesis: Some students may benefit from reiterating the patterns of adding zero and adding one. Make a connection between the two patterns students should notice. For example, “Cuando suman cero a cualquier número, obtienen el mismo número porque sumar cero es agregar nada” // “When you add zero to any number you get the same number because adding zero is adding nothing”, “Cuando le suman uno a cualquier número, el total es el siguiente número de la secuencia de conteo, o en otras palabras, uno más” // “When you add one to any number the total is the next number in the count sequence, or one more.”
Supports accessibility for: Conceptual Processing, Organization

### Launch

• Groups of 2
• Display student book
• “Diego y Mai escribieron sus expresiones de suma y los valores de las expresiones en esta página. ¿Qué observan? ¿Qué se preguntan?” // “Diego and Mai recorded their addition expressions and their values on this page. What do you notice? What do you wonder?” (They always added 1 or 0. Sometimes the first and last number are the same.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.

### Activity

• “¿Cuáles expresiones muestran que sumaron 0?” // “Which expressions show that 0 were added?” ($$4 + 0$$, $$2 + 0$$, and $$8 + 0$$)
• 30 seconds: quiet think time
• Share responses. Highlight or circle the expressions that show $$+ 0$$.
• “Cuando jugaron el juego, ¿qué hicieron cuando tenían que sumar 0?” // “When you played the game, what did you do when you had to add 0?” (Nothing. Zero means none so none were added.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “¿Qué observan en el valor de las expresiones cuando suman 0?” // “What do you notice about the value of the expressions when 0 are added?” (It stays the same.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Cuando sumamos 0, el total es el mismo número con el que empezamos porque nada se agregó” // “When we add 0, the total is the same number that we started with, because nothing was added.”
• Repeat the steps above with $$+ 1$$.

### Student Facing

$$4 + 0$$

4

$$2 + 0$$

2

$$8 + 0$$

8

$$3 + 1$$

4

$$9 + 1$$

10

$$1 + 1$$

2

### Activity Synthesis

• “¿$$3 + 0$$ es cuánto?” // $$3 + 0$$ is how many?” ($$3 + 0$$ is 3.)
• “¿$$2 + 0$$ es cuánto?” // $$2 + 0$$ is how many?” ($$2 + 0$$ is 2.)
• “¿Cómo saben que $$2 + 0$$ es 2?” // “How do you know that $$2 + 0$$ is 2?” (Because we didn’t add any more, so the 2 stayed the same.)
• Repeat with $$2 + 1$$.

## Activity 3: Conozcamos “Encuentra el valor de expresiones: Colorea el total o la diferencia” (25 minutes)

### Narrative

The purpose of this activity is for students to learn stage 1 of the Find the Value of Expressions center. Students take turns choosing an expression card and finding the value of the expression. Students may use their fingers, connecting cubes, two-color counters, or draw a picture to find the value of the expression. After they participate in the center, students choose from any stage of previously introduced centers.

• Shake and Spill
• Number Race
• Math Stories

### Required Materials

Materials to Gather

Materials to Copy

• Find the Value of Expressions within 10 Stage 1 Recording Sheet
• Find the Value of Expressions within 10 Stage 1 Cards

### Required Preparation

• Gather materials from:
• Roll and Add, Stages 1 and 2
• Shake and Spill, Stages 1-3
• Number Race, Stage 1
• Math Stories, Stages 1 and 2

### Launch

• Groups of 2
• Give each group of students a set of expression cards and access to connecting cubes and two-color counters. Give each student a recording sheet.
• “Vamos a conocer un centro llamado ‘Encuentra el valor de expresiones’. Un compañero va a escoger una tarjeta de expresión. El otro compañero va a encontrar el valor de la expresión. Cuando estén de acuerdo, coloreen el número en la hoja de registro. Tomen turnos para escoger una tarjeta de expresión” // “We are going to learn a center called Find the Value of Expressions. One partner will choose an expression card. The other partner will find the value of the expression. When you agree, color in the number on the recording sheet. Take turns choosing an expression card.”

### Activity

• 8 minutes: partner work time
• “Ahora pueden escoger otro centro. También pueden seguir jugando ‘Encuentra el valor de expresiones’” // “Now you can choose another center. You can also continue playing Find the Value of Expressions.”
• Display the center choices in the student book.
• Invite students to work at the center of their choice.
• 10 minutes: center work time
• If time, invite students to choose another center.

### Student Facing

Escoge un centro.

Encuentra el valor de
expresiones

​​​​​​

Lanza y suma

Revuelve y saca

Historias matemáticas

Carrera con números

### Activity Synthesis

• Write the number 4.
• “Elena coloreó el número 4. ¿Qué expresión piensan que estaba en su tarjeta?” // “Elena colored in the number 4. What expression do you think was on her card?” ($$2 + 2$$, $$5 - 1$$, $$3 + 1$$)

## Lesson Synthesis

### Lesson Synthesis

Write $$4 + 0$$

“¿Cómo podemos mostrar esta expresión?” // “How can we show this expression?” (We can draw 4 dots. We can hold up 4 fingers or take out 4 connecting cubes. We don’t need to add any more because 0 are added.)

Draw 4 circles.

“¿Qué expresión podemos usar para mostrar que teníamos 4 puntos y agregamos 0?” // “What expression can we use to show that we had 4 dots and we added 0?” ($$4 + 0$$)

“Si agrego 1 punto, ¿cuántos puntos tendré? ¿Cómo lo saben?” // “If I add 1 dot, how many dots will I have? How do you know?” (5. Adding one gives you the next number. 5 is one more than 4.)

“¿Qué expresión podemos usar para mostrar que teníamos 4 puntos y agregamos 1 más?” // “What expression can we use to show that we had 4 dots and we added 1 more?” ($$4 + 1$$)

## Student Section Summary

### Student Facing

En esta sección, usamos números y símbolos para mostrar cuándo se agregan cosas y cuándo las cosas se restan, o se quitan.

Asociamos expresiones con problemas-historia y dibujos.

$$8-6$$

$$2+1$$

Usamos nuestros dedos, objetos y dibujos para encontrar el valor de expresiones.

$$4 + 2$$