# Lesson 2

Encontremos el sumando desconocido

## Warm-up: Conteo grupal: Contar hacia atrás de 10 en 10 (10 minutes)

### Narrative

The purpose of this Choral Count is to invite students to practice counting by 10 and notice patterns in the count. As students make sense of patterns in the way that this choral count is recorded, they may notice and explain patterns in the way the tens place changes in the numbers arranged in rows (MP7). For example, students may notice that the numbers across each row change by 2 tens and change by 5 tens in each column. The counting practice and conversations in this activity helps students develop fluency and will be helpful later in this lesson when students will need to use or make sense of computation methods based on place value or counting by 10.

### Launch

• “Cuenten hacia atrás de 10 en 10, empezando en 97” // “Count back by 10, starting at 97.”
• Record as students count.

97     87     77     67     57

47     37     27     17       7

• Stop counting and recording at 7.

### Activity

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

### Student Response

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### Activity Synthesis

• “¿Quién puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
• “¿Alguien quiere compartir otra observación sobre por qué ocurre ese patrón aquí?” // “Does anyone want to add an observation on why that pattern is happening here?”
• “¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”

## Activity 1: ¿Cómo lo encontraste? (20 minutes)

### Narrative

The purpose of this activity is for students to find the unknown addend in an equation in a way that makes sense to them and compare their methods. In the launch, students are introduced to base-ten blocks and compare them to connecting cubes. During the launch, students should be given time to observe the image and touch the connecting cubes and base-ten blocks.

Students may find the unknown addend using any method that makes sense to them. Monitor and select students with the following methods to share in the synthesis:

• count on or count back using connecting cubes or base-ten blocks
• use base-ten blocks to show combining or separating tens and ones
• use base-ten drawings to show combining or separating tens and ones

Students have the opportunity in the activity and the activity synthesis to consider the available tools and make a choice that best helps them find the unknown addend (MP5). To support student reflection on the utility of each tool, provide each group with towers of ten connecting cubes, but not enough to represent the numbers in the equation without needing to create new towers of ten.

MLR8 Discussion Supports. When groups compare methods, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “Te escuché decir . . .” //  “I heard you say . . . .” Original speakers can agree or clarify for their partner.
Advances: Listening, Speaking

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 90–100 connecting cubes, but no more than 35 towers of 10 cubes should be included in their collection. Break apart any extra towers for this activity.

### Launch

• Groups of 2
• Give each group towers of 10, single connecting cubes, and base-ten blocks.
• Display the image.
• “Cada grupo tiene algunos cubos encajables y algunos bloques en base diez” // “Each group has some connecting cubes and some base-ten blocks.”
• “¿En qué se parecen y en qué son diferentes estas herramientas?” // “What is the same and what is different between these tools?” (They both are cubes or towers of cubes. The connecting cubes are in towers of 10, single cubes, and some are in towers of different sizes. The blocks are only in tens and ones. The blocks in tens do not come apart.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “Juntos, encuentren el número que hace que la ecuación sea verdadera. Pueden usar cubos encajables, bloques en base diez u otras representaciones para encontrar el número o para mostrar cómo pensaron. Prepárense para explicar cómo pensaron” // “Work together to find the number that makes the equation true. You can use the connecting cubes, base-ten blocks, or other representations to help find the number or show your thinking. Be prepared to explain your thinking.”
• 6 minutes: partner work time
• As students work, consider asking:
• “¿Por qué escogieron esta herramienta?” // “Why did you choose this tool?”
• “¿Cómo encontraron el número que hace que la ecuación sea verdadera?” // “How did you find the number that makes the equation true?”
• “¿Cómo más podrían usar esta herramienta para encontrar el número desconocido?” // “What is another way you could use this tool to find the unknown number?”
• “Ahora comparen su método con el de otro grupo. ¿En qué se parecen sus métodos? ¿En qué son diferentes?” // “Now compare your method with another group. How are your methods the same? How are they different?”
• 2 minutes: group discussion

### Student Facing

1. ¿En qué se parecen y en qué son diferentes estas herramientas?

2. Encuentra el número que hace que la ecuación sea verdadera. Muestra cómo pensaste. Usa cubos, bloques o dibujos.

$$41 + \underline{\phantom{\hspace{1.05cm}}}=84$$

### Student Response

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### Activity Synthesis

• Invite previously identified groups to share their methods in the given order.
• Consider asking:
• “¿Por qué escogieron esta herramienta como ayuda para encontrar el número?” // “Why did you choose this tool to help you find the number?”
• “¿En qué se parecen los métodos? ¿En qué son diferentes?” // “How are the methods the same? How are they different?” (Some methods are the same, they just used different tools to show it. Some methods used the same tool, but are different because one group added tens and ones to find the unknown number, but another group took away tens and ones to find the unknown number.)

## Activity 2: Ve tú por allí, yo iré por allá (15 minutes)

### Narrative

The purpose of this activity is for students to find the unknown addend in an equation using addition and subtraction within 100 without composing or decomposing a ten. The synthesis focuses on which method students prefer and why. They continue to develop their understanding of the relationship between addition and subtraction as they describe and connect different methods that find the same unknown number.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. Give feedback on whether or not they are using the tools strategically and the efficiency of their strategies.
Supports accessibility for: Conceptual Processing, Language, Visual-Spatial Processing

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give access to towers of 10, single cubes, and base-ten blocks.
• Display $$17 + \underline{\phantom{\hspace{1.05cm}}}=48$$.
• “Han y Mai están usando bloques para encontrar el número que hace que esta ecuación sea verdadera. Los dos usan bloques, pero empiezan mostrando números diferentes” // “Han and Mai are using blocks to find the number that makes this equation true. Both use blocks, but they start by showing different numbers.”

### Activity

• “Juntos, muestren el método de Han y el método de Mai usando bloques en base diez” // “Work together to use the base-ten blocks to show Han’s method and Mai’s method.”
• “Después de seguir el método de Han y el método de Mai, decidan quién empieza con 21 y quién empieza con 96. Usen los bloques para encontrar el número desconocido solos" // “After you do Han’s method and Mai’s method together, decide who will start with 21 and who will start with 96. Use the blocks to find the unknown number on your own.”
• 8 minutes: partner work time

### Student Facing

Han y Mai usan bloques para encontrar el número que hace que la ecuación sea verdadera.

$$17 + \underline{\phantom{\hspace{1.05cm}}}=48$$

1. Han empieza usando bloques y muestra 17. Muestra cómo puede encontrar el número que hace que la ecuación sea verdadera.

2. Mai empieza usando bloques y muestra 48. Muestra cómo puede encontrar el número que hace que la ecuación sea verdadera.

3. Intenta esta solo. Decide con tu pareja quién empieza con 21 y quién empieza con 96.

$$21 + \underline{\phantom{\hspace{1.05cm}}}=96$$

4. Muéstrale a tu pareja cómo encontraste el número que hace que la ecuación sea verdadera.

### Student Response

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### Activity Synthesis

• “¿Cuál fue el método que más les gustó? ¿Empezar con el total y quitar, o empezar con el sumando que conocen y sumar?” // “Which method did you like best? Starting with the total and taking away or starting with the addend you know and adding on?” (I like subtracting because it’s easier for me to see what the unknown number is when I use blocks or drawings. I prefer to add on because the equation shows addition.)
• “¿Por qué encontraron el mismo número que su pareja, aunque una persona sumó y la otra persona restó?” // “Why did you and your partner find the same number even though one person added and one person subtracted?” (The amount one partner added was the same as what the other partner subtracted. When you subtract, it’s like finding the unknown addend. Addition and subtraction are related.).

## Lesson Synthesis

### Lesson Synthesis

Display:

• $$67 - 55 = \underline{\phantom{\hspace{1.05cm}}}$$
• $$55 + \underline{\phantom{\hspace{1.05cm}}}=67$$

“¿En qué se parecen estas ecuaciones? ¿En qué son diferentes?” // “How are these equations the same? How are they different?” (They are the same because the unknown number will be the same. Subtraction is like finding an unknown addend. They are different because one equation is subtraction and the other is addition.)

“¿Qué herramienta usarían para encontrar el valor que hace que cada ecuación sea verdadera? Expliquen cómo la usarían” // “What tool would you use to find the value that makes each equation true? Explain how you would use it.”

## Cool-down: Encuentra el sumando desconocido (5 minutes)

### Cool-Down

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