# Lesson 15

Conversación numérica

## Warm-up: Conversación numérica: Suma (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 1,000. These understandings help students develop fluency and will be helpful when students create their own Number Talk activities.

In the synthesis, discuss what students know about Number Talks and what they need to think about to create one like this example.

### Launch

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$300 + 400$$
• $$300 + 437$$
• $$321 + 437$$
• $$425 + 514$$

### Activity Synthesis

• “¿Qué saben sobre las actividades tipo ‘Conversación numérica’?” // “What do you know about Number Talks?” (They always have four expressions and we find their values in our head. Sometimes we can use the same method for each expression. Sometimes we can use the first couple of expressions to help us find the value of other expressions.)
• Consider asking: “¿En qué tendrían que pensar si fueran a diseñar una actividad tipo ‘Conversación numérica’ como esta?” // “What would you have to think about if you were going to design a Number Talk like this one?” (How one expression might relate to the next. What strategies might make it possible for someone to find the value mentally. Whether it's possible to use one expression to find the value of other expressions.)
• Record and display responses for all to see.

## Activity 1: Conversación numérica: Diseño 1 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about subtraction and write another subtraction expression to complete a partially-completed Number Talk activity. If there is time, students can facilitate their Number Talk with another group. Students are given three expressions and prompted to think of ways that they could be evaluated mentally. They then write a fourth expression in which similar reasoning could be used, or by making use of the first three expressions.

MLR8 Discussion Supports. Synthesis: Create a visual display of the task. As students share their expression, annotate the display with the expression and its connection to the third expression in the Number Talk. For example, if students share $$500 - 299$$, write “100 menos que 399” // “100 less than 399” next to the expression.

### Launch

• Groups of 2 - 4
• “Estas son tres expresiones como las que podríamos ver en una actividad tipo ‘Conversación numérica’” // “Here are three expressions like the kinds you might see in a Number Talk.”

### Activity

• “¿Cómo encontrarían el valor de cada expresión, sin escribir? Piensen en al menos dos maneras de hacerlo para cada expresión. Después, compartan con su grupo cómo pensaron” // “How would you find the value of each expression, without writing? For each expression, think of at least two ways. Then, share your thinking with your group.”
• Reiterate to students that they are to consider how someone might reason about each difference, rather than only finding the value.
• 4 minutes: independent work time
• 4 minutes: small-group discussion
• “Escriban una expresión que, junto con las otras tres, pueda completar una actividad tipo ‘Conversación numérica’” // “Write one more expression that could go with the other three expressions and would complete a Number Talk activity.”
• 4 minutes: small-group work time
• Monitor for groups who consider the following strategies in writing their expression:
• adjust the 399 to a different number, but keep the 500
• leave the 399, but adjust the 500
• adjust both the 500 and the 399, but create a problem that can be reasoned as in previous expressions
• Identify groups who chose different strategies to share in the synthesis.

### Student Facing

Estas son tres expresiones de resta.

• $$600 - 400$$
• $$600 - 399$$
• $$500 - 399$$
• $$\underline{\hspace{2.5in}}$$
1. Piensa en al menos dos maneras diferentes de encontrar mentalmente el valor de cada diferencia.
2. Escribe una cuarta expresión de resta que tenga un valor que se pueda encontrar usando una de las estrategias que pensaste.

### Activity Synthesis

• Select groups to share their last expression and their reasoning.
• As each group shares, ask others in the class if they had used the same strategy to write their expression and if they arrived at a similar expression.

## Activity 2: Conversación numérica: Diseño 2 (15 minutes)

### Narrative

The purpose of this activity is for students to reason about addition and apply their reasoning to complete a partially-completed Number Talk activity. This time, students are given addition expressions and are asked to think about how the value of the sums could be found mentally. They then write two new addition expressions to complete the set.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

### Launch

• Groups of 2 - 4
• “Estas son dos expresiones como las que podríamos ver en una actividad tipo ‘Conversación numérica’” // “Here are two expressions like the kinds you might see in a Number Talk.”

### Activity

• “¿Cómo encontrarían el valor de cada expresión, sin escribir? Piensen en al menos dos maneras de hacerlo para cada expresión. Después, compartan con su grupo cómo pensaron” // “How would you find the value of each expression, without writing? For each expression, think of at least two ways. Then, share your thinking with your group.”
• Reiterate to students that they are to consider how someone might reason about each sum, rather than only finding the value.
• 3 minutes: independent work time
• 3 minutes: small-group discussion
• “Escriban otras dos expresiones que, junto con las otras dos, puedan completar una actividad tipo ‘Conversación numérica’” // “Write two more expressions that could go with the other two expressions and would complete a Number Talk activity.”
• 5 minutes: small-group work time
• Monitor for groups who consider the following strategies in writing their expression:
• adjust the 504 to a different number, but keep the 199
• leave the 504, but adjust the 199
• adjust the 504 and the 199, but create a problem that can be reasoned as in previous expressions
• Identify groups who chose different strategies to share in the synthesis.

### Student Facing

Estas son dos expresiones de suma.

• $$500 + 199$$
• $$504 + 199$$
• $$\underline{\hspace{2.5in}}$$
• $$\underline{\hspace{2.5in}}$$
1. Piensa en al menos dos maneras diferentes de encontrar mentalmente el valor de cada suma.
2. Escribe otras dos expresiones de suma que tengan un valor que se pueda encontrar usando las estrategias que pensaste.

### Activity Synthesis

• Select groups to share their two expressions and their reasoning.
• As each group shares, ask others in the class if they had used the same strategy to write their expressions and if they arrived at similar expressions.

## Activity 3: Conversación numérica: Diseño 3 (15 minutes)

### Narrative

The purpose of this activity is for students to write a sequence of three subtraction expressions to complete a Number Talk with only one given expression. As in earlier activities, students consider strategies that they or others might use to mentally subtract numbers within 1,000.

### Launch

• Groups of 2 - 4
• “En grupo, completen una actividad tipo ‘Conversación numérica’ con las tres expresiones que faltan. Escríbanlas en las tres líneas” // “Work with your group to complete a Number Talk with three expressions missing. Write them in the blank lines.”

### Activity

• 10 minutes: small-group work time
• Monitor for groups who:
• adjust the 900 or 400 to emphasize a certain subtraction strategy
• make slight adjustments in each expression but promote the same reasoning strategy throughout
• Identify groups who choose different strategies to share in the synthesis.

### Student Facing

Escriban tres expresiones de resta para completar la actividad tipo “Conversación numérica”.

• $$900 - 400$$
• $$\underline{\hspace{2.5in}}$$
• $$\underline{\hspace{2.5in}}$$
• $$\underline{\hspace{2.5in}}$$

### Activity Synthesis

• Select groups to share their completed Number Talk and ask the class how the groups might have chosen the expressions.

## Activity 4: Conversación numérica: Diseño 4 (15 minutes)

### Narrative

The purpose of this activity is for students to design a Number Talk from a blank slate. They can choose to write addition or subtraction expressions, but still consider possible ways that others might find the value of the expressions mentally. If there is time, allow students to facilitate their Number Talk with another group.

### Launch

• Groups of 1 - 4
• “Individualmente o en grupo, creen una actividad tipo ‘Conversación numérica’. Pueden escoger si escriben expresiones de suma o expresiones de resta” // “Work independently or with your group to create a Number Talk activity. You can decide whether to write addition or subtraction expressions.”

### Activity

• 10 minutes: independent or small-group work time
• Monitor for groups who design their expressions based on certain strategies for subtracting numbers mentally, such as:
• adding hundreds to hundreds, tens to tens, and ones to ones
• relating to benchmarks such as multiples of 100 or 10

### Student Facing

Escribe cuatro expresiones de suma o de resta para crear una actividad tipo “Conversación numérica”.

• $$\underline{\hspace{2.5in}}$$
• $$\underline{\hspace{2.5in}}$$
• $$\underline{\hspace{2.5in}}$$
• $$\underline{\hspace{2.5in}}$$

### Activity Synthesis

• Invite 1–2 groups to share their completed Number Talk or to facilitate it for the class.
• Alternatively, if time permits, allow groups to take turns facilitating their Number Talk with another group.

## Lesson Synthesis

### Lesson Synthesis

“¿Qué cosas importantes tuvieron en cuenta cuando crearon expresiones para su actividad tipo ‘Conversación numérica’? ¿Por qué fueron importantes estas cosas?” // “What were some important things you considered as you created expressions for your Number Talk? Why were these things important?” (I thought about what method I wanted other students to think about, because this helped me think about which expressions to write. I thought about how one problem was related to the next, to make sure the Number Talk made sense.)