# Lesson 11

Sumemos decenas a números de dos dígitos

### Narrative

The purpose of this True or False is to elicit insights students have about adding two-digit numbers using place value understanding. This will be helpful later when students add a two-digit number and a multiple of 10.

### Launch

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time
Activity
• Share and record answers and strategy.
• Repeat with each equation.

### Student Facing

Prepárate para explicar tu razonamiento.

• $$80 + 5 = 5 + 80$$

• $$70 + 1 = 80 + 1$$

• $$20 + 6 = 6 + 30$$

### Activity Synthesis

• “¿Cómo pueden usar lo que saben sobre decenas y unidades para razonar sobre las ecuaciones?” // “How can you use what you know about tens and ones to reason about the equations?” (Two numbers are not equal if the number of ones is the same but the tens is different.)

## Activity 1: Sumemos decenas y números de dos dígitos (20 minutes)

### Narrative

The purpose of this activity is for students to add multiples of 10 and two-digit numbers in a way that makes sense to them. Students may use connecting cubes in towers of 10 and singles. They represent their thinking using drawings, numbers, or words. Some students may make base-ten drawings to show the addition, while others may find the sum mentally, applying what they have learned about place value in previous lessons. Some students may use both methods, depending on the numbers in the problem.

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

### Activity

• 10 minutes: partner work time
• Monitor for students who find the sum of 30 + 65 by:
• drawing and counting by ten, then one
• count on from 65 by ten: 75, 85, 95
• combine 3 tens and 6 tens, then add 5 ones

### Student Facing

En cada caso, encuentra el número que hace que la ecuación sea verdadera.
Muestra cómo pensaste. Usa dibujos, números o palabras.
1. $$37 + 20 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

2. $$60 + 23 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

3. $$48 + 50 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

4. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 54 + 20$$

5. $$30 + 65 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

### Activity Synthesis

• Invite previously identified students to share.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (They all added tens to tens. Some people started with the first number and other people started with the second number.)

## Activity 2: El dígito desconocido (15 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of place value to make an equation true when a digit in a two-digit number is “missing.” Students consider the values of the digits in order to justify their thinking. Students may use connecting cubes in towers of 10 and singles, create drawings, or write about their reasoning.

MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Action and Expression: Internalize Executive Functions. Invite students to decide with their partners what tools they will use to find the missing digit. Allow time for students to organize tools.
Supports accessibility for: Organization, Attention

### Launch

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.

### Activity

• 10 minutes: partner work time

### Student Facing

¿Qué dígito está debajo de la mancha?
Muestra cómo pensaste. Usa dibujos, números o palabras.

2. Esta ecuación no es verdadera.
Muestra por qué no es verdadera. Usa dibujos, números o palabras.

### Activity Synthesis

• Invite students to share how they determined the missing digit in the first equation.
• Invite students to share how they know the second equation cannot be true.

## Lesson Synthesis

### Lesson Synthesis

Display $$34 + 40$$.

“Hoy sumamos decenas a números de dos dígitos. ¿Qué sabemos sobre la suma de estos números?” // “Today we added tens to two-digit numbers. What do we know about adding these numbers?” (It’s like counting on by tens. You can think of it as 34 and 4 more tens. You can just add the number of tens in each number. For example, 3 tens + 4 tens is 7 tens.)

## Student Section Summary

### Student Facing

Aprendimos que los números de dos dígitos están formados por decenas y unidades.

Representamos números de dos dígitos de diferentes formas.

$$60+5$$
$$42 + 50 = \boxed{92}$$