# Lesson 12

Sumemos y restemos decenas mentalmente (optional)

## Warm-up: Conversación numérica: Sumar y restar 10 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding and subtracting 10. These understandings help students develop fluency and will be helpful later in this lesson when students mentally add and subtract 10 from larger two-digit numbers.

### 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.

• $$3 + 10$$

• $$10 + 5$$

• $$13 - 10$$

• $$15 - 10$$

### Activity Synthesis

• “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”

## Activity 1: Conozcamos “Escribe números: Números hasta el 99 de 10 en 10” (20 minutes)

### Narrative

The purpose of this activity is for students to learn stage 2 of the Write Numbers center. Like the last stage of this center, students take turns writing the next one, two, or three numbers. The player who writes the last number on the board wins. Students may choose to count forward or backward. In this stage, students count by 10 starting at numbers other than 10.

MLR8 Discussion Supports. Revoice student ideas to demonstrate and amplify mathematical language use. For example, revoice the student statement “the first number changes” as “the number in the tens place increases by one.”

### Required Materials

Materials to Gather

Materials to Copy

• Write the Number Stage 2 Gameboard, Spanish

### Required Preparation

• Put each gameboard in a sheet protector.

### Launch

• Groups of 2
• Give each group a gameboard and a dry erase marker.
• “Vamos a aprender una nueva forma de trabajar en el centro ‘Escribe números’” // “We are going to learn a new way to do the Write Numbers center.”
• Display the gameboard.
• “Ustedes y sus parejas van a practicar la escritura de números. Como la última vez que jugamos este juego, van a completar el camino de números en el tablero de juego. Pueden decidir si empiezan con el número más pequeño y cuentan hacia adelante, o si empiezan con el número más grande y cuentan hacia atrás. En cada turno, pueden decidir si les gustaría escribir uno, dos o tres números en el tablero. Gana la persona que escriba el último número en el tablero” // “You and your partner will practice writing numbers. Just like the last time we played this game, you will fill in the number path on the gameboard. You can decide to start with the smaller number and count forward, or start with the larger number and count backward. On each turn, you can decide whether you would like to write one, two, or three numbers on the gameboard. The person who writes the last number on the board is the winner.”
• “Hoy no van a escribir todos los números de la secuencia. Van a contar de 10 en 10 y a escribir cada número que digan” // “Today you will not write every number in the sequence. You will count by ten and write each number you say.”
• Demonstrate playing one round with the students.
• “Ahora van a jugar con su pareja” // “Now you will play with your partner.”

### Activity

• 10 minutes: partner work time

### Activity Synthesis

• “¿Qué observan sobre cada número del tablero de juego?” // “What do you notice about each number on the gameboard?” (They all have the same amount of ones. The tens go up by one in each number.)

## Activity 2: Sumemos y restemos 10 (20 minutes)

### Narrative

The purpose of this activity is for students to practice adding and subtracting 10 mentally from any two-digit number. The problems are organized into two sets. In the first set, students add and subtract 10 from the same number. Students may notice a pattern and generalize that when you add or subtract 10, the number of tens increases by one or decreases by one and that the ones place does not change (MP7). In the second set, students work with a range of numbers including adding or subtracting multiple tens to develop fluency.

Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were the most useful when adding or subtracting by 10. Display the sentence frame, “La próxima vez que sume o reste 10, le prestaré atención a . . .” // “The next time I add or subtract by 10, I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing, Memory

### Launch

• Groups of 2
• “Hoy van a sumarle o restarle 10 a números de dos dígitos y a encontrar el valor que hace que cada ecuación sea verdadera. Primero, van a completar algunas ecuaciones. Cuando terminen todas las ecuaciones, van a hablar con sus parejas sobre los patrones que observaron. Después, cada uno va a escribir sobre eso” // “Today you will add or subtract 10 from two-digit numbers and find the value that makes each equation true. First, you will complete some equations. When you finish all of the equations, you will talk with your partner about the patterns you noticed, then each partner will write about it.”
• “Luego, van a completar algunas ecuaciones más, pero después de cada conjunto de ecuaciones van a hablar con su pareja sobre lo que observaron y van a escribir sobre eso” // “Then, you will complete some more equations, but after each set of equations you will talk with your partner about what you notice then write about it.”

### Activity

• 15 minutes: partner work time

### Student Facing

1. En cada caso, encuentra el número que hace que la ecuación sea verdadera.
Después, expresa lo que observaste.
1. $$67 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$67 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

2. $$39 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$39 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

3. $$52 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$52 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

4. $$75 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$75 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

5. Habla con tu pareja. ¿Qué patrones observas?

Yo observo que cuando sumo 10,

Yo observo que cuando resto 10,

2. En cada caso, encuentra el número que hace que la ecuación sea verdadera.
Después de cada conjunto de ecuaciones, expresa qué patrón observas.
1. $$67 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$67 + 10 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$67 + 10 + 10 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
Yo observo que

2. $$99 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$99 - 10 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$99 - 10 - 10 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

Yo observo que

3. $$45 + 10 + 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$45 - 10 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
$$45 + 10 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

Yo observo que

### Student Response

If students find the values of the expressions by counting on or counting back by one, consider asking:

• “¿Cómo encontraste el número que hizo que esta ecuación fuera verdadera?” // “How did you find the number to make this equation true?”
• “¿Cómo podrías usar lo que sabes sobre decenas y unidades para encontrar el número que hace que la ecuación sea verdadera?” // “How could you use what you know about tens and ones to find the number that makes the equation true?”

### Activity Synthesis

• “¿Qué patrones observaron mientras sumaban o restaban 10?” // “What patterns did you notice as you added or subtracted 10?” (Only the tens place changes. In some of the equations I was adding 2 tens or 3 tens so it was like adding tens from before. I can skip count to add or subtract tens quickly.)

## Lesson Synthesis

### Lesson Synthesis

Display 67 and 77.

“Hoy le sumamos y le restamos 10 a otros números mentalmente. ¿Qué afirmaciones pueden hacer sobre estos dos números?” // “Today we added and subtracted 10 from other numbers in our head. What statements can you make about these two numbers?” (77 is more than 67. It is 10 more than 67. 67 is 10 less than 77. They both have 7 ones.)
If needed, ask, “¿Cuánto más es 77 que 67?” // “How much more is 77 than 67?”

Display 82 and 62.

“¿Qué afirmaciones pueden hacer sobre estos dos números?” // “What statements can you make about these two numbers?” (82 is more than 62. It is 20 more than 62. 62 is less than 82. It is 20 less than 82.)