# Lesson 23

Usemos una decena para restar

## Warm-up: Conversación numérica: Restemos para formar 10 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting. The expressions are explicitly chosen to encourage students to use their understanding of the 10 + n structure of teen numbers to subtract (MP7). This method will be discussed in more depth is this lesson's activities.

### 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.

• $$17 - 7$$
• $$17 - 7 - 1$$
• $$17 - 8$$
• $$17 - 9$$

### Activity Synthesis

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

## Activity 1: Resta con tarjetas de números y tableros de 10 (15 minutes)

### Narrative

The purpose of this activity is to play the same game from the previous lesson, with a focus on using the ten in the teen number to help find the difference. This time, all students use the double 10-frame to represent the teen number to encourage students to use a ten to help them subtract.

Students may start by taking away the ones from the teen number and then take additional ones from the 10-frame to determine the answer. Students may use a different method and take away the single digit number from the full 10-frame, then count the remaining counters across both 10-frames. Or, students may may count on from the one-digit number to the teen number. In each case, students write an equation to show the difference. Students may write subtraction equations or missing addend equations.

Action and Expression: Develop Expression and Communication. Provide students with alternatives to writing on paper: students can share their learning orally or using manipulatives.
Supports accessibility for: Language, Conceptual Processing

### Required Preparation

• Each group of 2 needs a set of Number Cards 0 - 10 and a set of Number Cards 11-20 used in a previous lesson.

### Launch

• Groups of 2
• Give each group a set of number cards 0–10, a set of number cards 11–20, double 10-frames, and connecting cubes or two-color counters.
• “Vamos a jugar el mismo juego de resta de ayer, pero esta vez van a representar sus números del 11 al 19 en el tablero de 10 doble” // “We’re going to play the same subtraction game as yesterday, but this time you will represent your teen number on the double 10-frame.”
• If needed, play a round of the game with the class, demonstrating using the double 10-frame.

### Activity

• 7 minutes: partner work time
• Monitor for students who:
• take away to 10, then take away some more
• take away from the 10, then count what is left
• “Individualmente, escojan su ronda favorita. Muestren cómo encontraron el valor de la diferencia. Usen dibujos, palabras o números” // “On your own, pick your favorite round. Show how you found the value of the difference using drawings, words, or numbers.”
• 3 minutes: independent work time

### Student Facing

1. Escoge una tarjeta de números del 11 al 19.
2. Forma el número en los tableros de 10.
3. Escoge una tarjeta de números para restar.
4. Encuentra la diferencia.
5. Escribe una ecuación.

Mis ecuaciones:

Escoge tu ecuación favorita.

Muestra cómo encontraste el valor de la diferencia. Usa dibujos, números o palabras.

### Activity Synthesis

• Invite previously identified students to share.
• “¿En qué es diferente el juego de hoy del juego de ayer?” // “How is the game different from yesterday?” (Yesterday we could solve any way we want, today we used 10-frames to build numbers and take away.)
• “¿Los tableros de 10 dobles ayudaron? ¿Por qué?” // “Did the double 10-frames help? Why?” (They helped me see how I could use 10 to take away easier.)

## Activity 2: Diego y Andre encuentran la diferencia (20 minutes)

### Narrative

The purpose of this activity is for students to analyze different take away methods used to find the difference between two numbers. During the launch, students discuss the two different methods to subtract. Then they solve two problems using one of the methods they discussed. Given the first step toward a calculation, students make sense of and then complete the calculation (MP3).

During the activity synthesis, the teacher records equations to match the method shared. It is important that each step is written as its own equation. For example, when solving $$13 - 6 = \boxed{\phantom{3}}$$, the teacher records:

• $$13 - 3 = 10$$
• $$10 - 3 = 7$$
MLR8 Discussion Supports. Invite students to begin partner interactions by repeating the question, “¿Cómo resolviste el problema?” // “How did you solve the problem?” This gives both students an opportunity to produce language.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “¿Alguna vez comenzaron a resolver un problema de matemáticas, pero tuvieron dificultades para terminar?” // “Have you ever started solving a math problem, and then had trouble finishing? Today we’re going to see some ways that students started to find the difference, and suggest ways they could finish.”
• Display the first problem with Diego's work.
• “¿Qué hizo Diego?” // “What did Diego do?” (He put 15 on his 10-frames and crossed out 5 to get to 10.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• “¿Qué podría hacer Diego la próxima vez para encontrar la diferencia?” // “What could Diego do next to find the difference?” (He already took away 5, so he needs to take 3 more away so that he subtracts 8 altogether.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Demonstrate crossing off three more.
• “¿Cuál es la diferencia?” // “What is the difference?”
• Repeat the discussion with Andre’s work. (Andre took 8 away from the full 10-frame and has 2 left. He needs to combine the 2 with the 5 in the other 10-frame to find the difference.)

### Activity

• 4 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for a student who uses and can explain each way to subtract $$14-5$$.

### Student Facing

Diego está jugando ‘Resta con tarjetas de números’.
Él comenzó con 15 y luego tomó un 8.
Empezó haciendo esto:

¿Qué puede hacer Diego ahora para encontrar la diferencia?

Andre también estaba encontrando el valor de $$1 5- 8$$.
Él empezó haciendo esto:

¿Qué puede hacer Andre ahora para encontrar la diferencia?

Encuentra el valor de cada diferencia como lo hizo Diego o como lo hizo Andre.

1. $$14 - 5$$
Muestra cómo pensaste. Usa dibujos, números o palabras.

2. $$13 - 6$$
Muestra cómo pensaste. Usa dibujos, números o palabras.

### Student Response

If students take away without using the ten, consider asking:

• “¿Puedes explicar cómo encontraste la diferencia?” // “Can you explain how you found the difference?”
• “¿Cuántas fichas quitarías para formar 10? ¿Cuántas más necesitarías quitar después?” // “How many counters would you take away to make 10? Then how many more would you need to take away?”

### Activity Synthesis

• Invite previously identified students to share.
• As each student shares, ask them to explain why they chose their method.
• “¿Alguien lo resolvió de otra forma? ¿Por qué?” // “Did anyone solve it a different way? Why?”

## Lesson Synthesis

### Lesson Synthesis

“Hoy usamos una decena como ayuda para restarle a números del 11 al 19” // “Today we used a ten to subtract from teen numbers.”

Display $$13 - 7$$.

“¿Cómo podemos usar una decena para ayudarnos a encontrar el valor de la diferencia?” // “How can we use a ten to help us find the value of the difference?” (I know that 13 is 10 and 3. I can take away the 3 and then I just have to take 4 more from 10. I know that is 6.)