# Lesson 24

Relacionemos contar con la suma y con la resta

## Warm-up: Conteo grupal: Contemos hacia atrás desde 50 (10 minutes)

### Narrative

The purpose of this Choral Count is to invite students to practice counting by one backwards and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students count back to find the value that makes the subtraction equation true.

### Launch

• “Cuenten hacia atrás de 1 en 1, empezando en 50” // “Count backward by 1, starting at 50.”
• Record as students count.
• Stop counting and recording at 20.

### Activity

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

### Activity Synthesis

• “¿Quién puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”

## Activity 1: Diferentes métodos para restar (20 minutes)

### Narrative

The purpose of this activity is for students to analyze and apply both counting on and taking away as methods to subtract. Both counting on and taking away are valid methods for finding a difference. Students should begin to notice that one method may be more efficient than the other, depending on the numbers in the problem. During the synthesis, students discuss how counting on and taking away are the same and different. This allows teachers to see the mathematical vocabulary students use to describe the strategies (MP6).

This activity uses MLR8 Discussion Supports. Activity: During partner work time, invite students to restate what they heard their partner say. Students may agree or clarify for their partner.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “¿Cómo encontró Diego la diferencia?” // “How did Diego find the difference?” (Diego put 15 counters on the 10-frames and took away 8. The counters that are still there show the difference.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Observen el trabajo de Tyler. Primero puso ocho fichas rojas en su tablero de 10. Luego, puso siete fichas amarillas. ¿Cómo le ayudó esto a encontrar la diferencia?” // "Look at Tyler's work. He started by putting eight red counters on his double 10-frame. Then he put on seven yellow counters. How did that help him find the difference?” (He kept adding counters until he got to 15. He knew the yellow counters were the difference.)
• 30 seconds: quiet think time
• 1 minute: partner discussion

### Activity

• 6 minutes: independent work time

MLR8 Discussion Supports

• “Después de que su pareja comparta cómo pensó, repitan lo que dijo” // “After your partner shares their thinking, repeat back what they told you.”
• Display the sentence frame: “Te escuché decir . . .” // “I heard you say . . .”
• 4 minutes: partner discussion

### Student Facing

Ayer vimos el método de Diego para encontrar el valor de $$15 - 8$$.

El método de Diego

El método de Tyler

Encuentra el valor de cada diferencia. Primero, usa el método de Diego y, después, el método de Tyler.

Método de Diego

Método de Tyler

1. $$16-3$$

Método de Diego

Método de Tyler

2. $$17-8$$

3. $$18-15$$

### Activity Synthesis

• Have a student share Diego’s way for $$18- 15$$.
• Display $$18- 15 = \boxed{3}$$
• “¿Cómo corresponde esta ecuación a su método?” // “How does this equation match their method?” (They started with 18 counters and then took away 15. They counted 3 left.)
• Have a student share Tyler’s way for $$18 - 15$$.
• Display $$15 + \boxed{3} = 18$$.
• “¿Cómo corresponde esta ecuación al método de Tyler?” // “How does this equation match Tyler’s method?” (Tyler started with 15 counters. Then he counted on to get to 18. He had to count on 3.)
• “¿Cuál método les gusto más para esta expresión? ¿Por qué?” // “Which method did you like better for this expression? Why?” (Tyler's because it was a lot faster to count on 3 more than to take away 15 and count what was left.)

## Activity 2: Encontremos el número que hace que la ecuación sea verdadera (20 minutes)

### Narrative

The purpose of this activity is for students to find the missing values that make subtraction and addition equations true. The numbers are selected to encourage students to use a ten to find the missing value and are presented as two sets: subtraction and addition. Students may notice that the first equation in Set B relates to a subtraction equation in Set A.

In the synthesis, students share methods for $$15 - 12$$. Highlight both counting on and taking away methods. Monitor for a student who found the difference between $$15 - 12$$  by subtracting 10 from 15 and then subtracting 2 more from the 5 ones that are left: $$15 - 10$$ is 5 and $$5 - 2$$ is 3. If a student does not use this method, teachers should demonstrate to students. When students break up 12 into 10 and 2 and subtract each number successively they are using their understanding of a teen number as 10 and some ones (MP7).

MLR7 Compare and Connect. Synthesis: After all methods have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “¿Cómo se resolvió el mismo problema de diferentes formas?” // “How was the same problem solved in multiple ways?” and “¿Por qué funciona resolver un problema de diferentes formas?” // “Why does it work to solve the same problem in multiple ways?”
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Social-Emotional Functioning, Attention

### Required Materials

Materials to Gather

### Launch

• Groups of 4
• Give students access to double 10-frames and connecting cubes or two-color counters.

### Activity

• 8 minutes: independent work time
• Monitor for students who solve $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$ by:
• Counting on from 12 to 15
• Taking away 12 from 15
• Taking away 10 and then 2 from 15
• “Comparen sus ideas con las de otros estudiantes de su mesa. Compartan los métodos que usaron para encontrar los números desconocidos. Si no están de acuerdo con una respuesta, trabajen juntos hasta llegar a un acuerdo” // “Compare your thinking with other students at your table. Share the methods you used to find the missing numbers. If you disagree about an answer, work together until you come to an agreement.”
• 4 minutes: small-group discussion

### Student Facing

Encuentra el número que hace que la ecuación sea verdadera.
Asegúrate de que puedes explicar cómo pensaste de una forma que los demás entiendan.

Grupo A:

1. $$12 – 7 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
2. $$18 - 5 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
3. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 14 - 6$$
4. $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
5. $$13 - 4 = \boxed{\phantom{\frac{aaai}{aaai}}}$$

Grupo B:

1. $$5 + \boxed{\phantom{\frac{aaai}{aaai}}} = 18$$
2. $$13 = \boxed{\phantom{\frac{aaai}{aaai}}} + 6$$
3. $$20 = 15 + \boxed{\phantom{\frac{aaai}{aaai}}}$$

### Student Response

If students use the same method for each equation, consider asking:

• “¿Cómo decidiste qué método utilizar?” // “How did you decide what method to use?”
• “¿Cómo podrías usar la suma para encontrar el número desconocido?” // “How could you use addition to find the missing number?”

### Activity Synthesis

• Display $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
• Invite previously identified students to share.
• “¿Por qué $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$ es diferente de las demás ecuaciones?” // “How is $$15 - 12 = \boxed{\phantom{\frac{aaai}{aaai}}}$$ different than all the other equations?” (All the others only subtract a one-digit number but this one is subtracting 12 so you can take away 10 and 2 more.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy usamos diferentes métodos para restar. ¿Qué método para restar les gusta más? ¿Por qué es su método favorito?” // “Today we used different methods for subtracting. What method do you like best for subtracting? Why is it your favorite method?”