# Lesson 2

Relacionemos contar con sumar

## Warm-up: Conversación numérica: 2 o 3 más (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding 2 or 3 more. These understandings help students develop fluency and will be helpful later in this lesson when students count on to add.

In this activity, students have an opportunity to notice and make use of structure (MP7). They may see patterns in the structure of the expressions by noticing that when an addend changes by one the sum changes by one.

### 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.

• $$4 + 2$$
• $$5 + 2$$
• $$5 + 3$$
• $$6 + 4$$

### Activity Synthesis

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

## Activity 1: Más "Revuelve y saca" (15 minutes)

### Narrative

The purpose of this activity is for students to solve Put Together, Total Unknown story problems through a context they are familiar with—the game Shake and Spill. To launch the lesson, the teacher plays a round of the game with students and reminds students to draw a box around the number in the equation that answers the question.

As students find sums, they relate addition to counting on and may apply what they know about the commutative property. Some of the story problems have the smaller addend first to encourage students to consider this property (MP7). Students should make sure that the answer to each question is clear in their representations.

In the activity synthesis, use physical counters as well as students’ representations to compare the two counting on methods.

MLR6 Three Reads. Keep books or devices closed. To launch this activity, display only the problem stem, without revealing the question. “Vamos a leer este problema-historia tres veces” // “We are going to read this story problem three times.” After the 1st Read: “Díganle a su pareja lo que ocurrió en la historia” // “Tell your partner what happened in the story.” After the 2nd Read: “¿Cuáles son todas las cosas de esta historia que podemos contar?” // “What are all the things we can count in this story?” Reveal the question. After the 3rd Read: “¿De qué formas diferentes podemos resolver este problema?” // “What are different ways we can solve this problem?”

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 10 two-color counters.
• Have one cup available to demonstrate Shake and Spill.

### Launch

• Groups of 2
• Juguemos juntos una ronda de ‘Revuelve y saca’” // “Let’s play a round of Shake and Spill together.”
• Demonstrate Shake and Spill.
• “¿Qué ecuación puedo escribir para representar el número total de fichas?” // “What equation can I write to represent the total number of counters?”
• 30 seconds: quiet think time
• Record responses.
• “¿Qué número en la ecuación representa el número total de fichas?” // “What number in the equation represents the total number of counters?”
• Draw a box around the total in the equation.

### Activity

• 6 minutes: independent work time
• “Compartan con su pareja cómo pensaron” // “Share your thinking with your partner.”
• 4 minutes: partner discussion
• Monitor for students who find the sum of 2 and 8 by:
• counting all
• starting at 2 and count on 8
• starting at 8 and count on 2

### Student Facing

1. Priya está jugando “Revuelve y saca“.
Ella saca 7 fichas rojas y 2 fichas amarillas.
¿Cuántas fichas sacó en total?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

2. Tyler saca 5 fichas rojas y 3 fichas amarillas.
¿Cuántas fichas sacó en total?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

3. Clare saca 2 fichas rojas y 8 fichas amarillas.
¿Cuántas fichas sacó en total?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

4. Han saca 3 fichas rojas y 6 fichas amarillas.
¿Cuántas fichas sacó en total?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

### Activity Synthesis

• Invite previously identified students to share in the sequence above.
• “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?” (They are the same because they all add 3 and 6 and get 9. They all counted to get the answer. They are different because they counted different amounts. The first one counted all of the counters. The second counted 6 counters and the third counted 3 counters.)

## Activity 2: ¿Los dos son correctos? (10 minutes)

### Narrative

The purpose of this activity is for students to analyze representations of the work of two students who counted on. Each student chose a different addend to count on from, which illustrates the commutative property. Methods are represented and students are asked to explain why both methods are correct using precise mathematical language (MP6).

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• 2 minutes: quiet think time
• 3 minutes: partner discussion

### Student Facing

Kiran y Clare están buscando el valor de $$2+ 7$$.

Kiran contó desde 2.

$$2 + 7 = \boxed{9}$$

Clare contó desde 7.

$$7 + 2 = \boxed{9}$$

¿Por qué los dos métodos son correctos?
Muestra cómo pensaste. Usa dibujos, números o palabras.

### Student Response

If students show that both equations are true without mentioning the 'add in any order' property, consider asking:

• “¿Cómo saben que los dos métodos son correctos?” // “How do you know that both methods are correct?”
• “¿Cómo podemos usar las mismas nueve fichas para pasar del primer método al segundo método?” // “How can we use the same nine counters to move from the first method to the second?”

### Activity Synthesis

• Invite 2–3 groups to share their thinking.
• “Kiran y Clare empezaron con números diferentes, pero obtuvieron el mismo valor. Con tal de que tengamos los mismos dos números, podemos sumarlos en cualquier orden. A esto lo llamamos ‘la propiedad de sumar en cualquier orden’” // “Kiran and Clare started with different numbers, but they both got the same value. As long as we add the same two numbers, we can add them in either order. This is called the add in any order property.”
• “¿Cuál método les gusta más? ¿Por qué?” // “Which method do you like best? Why?” (I like adding up from the larger number since it is faster than adding up from the smaller number.)

## Activity 3: Practiquemos sumas hasta 10 (10 minutes)

### Narrative

The purpose of this activity is for students to find the value of sums within 10. Students may apply what they learned about the commutative property and counting on. They may count on for certain equations, such as $$+1$$ or $$+2$$ equations as they can keep track easily, but count all for others. In the lesson synthesis, students return to the addition expressions cards they created in a previous lesson.

Action and Expression: Internalize Executive Functions. Invite students to plan a method, including the tools they will use, for finding the sum. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, Attention

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to 10-frames and connecting cubes or two-color counters.

### Activity

• 5 minutes: independent work time
• 3 minutes: partner discussion

### Student Facing

Encuentra el valor de cada suma.

1. $$7 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
2. $$3 + 5 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
3. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 8 + 2$$
4. $$3 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
5. $$5 + 2 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
6. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 4 + 4$$
7. $$2 + 6 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
8. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 1 + 9$$

## Lesson Synthesis

### Lesson Synthesis

“Hoy vimos diferentes maneras de sumar números. Mai está practicando sus sumas hasta 10. Ella tiene $$7 + 2$$ en su montón de ‘ya me la sé’ y $$2 + 7$$ en su montón de ‘todavía no’. ¿Qué le dirían a Mai?” // “Today we saw different ways we can add numbers. Mai is practicing her sums to 10. She has $$7 + 2$$ in her ‘got it’ pile and $$2 + 7$$ in her ‘not yet’ pile. What would you tell Mai?” (If you know $$7 + 2$$, you also know $$2 + 7$$.) You can change the order of the numbers and get the same value.

Give students access to their addition cards sorted into ‘got it’ and ‘not yet.’ “Revisen sus tarjetas de ‘todavía no’. Si ya se saben bien la suma, muévanla al montón de ‘ya me la sé’. Si todavía tienen que practicar una suma, déjenla en su montón de ‘todavía no’” // “Look through your ‘not yet’ cards. If you just know the sum, move it to your ‘got it’ pile. If you still need practice with a sum, keep it in your ‘not yet’ pile.”