# Lesson 16

Sumemos tres números

## Warm-up: Conversación numérica: Expresiones relacionadas (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding on to 10. These understandings help students develop fluency and will be helpful later in this lesson when students write equivalent expressions.

### 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.

• $$7 + 10$$
• $$7 + 2 + 8$$
• $$10 + 9$$
• $$4 + 9 + 6$$

### Activity Synthesis

• “¿Por qué el valor de algunas de las expresiones fue el mismo?” // “Why did some of the expressions have the same value?”

## Activity 1: Unamos expresiones del mismo valor (15 minutes)

### Narrative

The purpose of this activity is for students to match expressions with three addends to the $$10 + n$$ expression with the same value. This activity sets the groundwork for the next activity in which students make sense of addition equations with expressions on both sides of the equal sign. Students should have access to double 10-frames and two-color counters or connecting cubes.

MLR2 Collect and Display. Circulate, listen for, and collect the language students use as they work with partners. On a visible display, record words and phrases such as: equivalent, expression, the same, different, sum. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Representation: Develop Language and Symbols. Synthesis: Make connections between representations visible. Ask students to identify the correspondences between concrete representations (10-frames or connecting cubes) and expressions.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

### Required Materials

Materials to Gather

### Launch

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

### Activity

• 8 minutes: partner work time

### Student Facing

Une con una línea las expresiones que tengan el mismo valor.

expresiones que tienen 3 números

​​​​​​expresiones de tipo ​$$10 + \boxed{\phantom{3}}$$

1. $$4 + 6 + 8$$
2. $$3 + 6 + 7$$
3. $$9 + 1 + 1$$
4. $$8 + 4 + 2$$
5. $$5 + 5 + 9$$
6. $$7 + 3 + 3$$
7. $$5 + 10 + 5$$
8. $$4 + 7 + 6$$
9. $$9 + 5 + 1$$
10. $$1+ 10 + 1$$

$$10 + 1$$

$$10 + 2$$

$$10 + 3$$

$$10 + 4$$

$$10 + 5$$

$$10 + 6$$

$$10 + 7$$

$$10 + 8$$

$$10 + 9$$

$$10 + 10$$

Si te queda tiempo: escribe otra expresión que tenga 3 números. 2 de los números deben formar 10.

Pídele a tu pareja que piense en la expresión de tipo $$10 + \boxed{\phantom{\frac{aaai}{aaai}}}$$ que le corresponde.

### Student Response

If students find the value of each three addend expression, rather than making a ten first, consider asking:

• “¿Puedes explicar cómo sabes que estas expresiones corresponden?” // “Can you explain how you know these expressions match?”
• “¿Cómo podemos usar los números de esta expresión para formar 10? Después de formar 10, ¿qué número falta sumar? ¿A qué expresión le corresponde?” // “How can we use the numbers in this expression to make 10? After we make 10, what number is left to add? What expression does that match?”

### Activity Synthesis

• “¿Cómo supieron cuáles expresiones tienen el mismo valor?” // “How did you know which expressions have the same value?” (I looked for ways to make 10 and the amount left to add.)
• “¿Qué patrones observaron?” // “What patterns did you notice?” (They are all teen numbers. They are all 10 + facts.)

## Activity 2: ¿La ecuación es verdadera? (10 minutes)

### Narrative

The purpose of this activity is for students to determine whether equations with an expression on each side of the equal sign are true. Each equation has an expression with three addends on one side and a 10 +n expression on the other. Students do not need to find the value of each expression in order to determine if the equation is true, but some students may do so. In this activity, students have an opportunity to look for and make use of structure (MP7) because they apply the associative property and $$10 + n$$ pattern to determine whether equations are true.

### Required Materials

Materials to Gather

### Launch

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

### Activity

• 4 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for a student who uses 10-frames and counters or drawings to show $$3 + 7 + 8$$ as $$10 + 8$$ and a student who uses reasoning that $$3 + 7 = 10$$ and $$10 + 8 = 8 + 10$$.

### Student Facing

Prepárate para explicar cómo pensaste de una forma que los demás entiendan.

1. $$7 + 3 + 4 = 10 + 4$$

2. $$6 + 5 + 4 = 15 + 10$$

3. $$9 + 10 = 9 + 10 + 1$$

4. $$3 + 7 + 8 = 8 + 10$$

5. $$5 + 10 + 5 = 10 + 10$$

Si te queda tiempo:

1. Convierte las ecuaciones falsas en ecuaciones verdaderas.
2. Escribe 1 ecuación que sea verdadera y 1 que sea falsa.
Intercámbialas con tu compañero.

### Activity Synthesis

• Invite previously identified students to share.
• “¿Este razonamiento demuestra que la ecuación es verdadera? ¿Por qué sí o por qué no?” // “Does their reasoning prove whether the equation is true? Why or why not?” (Yes, we can see that it is $$10 + 8$$ on the 10-frame. Yes, we see that $$3 + 7$$ is 10 and then there are 8 left. That is the same as $$8 + 10$$.)

## Activity 3: Escribe expresiones (10 minutes)

### Narrative

The purpose of this activity is for students to write a $$10 + n$$ expression that is equal to a given expression. Each expression given has three addends, two of which make a ten.

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “Ahora, para cada expresión, van a escribir una expresión de tipo $$10 + n$$ que tenga el mismo valor” // “Now you will write a $$10 + n$$ expression with the same value as each of the given expressions.”

### Activity

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

### Student Facing

Para cada expresión, escribe una expresión de tipo $$10 + \boxed{\phantom{3}}$$ que tenga el mismo valor.

1. $$5 + 7 + 5$$
2. $$3 + 7 + 6$$
3. $$1 + 9 + 9$$
4. $$4 + 8 + 6$$
5. $$8 + 10 + 2$$

Si te queda tiempo, escribe todas las expresiones que puedas que tengan 3 números y que sean iguales a $$10 + 5$$.

### Activity Synthesis

• Display each $$10 + n$$ expression.
• “Para que sea más fácil sumar tres números, podemos reescribir cada expresión como una expresión de tipo $$10 + \boxed{\phantom{3}}$$” // “In order to make adding three numbers easier, we can rewrite each expression as a $$10 + \boxed{\phantom{3}}$$ expression.”
• Invite students to say the value of each $$10 + n$$ expression together.

## Lesson Synthesis

### Lesson Synthesis

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

Display $$2 + 6 + 8 = 7 + 3 + 6$$.

“Hoy trabajamos con expresiones de tres números y expresiones con 10. ¿Esta ecuación es verdadera o falsa? ¿Cómo lo saben?” // “Today we worked with expression with three numbers and expressions with 10. Is this equation true or false? How do you know?” (True. $$2 + 8 = 10$$, $$10 + 6 = 16$$. $$7 + 3 = 10$$. $$10 + 6 = 16$$.)

If needed, “¿Alguien decidió si es verdadera o falsa sin sumar todos los números?” // “Did anyone determine whether it is true or false without adding all the numbers?” (Yes. Both sides have a 6, so I looked to see if the other numbers made 10. $$2 + 8 = 10$$ and $$7 + 3 = 10$$, so both sides of the equation are equal to $$10 + 6$$.)