# Lesson 10

Suma y resta con una decena

## Warm-up: Conversación numérica: Una decena y algunas unidades (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for addition and subtraction equations with 10 and some more. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to solve story problems with 10 and some more.

### 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.

• $$10 + 4$$
• $$14 - 4$$
• $$5 + 10$$
• $$15 - 5$$

### Activity Synthesis

• “¿Cómo les puede ayudar el primer problema a encontrar la diferencia del segundo problema?” // “How can you use problem one to help you find the difference in problem two?” (If $$10 + 4 = 14$$, then I know that $$14 - 4 = 10$$.)
• “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”

## Activity 1: Problemas-historia con una decena (20 minutes)

### Narrative

The purpose of this activity is to elicit methods students have for solving story problems involving addition and subtraction with teen numbers. Students are presented with story problem types that are familiar to them to allow for discussion about methods they used to find the answer. Students solve the problems in any way that makes sense to them. They may build values and add-on or take-away, or use what they have learned about the $$10 + n$$ structure of teen numbers. Students write equations; they can write many different equations to represent the problem or how they solved it. It is important that students are able to relate their equations to the story problem and explain their work (MP2, MP4).

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: “Cuéntenle a su compañero 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

### Launch

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “El hobby de muchas personas es coleccionar cosas. ¿Alguno de ustedes colecciona cosas?” // “Many people have the hobby of collecting things. Do any of you collect something?”
• Share responses.
• “¿Qué cosas saben que la gente colecciona o qué cosas les gustaría coleccionar?” // “What are some things that you know people collect, or that you might like to collect?” (baseball cards, marbles, rocks)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Resolvamos algunos problemas-historia sobre colecciones” // “Let’s solve some story problems about collections.”

### Activity

• “En cada caso, escriban dos ecuaciones que nos muestren la historia” // “Write two equations to match each of these stories.”
• 6 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for a student who wrote an addition equation and one who wrote a subtraction equation for the problem about Priya.

### Student Facing

1. Kiran tenía una colección de 5 gorras de béisbol.

En su cumpleaños recibió algunas más.
Ahora tiene 15 gorras de béisbol en total.
¿Cuántas gorras de béisbol recibió?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

Ecuación: ________________________________

2. Priya tenía una colección de cómics.
Ella recibió 3 cómics nuevos.
Ahora tiene 13 cómics.
¿Cuántos cómics tenía al principio?
Muestra cómo pensaste. Usa dibujos, números o palabras.

Ecuación: ________________________________

Ecuación: ________________________________

### Activity Synthesis

• Invite previously identified students to share their equations for Priya’s problem.
• If no student writes a subtraction equation, display $$13 - 3 =\boxed{\phantom{10}}$$.
• “¿De qué forma las ecuaciones nos muestran el problema-historia? ¿Qué relación hay entre ellas?” // “How do the equations match the story problem? How are they related to each other?” (They show that the total number of comic books is 13 and that 3 is one part and 10 is the other part. They all show that 10 is the missing number. The subtraction equations takes 3 away from the 13 to find the other part. The addition equation adds 3 to some number to get 13.)
• “¿Cuál ecuación tiene más sentido para ustedes? ¿Por qué?” // “Which equation makes more sense to you? Why?” (Addition, because I know that to get from 3 to 13, I have to add 10. Subtraction, because I know what number to start with and how many to take away. I don't know what numbers to use in the addition equation.)

## Activity 2: Ecuaciones relacionadas (15 minutes)

### Narrative

The purpose of this activity is for students to discuss the relationship between addition and subtraction equations involving teen numbers. Students find the value that makes the addition and subtraction equations true with the unknown in all positions. Students may choose to use objects to represent the problems and find the value that makes the equation true (MP5).

Action and Expression: Internalize Executive Functions. Invite students to plan a method, including the tools they will use, for finding the missing value. 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 double 10-frames and connecting cubes or two-color counters.
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• 4 minutes: independent work time
• 4 minutes: partner discussion

### Student Facing

Mai está buscando el número desconocido en $$16 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$.

Ella dice: “Puedo usar como ayuda lo que sé sobre 10 y algunas unidades”.

¿Qué quiere decir Mai?

En cada caso, encuentra el número que hace que la ecuación sea verdadera.
Muestra cómo pensaste. Usa dibujos, números o palabras.

1. $$15 - 10 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
2. $$\boxed{\phantom{\frac{aaai}{aaai}}} = 13 - 3$$
3. $$8 = 18 -\boxed{\phantom{\frac{aaai}{aaai}}}$$
4. $$2 + \boxed{\phantom{\frac{aaai}{aaai}}} = 12$$

### Student Response

If students take away using drawings for each equation, consider asking:

• “¿Cómo encontraste el valor desconocido?” // “How did you find the missing value?”
• “¿Cómo podría ayudarte el tablero de 10 a encontrar el valor desconocido?” // “How could the double 10-frame help you find the missing value?”

### Activity Synthesis

• Share solutions for each problem.
• “¿Qué relación hay entre $$\boxed{\phantom3} = 13 - 3$$ y $$2 + \boxed{\phantom 3} = 12$$ ?” // “How are $$\boxed{\phantom3} = 13 - 3$$ and $$2 + \boxed{\phantom 3} = 12$$ related?” (One is an addition problem and one is a subtraction problem, but you can use addition or subtraction for either one. For $$\boxed{\phantom 3} = 13 - 3$$ you can subtract or change it to $$3+ \boxed{\phantom3} = 13$$. For $$2 + \boxed{\phantom3} = 12$$ you can add or change it to $$12 - 2=\boxed{\phantom3}$$. Both have a missing value of 10.)

## Lesson Synthesis

### Lesson Synthesis

Display 17 on a double 10-frame.

Display $$\boxed{\phantom{17}} - 10 = 7$$. “Hoy resolvimos problemas y completamos ecuaciones con 10 y unos cuantos más. Vimos que a veces podemos usar la suma como ayuda para restar. ¿Cómo les ayuda usar la suma a encontrar el número que hace que esta ecuación sea verdadera?” // “Today we solved problems and completed equations with 10 and some more. We saw that sometimes we can use addition to help us with subtraction. How can using addition help you find the number that makes this equation true?” (I know that $$7 + 10 = 17$$ so the missing number is 17.)

Display $$10 + \boxed{\phantom{3}} = 17$$. “¿Cómo les ayuda usar la resta a encontrar el número que hace que esta ecuación sea verdadera?” // “How can using subtraction help you find the number that makes this equation true?” (I see on the 10-frame that there’s 10 and 7 more. If I take away the 10, there’s 7 left.)