# Lesson 5

Encontremos la diferencia

## Warm-up: Conversación numérica: Valor desconocido hasta 10 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for the relationship between addition and subtraction. Students who relate the pairs of equations are observing regularity in how addition and subtraction are related (MP8).

### 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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

En cada caso, encuentra el número que hace que la ecuación sea verdadera.

• $$6 + \boxed{\phantom{\frac{aaai}{aaai}}} = 10$$
• $$10 - 6 = \boxed{\phantom{\frac{aaai}{aaai}}}$$
• $$8 +\boxed{\phantom{\frac{aaai}{aaai}}}= 10$$
• $$10 - 2 =\boxed{\phantom{\frac{aaai}{aaai}}}$$

### Student Response

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### Activity Synthesis

• “¿Alguien puede expresar el razonamiento de _______ de otra forma?” // “Who can restate _______ 's reasoning in a different way?”

## Activity 1: Distintas formas de encontrar la diferencia (15 minutes)

### Narrative

In this activity, students analyze three different ways to subtract. They see that taking away is one way to find the difference, but that you can also count on or use known addition facts. Students further solidify their understanding that addition and subtraction are related, which sets the groundwork for a later activity when students solve subtraction problems within 10.

### Launch

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

### Activity

• Read the task statement.
• “Primero van a trabajar solos. Piensen lo que quiso decir cada estudiante y prepárense para explicar cómo pensaron de una forma que los demás entiendan” // “First you will work on your own. Think about what each student means and be ready to explain your thinking in a way that others will understand.”
• 5 minutes: independent work time
• 4 minutes: partner discussion
• Monitor for students who can use the 10-frame with six red counters to explain the relationship between $$10 - 6$$  and  $$6 + \boxed{\phantom3} = 10$$ .

### Student Facing

Mai, Diego y Noah encontraron el valor de $$10 - 6$$.

1. Diego dijo: “Yo puedo quitar”.¿Qué quiso decir Diego?
Prepárate para explicar cómo pensaste de una forma que los demás entiendan.

2. Mai dijo: “Yo puedo contar hacia adelante”.¿Qué quiso decir Mai?
Prepárate para explicar cómo pensaste de una forma que los demás entiendan.

3. Noah dijo: “Yo puedo usar lo que sé sobre $$6 + 4$$ para ayudarme”.
¿Qué quiso decir Noah?
Prepárate para explicar cómo pensaste de una forma que los demás entiendan.

### Student Response

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### Activity Synthesis

• Invite previously identified students to share.
• “¿Alguien puede expresar de otra forma lo que ______ nos acaba de mostrar?” // “Who can restate what _____ just showed us?” (Diego subtracted by taking away 6 counters one at a time and saw that there were 4 counters left. Mai subtracted by thinking about addition. She counted on from 6 until she got to 10 and noticed she counted up 4. Noah knows his sums of 10. He knows 10 can be made by 6 and 4, so $$10 - 6 = 4$$.)
• “¿Cuál método les gusta más?” // “Which method do you like best?” (I know my sums to 10 so I would use that. I like counting on because I like to add more than take away.)

## Activity 2: Cadenas de restas (10 minutes)

### Narrative

The purpose of this activity is for students to identify patterns when subtracting (MP7). Students have access to connecting cubes and two-color counters to make sense of the problems and explain their thinking (MP1). As students subtract, they continue to develop relational thinking and notice that:

• as the subtrahend, or the number being subtracted, increases, the difference decreases.
• as the subtrahend decreases, the difference increases.

This vocabulary is not necessary to use with students. During the activity synthesis, select students who can explain each of the ideas. When students show their thinking using objects and mathematical language to explain why the concept is true, they construct viable arguments (MP3).

This activity uses MLR8 Discussion Supports. Advances: Listening, Representing

### Launch

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

### Activity

• Read the task statement.
• 8 minutes: partner work time
• Monitor for students who can explain the pattern for Set 1 and Set 2 using 10-frames or drawings and mathematical language.

### Student Facing

Encuentra el valor de cada diferencia en la cadena de restas.
Explica lo que observas.

Grupo 1:

$$6 - 1$$

$$6 - 2$$

$$6 - 3$$

$$6 - 4$$

¿Qué observas?
¿Por qué crees que esto ocurre?
Prepárate para explicar cómo pensaste de una forma que los demás entiendan.

Grupo 2:

$$9 - 8$$

$$9 - 7$$

$$9 - 6$$

$$9 - 5$$

¿Qué observas?
¿Por qué crees que esto ocurre?
Prepárate para explicar cómo pensaste de una forma que los demás entiendan.

### Student Response

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### Advancing Student Thinking

If students start over with a new drawing or set of objects for each expression, consider asking:

• “¿Puedes explicar cómo encontraste el valor de cada diferencia?” // “Can you explain how you found the value of each difference?”
• “¿Cómo puedes usar el mismo dibujo que hiciste en el caso de $$6 - 1$$ para encontrar el valor de $$6 - 2$$?” // “How can you use the same drawing you made for $$6 - 1$$, to find the value of $$6 - 2$$?”

### Activity Synthesis

MLR8 Discussion Supports
• Invite previously identified students to share.
• As students share, record their thinking with diagrams and equations.
• “Así como en la suma, también hay patrones en la resta. Entender los patrones les puede ayudar a encontrar diferencias” // “Just like addition, there are patterns in subtraction. Understanding patterns can help you find differences.”

## Activity 3: El valor de la diferencia (10 minutes)

### Narrative

The purpose of this activity is for students to find the value of differences within 10. Students are encouraged to think about how patterns in subtraction problems and knowing sums within 10 can help them find the value of the differences. Students may use take away or counting on methods. The problems are written for students to think about different methods for solving. For example, students may find the value of $$10 - 3$$ by taking away 3 to get 7, then see that they can find $$10 - 7$$ by knowing the relationship between 3, 7, and 10. Students should work in groups of 2, with a different partner than they had in the previous activity.

Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which problem to start with.
Supports accessibility for: Social-Emotional Functioning, Attention

### Launch

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

### Activity

• Read the task statement.
• “Primero, encuentren el valor de cada diferencia individualmente. Después, compartan cómo pensaron, esta vez con una pareja diferente a la de la actividad pasada” // “You will first find the value of each difference on your own. Then you will share your thinking with a different partner than last activity.”
• 5 minutes: independent work time
• 2 minutes: partner discussion

### Student Facing

Encuentra el valor de cada diferencia.

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

### Student Response

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### Activity Synthesis

• “¿Hubo expresiones que les ayudaron con otra expresión? ¿Cómo les ayudaron?” // “Were there any expressions that helped you with another expression? How did they help you?” ($$10 - 3$$ and $$10 - 7$$. They are related because $$3 + 7 = 10$$. $$9 - 6$$, $$9 - 5$$, and $$9 - 4$$. There is a pattern. Since the number being subtracted gets 1 bigger, the difference gets 1 smaller.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy encontramos diferencias hasta 10 y nos dimos cuenta de que podemos usar lo que sabemos sobre la suma para encontrar diferencias. Para encontrar la diferencia en un problema como $$9 - 5 = \boxed{\phantom{4}}$$, podemos pensar en las sumas de 9. Sabemos que $$5 + 4 = 9$$, así que $$9 - 5 = 4$$” // “Today we found differences within 10 and saw that you can use what you know about addition to find differences. To find the difference in a problem like $$9 - 5 = \boxed{\phantom{4}}$$, you can think about the sums of 9. I know that $$5 + 4 = 9$$, so $$9 - 5 = 4$$.”

“Decimos que 4, 5 y 9 están relacionados. Podemos escribir ecuaciones de suma y también ecuaciones de resta con estos números” // “We say that 4, 5, and 9 are related. We can write both addition and subtraction equations with these numbers.”

“¿Cuáles son las ecuaciones de suma y de resta que podemos escribir con 4, 5 y 9?” // “What are the addition and subtraction equations we can write with 4, 5, and 9?” ($$4 + 5 = 9$$, $$5 + 4 = 9$$, $$9 - 4 = 5$$, $$9 - 5 = 4$$.)

## Cool-down: Resta hasta 10 (5 minutes)

### Cool-Down

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