# Lesson 8

Relacionemos cocientes con productos que nos sabemos

## Warm-up: Conversación numérica: Multiplicación y división (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying and dividing within 100. These understandings help students develop fluency and identify division facts that are related to known products.

When students use the relationship between multiplication and division to find division facts they don’t know, they are looking for and making use of structure (MP7).

### 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.

• $$4 \times 10$$
• $$40 \div 4$$
• $$40 \div 10$$
• $$60 \div 6$$

### Activity Synthesis

• “¿Cómo muestran las primeras 3 expresiones que la multiplicación y la división están relacionadas?” //  “How do the first 3 expressions show that multiplication and division are related?” (The two division expressions both have one of the factors missing. In the first expression, the 10 is missing. In the second, the 4 is missing.)

## Activity 1: Clasificación de tarjetas: Multiplicación (20 minutes)

### Narrative

The purpose of this activity is for students to check-in on their progress towards fluent multiplication within 100. Students work in groups of 2 to sort products into groups they know right away, can find quickly, or don’t know yet. The launch provides time for a class discussion about what it means to know a fact quickly. Students identify five products with which they’d like to be more proficient, share their strategies, and practice finding the products they choose. The cards from this activity will be used in the next activity.

MLR8 Discussion Supports. Synthesis: Display a sentence frame to support whole-class discussion: “La próxima vez que multiplique _____ y ____, voy a . . .” // “The next time I multiply _____ and _____, I will . . . .”
Representation: Internalize Comprehension. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

### Required Materials

Materials to Copy

• Card Sort: Multiplication
• Card Sort: Multiplication Recording Sheet, Spanish

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.
• The Multiplication Fact sort cards from this activity will be used again in the next activity.

### Launch

• Groups of 2
• “Hoy vamos a retomar los hechos de multiplicación para ver cuántos se han aprendido hasta ahora. Pero recuerden que tienen el resto del año para aprendérselos” // “Today we’re going to revisit the multiplication facts to see how many you’ve learned so far. Remember, though, you have the rest of the year to learn them.”
• “Todos sabemos lo que significa saberse un producto de inmediato, ¿pero qué significa encontrar un producto rápidamente?” // “We all know what it means to know a product right away, but what does it mean to know a product quickly?” (We can figure it out in a couple of seconds with a strategy. We can figure it out in less than 5 seconds.)
• Discuss as a class and come to an agreement about what it means to find a product quickly.
• “¿Alguien quiere agregar algo a lo que _____ dice que significa encontrar un producto rápidamente?” // “Does anyone want to add on to what _____ says it means to find a product quickly?”
• “¿Alguien tiene otras ideas acerca de lo que significa encontrar un producto rápidamente?” // “Does anyone have different ideas about what it means to find a product quickly?”
• “A partir de esta discusión, ¿alguien quiere reconsiderar sus ideas acerca de lo que significa encontrar un producto rápidamente?” // “Based on this discussion, does anyone want to revise their ideas about what it means to find a product quickly?”
• Give each group one set of pre-cut cards and a sort table.

### Activity

• “Tómense un momento para hacerse preguntas mutuamente sobre hechos de multiplicación. Mientras le hacen preguntas a su compañero, usen la tabla para clasificar las expresiones en tres grupos que muestren si su compañero se lo sabe de inmediato, si lo puede encontrar rápidamente o si todavía no se lo sabe” // “Take some time to quiz each other on multiplication facts. As you quiz your partner, use the table to sort the expressions into three groups that show if they know it right away, they can find it quickly, or they don’t know it yet.”
• 7–10 minutes: partner work time
• “Escojan 5 hechos de multiplicación que todavía no se sepan y escriban las expresiones. Estos son los productos que van a practicar” // “Choose 5 multiplication facts that you don’t know yet and write down the expressions. These are the products you will practice finding.”
• 1 minute: independent work time
• “Ahora, compartan con su compañero los productos que quieren practicar. Pídanle que les ayude a pensar en algunas estrategias que pueden usar para encontrar los productos rápidamente” //  “Now, share the products you want to practice with your partner and have them help you think of some strategies you could use to find the products quickly.”
• “Una vez que tengan algunas estrategias, tómense un momento para practicar los productos que escogieron” // “After you have some strategies, take some time to practice finding the products you chose.”
• 5–7 minutes partner work time

### Student Facing

Hazle preguntas a tu compañero sobre sus hechos de multiplicación. Clasifica los hechos de tu compañero en una de estas columnas:

1. se lo sabe de inmediato
2. lo puede encontrar rápidamente
3. todavía no se lo sabe

Expresiones de multiplicación que voy a practicar:

### Student Response

If students don’t yet have a strategy for one of the facts they’ve chosen to practice, consider asking:

• “¿Qué has intentado hasta el momento para encontrar este producto?” // “What have you tried so far to find this product?”
• “¿Podrías hablar con otro grupo para ver si te pueden sugerir una estrategia para encontrar este producto?” // “Could you check in with another group to see if they could suggest a strategy for finding this product?”

### Activity Synthesis

• “¿Qué estrategias les sirvieron para encontrar los productos que todavía no se sabían?” // “What were some useful strategies for finding products you didn’t know yet?” (Thinking of a product I already know and using that product to find the one I didn’t know yet. Using products of 2, 5, and 10 to figure out other products.)

## Activity 2: Si sé que..., entonces sé que... (15 minutes)

### Narrative

The purpose of this activity is for students to identify division facts that are related to multiplication facts that they know. Students complete “If I know, then I know” statements using their multiplication fact cards from the previous activity. Give students time, if needed, to determine the product before generating the related division equation. Some students may generate 4 related division equations for each product by moving the quotient to the left side of the equal sign. If this comes up, recognize that this is possible, but keep the emphasis on generating two related division facts, one for each of the factors as the unknown number.

When students use the relationship between multiplication and division identify two division facts from a multiplication fact, they look for and make use of structure (MP7).

### Required Preparation

• Each group of 2 needs a set of cards from the previous activity.

### Launch

• Groups of 2
• “Lean la primera frase de la actividad. Hablen con su compañero sobre cómo pueden completar la frase” // “Read the first statement of the activity. Talk with your partner about how you could finish the statement.”
• 1 minute: partner discussion
• Share responses.

### Activity

• “Ahora, por turnos, van a tomar una tarjeta y van a usar el hecho que escogieron para completar una frase como esta: ‘Si sé que..., entonces sé que...’. La van a completar con el hecho de multiplicación de la tarjeta que tomaron y los hechos de división relacionados. Si es necesario, tómense un momento para averiguar el hecho de multiplicación con su compañero. Después de cada turno, en la tabla, escriban la ecuación de multiplicación y las ecuaciones de división relacionadas” //   “Now, you’re going to take turns drawing a card and using the fact you chose to complete an ‘If I know, then I know’ statement with the multiplication fact that you drew and the related division facts. Take some time to figure out the multiplication fact together if you need to. After every turn, record the multiplication equation and related division equations in the table.”
• 7–10 minutes: partner work time

### Student Facing

Si sé que $$4 \times 5 = 20$$, entonces sé que _____.

1. Coloquen las tarjetas de hechos de multiplicación en un montón, boca abajo.
2. Por turnos, tomen una tarjeta de hechos de multiplicación.
3. Usen el hecho de multiplicación de la tarjeta para escribir una ecuación de multiplicación en la columna “Si sé que . . .”.
4. Después, anoten las ecuaciones de división relacionadas en la columna “Entonces sé que . . .”.
Si sé que . . . , entonces sé que . . .

### Activity Synthesis

• “¿Cuántas ecuaciones de división se les ocurrieron para cada ecuación de multiplicación? Expliquen su razonamiento” // “How many division equations were you able to come up with for each multiplication equation? Explain your reasoning.” (2, because I could come up with 1 equation where the quotient was 1 factor and 1 equation where it was the other factor. 4, because I could come up with 1 for each of the factors being the quotient, and I could have the quotient on the right or the left of the equal sign.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy pensamos sobre los hechos de multiplicación que nos sabemos y trabajamos en algunos que todavía no nos sabemos. ¿Cómo les ayudó esto a encontrar hechos de división?” // “Today we thought about multiplication facts that we know and worked on some that we don’t know yet. How did this help you with finding division facts?” (We could use a multiplication fact to find related division facts. We realized that if we know a multiplication fact, then there are some division facts that we know too.)