Lesson 8

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100 and to help students develop fluency.

When students use known multiplication and division facts to divide larger numbers, they look for and make use of structure (MP7).

• 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

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

• “¿Cómo usaron los hechos de división que ya conocen para encontrar algunos de los otros cocientes?” // “How did you use division facts that you already know to find some of the other quotients?” (I knew that \(60\div3\) would be double the answer of \(30\div3\). Once I knew \(60\div3\), I was able to find \(63\div3\) by adding another group of 3 and \(54\div3\) by taking groups of 3 away.)

The purpose of this activity is for students to estimate liquid volumes in liters. First, students consider the number of liters it could take to fill a bathtub. Then, students match a variety of containers to the number of liters they could hold, using their experience from the previous lesson to support their reasoning. 

In order to solve these problems, students rely on their experience as well as information provided by the photos of different objects. They also rely on their ability to make reasoned estimates (MP4). The activity provides students an opportunity to share their thinking and critique the reasoning of others (MP3).  

• Groups of 2
• “Hoy vamos a pensar en algunos recipientes que contienen líquidos. ¿Qué recipientes que contienen líquidos han visto?” // “Today we’re going to think about some containers that hold liquids. What are some containers that you've seen that hold liquid?” (cups, bowls, buckets, sinks, milk cartons, a pool)
• 30 seconds: quiet think time
• Share responses.
• Display the image and Clare, Jada, and Kiran’s ideas about how much water the bathtub holds.
• “Tómense un momento para pensar en cuántos litros de agua le caben a la bañera y con cuál razonamiento están de acuerdo” // “Take a moment to think about how many liters of water the bathtub holds and whose reasoning you agree with.” (I agree with Kiran because 2 liters is less than the amount we put in the jug yesterday and I don’t think 20 liters would fill the bathtub. I think it would take 200 liters.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “¿A qué otros recipientes les caben aproximadamente 200 litros?” // “What other containers could hold about 200 liters?” (a larger trash can, a kiddie pool)
• Share responses.

• “Ahora, con su compañero, estimen cuántos litros les caben a otros recipientes” // “Now, work with your partner to estimate how many liters some other items hold.”
• 5–7 minutes: partner work time
• Monitor for students who refer back to the experiences in the previous lesson as they reason about the liquid volume each container can hold.

• Select previously identified students to share their responses and reasoning.
• “¿Qué estrategias les ayudaron a estimar el volumen líquido que le cabe a los diferentes recipientes?” // “What strategies were useful as you estimated the liquid volume that different containers can hold?” (I thought about how much 1 liter was and how many times it could be poured into the container before it was full. I thought about the marks on the container we filled and whether the container would be more or less.)

The purpose of this activity is for students to measure liquid volume using liters. Students compare the liter marks on a container for measuring liquid volume to the marks on a ruler before they use images of containers marked in liters to determine or show the volume of liquid in each container.

• Groups of 2
• Display the images.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (Students may notice: The ruler and the containers have marks for measuring. The marks on the ruler go side to side, but the marks on the container go up and down. They both show zero, but on the ruler there is a zero mark and for the container it’s just the bottom. Students may wonder: What is the diagram supposed to be? Could we use a ruler to measure liquid volume?)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• “¿En qué se parecen las marcas del recipiente y las marcas de la regla? ¿En qué son diferentes?” // “How are the marks on the container and the marks on the ruler alike? How are they different?” (They are all used to measure. The ruler measures length, but the containers measure volume. The scale on the containers is vertical, but the ruler is horizontal.)
• 1 minute: partner discussion
• Share responses.
• If no students mention the zero mark, ask “¿En qué parte de los recipientes está el cero?” // “Where is zero on the containers?”

• “El recipiente de cada imagen está marcado en litros. Con su compañero, encuentren el volumen si se muestra el líquido y muestren el líquido si les dan el volumen” // “The container in each image is marked in liters. Work with your partner to find the volume when the liquid is shown, and to show the liquid when the volume is given.”
• 7–10 minutes: partner work time
• If students finish early, have them answer the following questions:
  • “¿Cuántos litros obtendrían si combinaran los dos recipientes que tienen la mayor cantidad de líquido? Muestren o expliquen cómo razonaron” //“How many liters would you have if you combined the two containers with the most liquid? Show or explain your reasoning.”
  • “Encuentren una combinación de volúmenes líquidos que pueda llenar el recipiente más grande hasta la marca superior” // “Find a combination of liquid volumes that would fill the largest container to the top mark?”

If students interpret the shorter tick marks on the container as fractional amounts, consider asking:

• “Mira las marcas del recipiente D. ¿Qué número está en la mitad entre 2 y 4 o en la mitad entre 4 y 6?” // “Look at the marks on container D. What number is halfway between 2 and 4, or between 4 and 6?”
• “Mira las marcas del recipiente F. Hay 4 marcas entre 10 y 15 que están separadas por la misma distancia. ¿Qué números podrían representar?” // “Look at the marks on container F. There are 4 tick marks that are equally spaced between 10 and 15. What numbers could they represent?”

• “Si el nivel del líquido estaba entre dos números, ¿cómo averiguaron lo que representaban las marcas?” // “If the level of the liquid was between two numbers, how did you figure out what the marks represented?” (I thought about what was between the numbers. I knew that 7 was between 6 and 8, but \(3\frac{1}{2}\) is between 3 and 4. For the last one, I saw that the numbers went up by 5, so I thought each mark would be a liter.)