Lesson 7

The purpose of this warm-up is to elicit the idea that liquid volume is a measurable attribute, which will be useful when students use informal units and liters to measure liquid volume in later activities. While students may notice and wonder many things about these containers, ideas around how much each container holds and which container holds more are the important discussion points.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “¿A cuál recipiente creen que le cabe la mayor cantidad de agua? ¿Por qué?” // “Which container do you think can hold the most water? Why?” (I think the bowl would hold more because it’s so wide. I think the cup would hold the most since it’s so tall. I’m not sure because they are such different shapes.)
• “Cuando pensamos en cuánto le cabe a un recipiente, estamos pensando en el volumen líquido. El volumen líquido es la cantidad de espacio que ocupa un líquido” // “When we think about how much a container can hold, we are thinking about the liquid volume. Liquid volume is the amount of space that a liquid takes up.”
• “¿Cómo podemos saber con seguridad a cuál recipiente le cabe la mayor cantidad de líquido?” // “How might we find out for sure which container holds the largest liquid volume?” Sample responses:
  • Fill up the bowl and the jar, and pour the liquid into a third container one at time and compare how high the liquid goes.
  • Fill up the bowl and pour into an empty jar. If it doesn't fill up the jar, that means the bowl holds less than the jar. If it spills over, that means the bowl holds more than the jar.
  • Use a smaller container, like a spoon or a small cup, to fill both and see how many spoonfuls or cupfuls are needed for each.

In this activity, students explore liquid volumes by estimating and comparing them. They use a unit container to fill two containers, A and B, to determine which container holds a greater liquid volume.

To make the comparison interesting, containers A and B should be different in size and shape but could hold similar liquid volumes. Consider, for example, a bowl and a cup. The unit container should be small enough so that multiple iterations are needed to fill and compare containers A and B. Consider a large spoon or a small measuring cup.

To involve every student in the measuring process, consider assigning roles of “filler” and “recorder” for container A, then switch roles for container B.

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. It gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3). Asking oneself “Does this make sense?” is a component of making sense of problems (MP1). Making an estimate or a range of reasonable answers with incomplete information is a part of modeling with mathematics (MP4).

Each group of 4 needs:

• a supply of water (1 liter bottles would work and could be reused for the next activity)
• two containers that are different in shape, but close in size, each labeled with “A” and “B”
• a small container labeled with “unit,” such as a large spoon, film canister, or a small measuring cup
• a tray or towel to work on (optional)

• Groups of 4
• Give each group of 4 students a tray with water and containers labeled with “A,” “B,” and “unidad” // “unit”.
• Display three containers labeled “A”, “B”, and “unidad” // “unit” for all to see.
• “¿Cómo podríamos usar el recipiente pequeño, el que está marcado con la palabra ‘unidad’, para comparar los recipientes A y B?” // “How could we use the small container labeled ‘unit’ to compare containers A and B?” (We could see how many of the small containers full of water fit in containers A and B. The one that holds the most holds the most liquid volume.)

• “Tómense un minuto para estimar cuántos recipientes de los que se usan como unidad, si se llenan de agua, caben en el recipiente A y en el B. ¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “Take a minute to estimate how many unit containers of water will fit in containers A and B. What is an estimate that’s too high? Too low? About right?”
• 1–2 minutes: independent work time
• “Compartan sus respuestas y su razonamiento con su grupo” // “Share your responses and reasoning with your group.”
• 1–2 minutes: group discussion
• “Ahora, con su grupo, comparen los volúmenes líquidos que le caben a los recipientes A y B” // “Now work with your group to compare the liquid volumes that containers A and B hold.”
• 5–7 minutes: group work time

• “¿Cómo nos ayudó el recipiente que se usa como unidad a comparar los volúmenes líquidos que le caben a los otros dos recipientes?” // “How did the unit container help us compare the liquid volume the containers can hold?” (We can count how many units fit in each container so we could compare them.)

The purpose of this activity is to introduce students to liters as a formal unit to measure liquid volume. Students learn how much liquid is contained in a liter, then the whole class fills a large clear container with water one liter at a time. As the container is filled students mark the container with a dry erase marker to show the amount of liters in the container.

While it is highly recommended that the class has the experience of filling and marking the container, a video has been provided to show the process and could be used for a class demonstration. Having more than one 1-liter container or some prefilled 1-liter containers will make the process of filling and marking the container go faster.

Gather the following materials:

• a large clear container that can be written on, such as a gallon water jug with top removed or clear storage bin
• 1-liter container (1-liter water bottle, measuring cup, etc.)
• a supply of water (enough to fill the larger container)
• OR the Liquid Volume in Liters video: https://vimeo.com/451620298

• Display the large clear container and 1 liter of water, or the image of the container and 1 liter of water at the beginning of the video if using the video for this activity.
• “Esta es una unidad métrica que podemos usar para medir cuánto espacio ocupa un líquido. Se llama un litro. Podemos usar un litro para medir el volumen líquido, de la misma forma en la que podemos usar una pulgada para medir la longitud” // “This is a metric unit that we can use to measure how much space a liquid takes up. It’s called a liter. We can use a liter to measure liquid volume, just like we can use an inch to measure length.”
• “¿Cuántos litros le caben al recipiente grande? ¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “How many liters will fit in the large container? What is an estimate that’s too high? Too low? About right?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “Para ver cuántos litros de agua le caben a este recipiente, llenémoslo de a un litro en un litro y pongamos marcas para llevar la cuenta de cuántos litros usamos” // “Let’s see how many liters of water will fit in this container by filling it one liter at a time and marking it to keep track of how many liters we use.”
• Invite groups of 2 students to pour water and mark the container, one liter at a time. One partner pours, then the other marks the container with a line at the new level of the liquid.
• Continue pouring and marking until the container can no longer fit a liter. 
• “¿Cuántos litros le caben al recipiente?” // “How many liters fit in the container?” (It fit 9 liters, but there was space for a little more. It was almost 10 liters. It was about \(9\frac{1}{2}\) liters.)

• “¿Qué números pondríamos en cada marca para mostrar el número de litros que le corresponde?” // “How would we label the marks to show the number of liters each mark shows?” (We would label the bottom mark with 1, then the one above it with 2, and keep labeling up to the top mark. The bottom of the container would be 0 liters.)
• Label the marks with numbers.
• “¿En qué se parece el fondo del recipiente al borde de una regla?” // “How is the bottom of the container like the edge of a ruler?” (They both show zero. The bottom of the container is like the zero mark on a ruler.)
• “La palabra ‘litro’ se puede abreviar con una L mayúscula. Podemos mostrar que cada número representa un número de litros escribiendo una L mayúscula al lado de cada número” // “Liters can be abbreviated with an upper case L. We could show that each number represents a number of liters by writing an uppercase L next to each number.”
• Write “L” next to each number on the container that was marked and labeled.
• “A este recipiente le caben __ litros. ¿A qué otros recipientes que hayan visto antes les cabe aproximadamente el mismo volumen líquido?” // “This container can hold __ liters. What are some other containers that you’ve seen that can hold about the same liquid volume?” (A large sink. A storage bin. A large jug of water. A bucket. A small trash can.)