Lesson 9

The purpose of this warm-up is for students to observe the relationship between the different types of units in the metric system. By contrast, in the standard system, it is not easy to see the relationship between inches, cups, and pounds. While students may notice and wonder many things about this image, conversions between liquid volume units (cups, gallons, liters) and regular volume units (cubic centimeters, cubic inches, cubic feet) 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.

• Highlight that the cube represents 1 cubic centimeter or 1 mL of water and one mL of water weighs 1 g.
• The picture shows the relationships between length, capacity (or volume), and weight in the metric system.

The purpose of this activity is for students to estimate how much water falls on the roof of a house, given a particular amount of rainfall. For this calculation, standard units work well as the area of the roof could be given in square feet, for example, and the rain in inches. A conversion would readily give the volume in cubic feet or inches. But, the standard units used to measure volume are cups, pints, quarts, and gallons so more work would need to be done in order to figure out how many gallons, for example, there are in a cubic foot. With the metric system, liquid volume units (liters) and regular volume units (cubic centimeters) are naturally connected.

• Groups of 2
• “¿Aproximadamente qué tan grande es un metro cuadrado?” // “About how big is a square meter?” (It's about the size of my desk top.)
• “¿Aproximadamente cuántos metros cuadrados creen que hay en el piso del salón?” // “About how many square meters do you think there are in the classroom floor?” (maybe 100)

• 5 minutes: independent work time
• 5 minutes: partner work time

• “¿En qué momento de la actividad tuvieron que convertir unidades?” // “When did you have to convert units during the activity?” (I needed to convert meters to centimeters since the roof is given in meters and the rain is given in centimeters. I needed to convert cubic centimeters to liters.)
• “¿Cómo hicieron los cálculos para hacer las conversiones?” // “How did you make the calculations for the conversions?” (the conversions required multiplying or dividing by powers of 10. I multiplied by 100 to convert m to cm and I divided by 1,000 to convert cubic centimeters to liters.)
• “¿Ustedes creen que podrían hacer un contenedor para recoger toda el agua de lluvia?” // “Do you think that you could make a container to capture all of the rainfall?” (Yes, I think that a 2 meter cube is big but it's not so big that it would not fit near the house. Or we could use several containers that are a little smaller.)

The purpose of this activity is for students to find out if the amount of water that falls on the house is sufficient for many of the daily household chores that use water. This will require a lot of estimation and will vary from house to house. How much of the calculations to leave up to the students is an individual teacher choice and this lesson could easily be extended for another day if the students make well reasoned estimates (some values are given in parentheses) for how much water is used for different activities such as:

• taking baths or showers (150 liters or 80 liters)
• washing clothes (100 liters)
• washing dishes (100 liters)
• washing hands (1 liter)
• flushing the toilet (10 liters)

More estimation comes into play for how often each of these activities happens and this will vary greatly depending on the student. When students make a list of the different things they do in the house that use water and then estimate how much water is used they model with mathematics (MP4).

Consider inviting students to check their estimates by looking at the one of their monthly water bills. The bill will usually give the number of gallons of water used and there are almost 4 liters in a gallon.

• Groups of 2
• After students work on the first problem, pause the class and make a list of the main daily uses of water.
• Depending on how much time is available and the modeling demand level desired, consider estimating together or providing estimates for how much water is used for each purpose.

• 5 minutes: independent work time
• 10 minutes: partner work time

• “¿Cómo se pueden imaginar el volumen de agua que se usa para darse un baño?” // “How can you visualize the volume of water that it uses to take a bath?” (I can picture the bathtub filled up partway with water.)
• “¿Cómo podrían medir el volumen de agua que hay en la bañera?” // “How could you measure the volume of water in the bathtub?” (I could measure the length and width of the tub and the height of the water and multiply them.)
• “¿Les sorprende alguna de las cantidades de agua que se usan para las distintas actividades? ¿Por qué?” // “Are any of the amounts of water used for different things surprising to you? Why?” (I am surprised by how much water it takes to wash the dishes. It’s almost as much as when you take a bath.)