Illuminations: Water, Water

# Water, Water

 Students compare the amount of water they use in daily life with the amount allotted for each person each day on a Space Shuttle. Within this context, students estimate and measure the weight of, and amount of space occupied by, a gallon of water. They collect, organize, graph, analyze, and interpret data from their investigations. The activities in this lesson are designed to span 2‑3 class periods.

### Learning Objectives

 Students will: recognize a gallon as a unit of capacity estimate and measure the weight of 1 gallon of water estimate and measure in cubic inches (or cubic centimeters) the volume of containers that hold 1 gallon compare the shapes of different containers with equivalent volumes design a container to hold 1 gallon and a container to hold 6 gallons collect, analyze, and graph data

### Materials

 1 plastic gallon jug with top cut off and one-pint containers for each group 1-inch cubes (231 per group) Yardsticks for each group Cardboard, scissors, colored pencils, and tape for each group Scale calibrated to the ounce Graph Paper 1 blank sheet of paper per group, 11 inches × 14 inches or larger Rectangular containers that could hold 1 gallon of water

### Instructional Plan

 Background Information NASA has designated that each Shuttle astronaut be allotted 6 gallons of water a day. This restriction is necessary because water is heavy. Each extra pound adds to the weight of the Shuttle at liftoff and, therefore, requires extra fuel. In addition, water takes space that can be used for other payloads and experiments.           Part I: How Heavy Is a Gallon of Water? Ask students to work in small groups and list all ways they use water during a day. In a whole-class discussion, compile on a chart a list from the groups. Keep the list posted. Students should discuss with their groups how much water they use each day. Members of each group then record their estimates, and each group's estimates are reported in a new class chart. You may want to prompt a class discussion in which students share their rationale for their estimates. Such discourse can help both you and your students assess their prior knowledge of units of measure for capacity and the relationships among those units. Pose the following questions to the class: Do you think that you could manage with 6 gallons of water a day? What changes would you have to make in the way you use water? How much water is eight 8-ounce glasses? How much water do you think that you drink each day?   After students have had an opportunity to reflect on how much water they use daily, review or introduce the vocabulary words gallon, pint, and weight. Place a waterproof 1-gallon container on a scale, and calibrate the scale to zero. Ask students why you calibrated the scale to zero with the container on it. [When you obtain the weight, it will be of the water alone, not of the container, as well.] Present the following questions to the class: Have you ever carried a gallon of water? Did it seem heavy or light? About how heavy is a gallon of water? How many pints of water can we pour into a gallon container to fill it? How heavy is 1 pint of water?   Students take turns filling the container by pouring in pints of water, one at a time. They should stop before each pint is added and estimate the weight. After each pint is added, they should measure and record the weight and discuss their observations. After the first pint is poured into the gallon container, ask them how heavy they think two points will be. Have them predict the weight of three pints. After the second pint of water is poured, ask students to evaluate how close their predictions were. Students then add a third pint. Have them answer these questions.  How many pints have we put in the gallon container? Is the gallon more than half full? Do you want to change your estimate of the number of pints needed to fill the gallon or your estimate of the heaviness of the gallon of water?   Students continue to fill the container until they have measured and recorded the weight of 1 gallon. When they have recorded the number of pints they used to fill the gallon container and the weight at each stage, encourage them to describe any patterns in the measurements. Emphasize that during the investigation, students recorded several estimates and predictions. Have them name some of the things that they estimated and predicted. Encourage them to think of ways to organize and show these estimates and predictions. Invite students to work together in small groups to complete the following activity. Each group should decide how to organize and display their data from the investigation: their estimates, predictions, and measurements. Then they share their graphs with the class and help the class interpret them. Students should create their graphs on graph paper. Encourage an open discussion of different ways to show the estimates, predictions, and measures.  Pose questions such as the following to the students: What are some appropriate ways to display our measure of the weight of the container as each pint of water was added? What do you think are the best ways to graph our estimates of the number of pints in 1 gallon? The predicted weight? What patterns or relationships can we show in our graphs?   If appropriate for your students, you may want to begin an analysis of the data by helping students find the mean of the their predictions of the weight as each pint was added to the gallon container. This analysis can be done with concrete materials or calculators, depending on the prior experiences of the class in finding means.  Ask groups to share their graphs and finding with the class. Encourage class discussion of the different strategies used for displaying their data. To being the interpretation of their graphs, ask each group what its graph shows. The class will find that the weight of each gallon of water is about 8 pounds. Discuss with students the following factors that would give variations in the results: the care in measuring, the use of different measuring tools, and the ease and accuracy of reading calibrations on the measuring tools. Connect the students' investigation to the astronauts' limited amount of water with the following questions: If 1 gallon has a weight of 8 pounds, how heavy is the water for each astronaut for one day? Assume that seven astronauts are in the Shuttle crew. How heavy is the water for the entire crew for one day? If appropriate, ask students if weights stay the same no matter where they are located in the solar system. Students should realize that the weights they estimated are earth weights.   Part II: Designing Containers For Water This activity helps students understand that water for astronauts on Shuttles does not have to be stored in containers that look like milk jugs. Other shapes of containers have the same capacity (volume). To help students relate to limited storage spaces, ask them to think about storing 4 to 6 gallons of water in their home refrigerator. Would this amount of water take up a lot of space in the refrigerator? Teacher Note: Before the activity: make one or two different rectangular containers with a capacity of 1 gallon, for example, with dimensions of 3" × 11" × 7" or 5.5" × 6" × 7".     After reviewing or introducing the vocabulary words capacity and volume, show students a 1‑gallon milk container. Ask them what other shapes of containers could be used to store 1  gallon of water. Have students find the volume of a 1-gallon jug by counting the number of 1-inch cubes (or, if working in the metric system, 1‑centimeter cubes) needed to fill the container. They should find that it takes 231 cubic inches. (If students were to use 1‑cm cubes, they would need significantly more cubes, as 1 gallon is approximately 3,785 cm3.) Next, have students explore the volume of the previously prepared containers by counting the number of 1-inch cubes needed to fill them. Students then work in small groups to construct their own versions of containers that would have the same volume, approximately 231 cubic inches. Pose the following scenario to students: A group of NASA engineers is planning the best uses of available space in Space Shuttles and the International Space Station. Your group is to design a container that can hold 6 gallons of water — the amount an astronaut is allowed for one day. Students should work in groups to design a container which can hold 6 gallons. Bring the class together. Remind them to address the problem of conserving space on the Shuttles and on the space station. Ask the groups to show their designs. Encourage each group to share its strategies and solutions for solving the space problem and to see how its design is similar to, or different from, those of the other groups. When all groups have completed their reports, ask students how they know that a container is big enough to hold 6 gallons. About how heavy would their container be if it were filled with 6 gallons of water? [48 pounds (on Earth).]

### Questions for Students

 How many pints are in 1 gallon? [8 pints.] Approximately how many pounds, on Earth, is one gallon of water? [8 pounds.] How many cubic inches are in 1 gallon? [231 in3.] When we weighed the gallon of water, why did we calibrate the scale to zero with the empty container on top of the scale? [To make sure we would have the weight of the water, not including the container.] Compare your container to another group's container. What was similar? What was different? [Student responses may vary, but similarities should include the same volume, as well as similar shapes; differences may include different dimensions.]

### Extensions

 Water-Consumption Investigation: Revisit the chart created by the class to record the ways they use water, and add additional ideas. Ask the class to brainstorm ideas about water consumption that they would like to investigate. Possible suggestions follow: How much water do we drink each day? How much water is used in food preparation? How much water goes down the drain while we are waiting for the warm water to come? Central Tendency: Discuss the term statistics. Students may know about the mode (most frequent), the median (middle number), and the mean (the sum of the values divided by the number of students). Talk about which statistic is most appropriate for their study. Make a Model: Students record how much water they use in a day and make a physical model of the volume for this amount. Conservation Plan: Students make a plan for conserving water in their daily lives or think of ways in which astronauts can conserve water in space. Algebraic Thinking: Students may be able to use their models to create a formula that gives the mass of the water each astronaut would need for a mission. For example, let n represent the number of days. Then mass = n × 6 gallons a day × 8 pounds per gallon. Have students use the formula to make a table to show the mass of water for different numbers of days in the mission.

### NCTM Standards and Expectations

 Data Analysis & Probability 3-5Collect data using observations, surveys, and experiments. Represent data using tables and graphs such as line plots, bar graphs, and line graphs. Measurement 3-5Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles. Select and use benchmarks to estimate measurements.

### References

 Adapted from "Water, Water," Mission Mathematics, Linking Aerospace and the NCTM Standards, K-6, Reston, VA: NASA/NCTM, 1997. (Revised versions of the books from this profect were released in 2000: Mission Mathematics II: Grades preK‑2 and Mission Mathematics II: Grades 3‑5.)

3 periods

### NCTM Resources

 More and Better Mathematics for All Students
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