### 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.

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 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 cm^{3}.)

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).]

### Reference

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 project were released in 2000: Mission Mathematics II: Grades preK‑2 and Mission Mathematics II: Grades 3‑5.)