The power used by satellites and by astronauts living in a space station comes from the sun. Energy is collected with solar panels and converted into electricity. Here on Earth, we use passive solar collectors to capture the sun's heat energy.
International Space Station
Ask students if they have ever seen solar panels, such as while they have been driving, or in other locations. Discuss the solar panels on the space station. Brainstorm with students and then list the features that they think are necessary for a good solar collector. Students may suggest the following features:
- flat
- large surface area
- dark color to absorb light
- and so on.
Next, ask students, "Will shape make a difference?" After students have had time to discuss different ideas, suggest that they conduct experiments to explore the effects of changing the dimensions of one possible shape for a solar collector, a rectangular prism.
Ask students to plan how to construct several boxes with the same volume but with different measurements for the length, width, and height.
Using the pattern below, have each group of students remove a 1" × 1" square from each corner of a 6" × 8" rectangle and construct a box with sides of 4" and 6".
Note that the above image is also available as an Overhead pattern.
Ask them to work with their group to estimate how many cubes will fill the box. Each group should be prepared to support its estimate.
Ask a representative from each group to give the group's estimate and explain its reasoning. Then have students find the volume of the box using 1-inch cubes. They should find that 24 cubes fit into the box, so the volume of the box is 24 cubic inches.
Ask students to use the cubes to find other rectangular prisms that have a volume of 24 cubic inches. Explain that they should record the factor triple for the 1" × 4" × 6" box as (1, 4, 6). Discuss the order of the dimensions in each triple. Show which dimension corresponds to the 1-inch measure, the 4-inch measure, and the 6-inch measure.
Ask students to work in groups to find other factor triples of 24. They can use the blocks to model the rectangular prism that corresponds to each triple.
Record on a class chart the factor triples for the different prisms that the class discovers.
Whole-Number Factor Triples of 24
|
1, 1, 24 |
1, 2, 12 |
1, 3, 8 |
|
1, 4, 6 |
2, 2, 6 |
2, 3, 4 |
Ask students to explore other ways to determine the volume of boxes without using the cubes. Let them work with their groups to discover the formula for the volume of a rectangular prism, l × w × h.
After they have discovered the formula, ask students to find the factor triples that correspond to a volume of 36 cubic inches. Assign each group the task of constructing one of the rectangular prisms with a volume of 36 cubic inches. Each group should be prepared to prove to the class that its rectangular prism has a volume of 36 cubic inches, either by applying the formula or by filling the prism with cubes.
Whole-Number Factor Triples of 36
|
1, 1, 36 |
1, 2, 18 |
1, 3, 12 |
1, 4, 9 |
|
1, 6, 6 |
2, 2, 9 |
2, 3, 6 |
3, 3, 4 |
Some students may decide to use the formula to explore sides with decimal or fraction dimensions, such as 0.5 inch x 9 inches x 8 inches.
Once students have explored triples for 24 and 36, tell them they will be creating models of solar panels. The goal will be 36 in this case. When constructing the boxes, students may need to add interior supports. To have consistent measures in the following experiment, be sure that the supports do not restrict the flow of air.
After the students have constructed their boxes, ask this question:
Which of these boxes with a volume of 36 cubic inches will collect the
most solar energy?
With the class, discuss procedures for conducting an experiment to determine which box is the best collector of solar energy. Encourage their decisions about such factors as these:
- Should the boxes be located indoors or outdoors? [On a clear, sunny day, the boxes can either be placed outside or on a window sill; in both instances, the box should receive direct sunlight. On a cloudy day, a light bulb can be used to simulate the sun. All boxes should be placed at the same distance from the light bulb.]
- How and where should the thermometers be placed in the boxes? On the floor of the box? With the thermometer taped to the back of the box?
- Should they cut a hole in the box, cover it with clear material, and read the thermometer through a "window"?
- How much time should pass between temperature readings? Fifteen minutes? An hour?
Make sure that all boxes are the same color and have no insulation.
Each group of students should check on its own box. Each student in the group should independently collect, organize, and display the data on an appropriate
graph. Students may elect to graph the data on a line graph to show the temperatures at different times. This type of graph is useful for showing change over time.
After the experiments are complete, have the students post their data and graphs next to the boxes. As a whole class, discuss the results.
