The Solar System

In this example, students engage in an inquiry activity that includes both science and mathematics providing prerequisite knowledge for constructing physical models. Ms. B. begins by asking students what they already know about the solar system and maintains their interest by pointing out that some science and technology that they accept as ordinary have not always existed. In a careful sequence, each lesson in the inquiry builds on previous lessons. Students observe stars for a period of time, discuss patterns they observe, and seek confirmation of the patterns through additional observations. Students use manipulatives such as globes, rulers, and protractors to develop understanding. Mathematics is integral to this inquiry, so Ms. B has worked with the mathematics instructor to ensure coordination.

[This example highlights some elements of Teaching Standards A, B, D and E; 5-8 Content Standards A, B, F, and G, as well as Unifying Concepts and Processes; and Program Standards A, B, C, and D.]

Ms. B. was beginning the study of the solar system with the eighth grade class. In preparation for building models of the solar system, she wanted the students to estimate the circumference of the earth. The activity was designed to allow students to think and act like astronomers 500 years ago. She had spent some time with the mathematics teacher in order to coordinate part of the study with him. In fact, some of the science work would actually take place in the math class.

Ms. B. set the stage by reviewing what the students already knew about the solar system, especially about the earth, sun, and moon. Then they talked briefly about building models and determined that to make a scale model they would have to know how big each object in the solar system was and also the distances between them. Ms. B. asked whether they knew these facts about the sun, moon and earth. Someone said they could look it up. But Ms. B. said that although they could get the answer this way, instead they were going to try to find out for themselves, similar to the way astronomers learned new things.

She asked the students how they thought the circumference of the earth was measured. Someone said by measuring on a map. Someone else said by flying around it keeping track of the distance. Ms. B. told them, however, that Columbus had an approximate, but limited, idea of how big the earth was before anyone had gone around it. She said they were going to determine the circumference of the earth using the North Star. Ms. B. gave each student a diagram of the North Star and the stars of the Big and Little Dipper, drawn to scale. The stars were oriented the way they would be looking due north at about 8:00 p.m. in their town. She directed the students to observe and make sketches of the positions of the Big Dipper, the Little Dipper, and the North Star at dark and at least two hours later.

Several days later students compared notes on the stars. Almost everyone had found them, many for the first time. When they compared their observations, everyone had seen the stars move, but most students noticed that the North Star seemed to stay in the same place. They agreed that everyone should observe one more time that night to confirm their observations. But for the moment it was agreed to assume--with the majority--that the North Star didn't seem to move at all.

With these observations, Ms. B. said, they were ready to try to find the circumference of the earth. She challenged each group of four to use their globes to answer the question: "Since the North Star didn't appear to move, what direction would it be if you were standing at the North Pole?" After some time for thinking, discussing and moving the globe around, the class shared their answers. Several groups said it would be right overhead. Asked to explain why, they used their globes to illustrate that if it were not, it wouldn't stay due north as the earth turned.

Ms. B. then drew a sketch of the earth, with the familiar Western Hemisphere facing her, on the blackboard. She drew an arrow straight up from the North Pole, pointing to the North Star, and she also made a dot on the equator at the edge of her sketch on the Gilbert and Ellis Islands in the Pacific. She asked: "Which way is the North Star for someone in the Gilbert and Ellis Islands?"

Figure 1. Ms. B's Sketch of the earth

Each group was directed to reach a consensus of where to draw the arrow from the Gilbert and Ellis Islands on the sketch, but some could not. Each group, and the holdouts, put an arrow on the board to illustrate their answer. One arrow pointed straight up, and the rest pointed at a range of angles, most toward a point near the top of the blackboard. How could they find out who was accurate? Ms. B. suggested that they use what they knew to try to decide who among the groups might be right. To help the students get started on this task, she asked each group how high up they thought the North Star was. According to where their arrows pointed, most had assumed that the North Star was only a few earth diameters above the North Pole. Ms. B. then asked what the students thought the distance to the North Star really was compared with the size of the earth. Now many students said that it must be very far away because it's a star and stars are very far away. In the end consensus was reached that if the North Star were very far away--a great many earth diameters--the straight up arrow in the sketch would point to this star, no matter where one was on the drawing of the earth.

Then Ms. B. drew a line straight across the top of the earth in her sketch to indicate the horizon at the North Pole, pointing out that on the blackboard the angle from the horizon to the North Star was 90 degrees. If you were standing on the North Pole you would look straight up to see the North Star. She asked the students where the inhabitants of the Gilbert and Ellis Islands on the equator, 1/4 of the way around the earth away, would look. She also made a mark on her diagram 1/8 of the earth's circumference south from the North Pole and asked at what angle above the horizon the inhabitants there would have to look to find the North Star. Discussion followed, with a variety of different quick answers. Ms. B. challenged the groups to use their compasses and protractors to make a drawing that would give them the answers. When the groups had come up with some ideas, she led them in a discussion on how the angle changed as the distance around the earth from the pole changed. They agreed that it got smaller and smaller, going from 90 degrees at the pole to 45 degrees 1/8 of the way around, and 0 degrees at the equator.

The next day, Ms. B. put a graph with the three points the students had found so far on the board. She asked how they could predict the angle of the North Star for two points, A and B, which she added to the graph, one halfway between the 45 degree point and the pole and the other halfway between the 45 degree point and the equator? The students suggested a straight line on the graph which fitted their three points would represent the relationship between the angle and distance around the earth. The students also agreed that this was just a guess. Ms. B. asked how they could be more certain and they decided they could go back to their drawing, use their protractors to put A and B on it, and measure what the angle of the North Star would be.

Figure 2. Ms. B's Graph

The result of their graphic investigation confirmed that a straight line seemed to be a good graph for the relationship between the angle formed by the North Star and the horizon and distance around the earth.

Ms. B. then told them that in Columbus' day it was known from ground travel that the distance between a town in Scandinavia where the North Star angle was 67 degrees and another in Italy where the North Star angle was 43 degrees was about 3,000 miles. People who knew what the students now knew could figure out the circumference of the earth. The groups were to take their data to math class where they would have time to figure out the earth's circumference and then proceed to look in the library for the best modern value.

The next day, the class discussed how well they had done in getting a value for the earth's size. In succeeding days they calculated the distance to the moon and its circumference and looked up the same information for the sun. They also learned how modern astronomers calculate distances and size. Finally, using the data, each group designed a scale model of the sun, moon, and earth.