The problem with parallax

Students will increase their understanding of astronomical measurements by using parallax to measure distances on their school campus. They will also gain an appreciation of the difficulties with such measurements by statistically analyzing the class' results.

A lesson plan for grades 7 and 9–12 Mathematics and Science

By Mark Clinkscales and Carrie Palmer

Learn more

• Parallax a lesson plan giving an explanation of parallax and its use in astronomy

Related pages

• A walk through the solar system: A practice in scientific notation, measurement, and scale distances, this lesson plan integrates mathematics into the science curriculum.
• Morehead Planetarium and Science Center: Located on the campus of the University of North Carolina at Chapel Hill, the Morehead Planetarium and Science Center is a fascinating place to visit to learn more about astronomy.
• KidSenses Children's InterACTIVE Museum: The interactive exhibits at this children’s museum spark the imagination and kids have fun as they play and learn.

Related topics

• Learn more about astronomic distance, astronomy, environmental science, measurement, parallax, science, and solar system.

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Learning outcomes

Students will:

• Use parallax to estimate distances on their school campus.
• Will statistically analyze the class’ results.
• Gain an increased understanding of astronomical distances and their measurement.
• Gain an increased appreciation of the variability in parallax measurements.

Teacher planning

Time required for lesson

50 minutes

Materials/resources

• Paper, pen or pencil, and scientific calculator for each student.
• Three or more distances of known measurement on the school campus (e.g., football field, parking lot)

Technology resources

• Scientific calculator for each student—capable of computing statistical means and standard deviations

Pre-activities

Prior to beginning this investigation, students should be able to compute means and standard deviations. Students should have already learned the basics of star classification, i.e. color and temperature, and understand the need to measure astronomical distances.

Activities

1. Teacher will begin the lesson by reviewing characteristics of stars, including classification by color and temperature. Also, s/he should review why it is important to be able to measure distances on an astronomic scale.
2. Teacher will introduce and explain the process of parallax. Good explanations can be found at the two websites listed below. Teacher will explain that parallax can be used to measure distances up to three-hundred light-years from Earth. Teacher will be sure to point out that this class involves estimates using parallax and not trigonometric calculations!
3. Teacher will guide class in using parallax to measure a distance within the classroom. Here is an example: everyone look at the model solar-system on the table in the back of the classroom. Now close one eye and extend your arm; with your hand in a “thumbs up” position, move your arm until your thumb blocks your view of the model. Your one eye is still closed. Now open the closed eye and shut the open eye. The model should appear to have moved from behind your thumb. With your second eye still closed, estimate how far it appeared to move, using something in the room as a reference, like a desk or the window. Open both eyes and estimate the distance the model moved, as in half a table width would be eighteen inches. The last step is to multiply your estimate of the distance moved by a factor of ten, i.e., eighteen inches times ten equals one-hundred eighty inches or fifteen feet. So by parallax you have estimated that the distance from you to the solar system model on the back table is fifteen feet. Teacher will want to monitor student results and apply questioning to ensure student understanding. Teacher should not proceed with the exercise until all students can competently make a parallax estimation.
4. The class should then move out onto the school campus to make parallax estimations of the pre-measured distances. The teacher may choose to have students work collaboratively and/or may choose to have multiple sites so all students do not measure every distance. Be sure, however, to have enough different measurements of each site for statistical analysis at the end.
5. Students collect their data with teacher checking for understanding and assisting as needed.
6. Class returns to the classroom and summarizes data for each site on board. At this point the teacher may choose to reveal the actual distances. Students should then calculate the mean and the standard deviation for each site. Again, the teacher may assign students to collaborative groups or choose to use this as an individual assignment to submit for grading. The teacher should be sure that the students understand the correlation between the variance in their measurements and the accuracy of astronomic measurements.
7. Teacher should close class by reviewing the process and use of parallax and its relevance to astronomic distance measurement. Teacher should also point out the variability inherent in using an estimation tool; the teacher may also choose to discuss the trigonometric calculations used in making astronomic measurements and the accuracy of such calculations. Teacher may choose to point out that this tool can be used by the student in everyday life in activities such as hiking or jogging that involve long distances.

Assessment

Informal teacher assessment is best suited to this exercise. The teacher should informally check each student’s classroom parallax measurement to assure comprehension of the steps involved and the purpose. Outside the teacher should check in with individuals/groups to check progress (on-task behavior), accuracy (effort put in to the exercise and successful application of this skill) and conceptual understanding (purpose of the exercise). The statistical analysis could be submitted and graded if the teacher so chooses.

Supplemental information

Comments

This lesson plan is meant to be a fun but informative application of a very abstract idea. Distances in space are so unreal to our students; a hands-on activity really helps bring it home to them. However, it is important to include the statistical analysis to point out the inherent dangers of estimation and perhaps open the way to discussing some of the difficulties of space science research. This lesson should be adaptable to almost any student; possible alternate measuring sites would need to be provided for any severely physically impaired student, who would undoubtedly benefit from a collaborative learning group. It is up to the individual teacher to modify this activity based on his/her knowledge of the particular student group being taught.